Loop-and-allied QG bibliography

[marcus]

http://arxiv.org/abs/1201.4151
Group field cosmology: a cosmological field theory of quantum geometry
Gianluca Calcagni, Steffen Gielen, Daniele Oriti
(Submitted on 19 Jan 2012)
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted to a field, the coordinates are minisuperspace variables, the kinetic operator is the Hamiltonian constraint operator, and the action features a nonlinear and possibly nonlocal interaction term. We discuss free-field classical solutions, the quantum propagator, and a mean-field approximation linearizing the equation of motion and augmenting the Hamiltonian constraint by an effective term mixing gravitational and matter variables. Depending on the choice of interaction, this can reproduce, for example, a cosmological constant, a scalar-field potential, or a curvature contribution.
14 pages, 2 figures

http://arxiv.org/abs/1201.3969
Breaking the uniqueness of the Shape Dynamics Hamiltonian
Henrique Gomes
(Submitted on 19 Jan 2012)
In Gomes 2011, a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was sketched in order to implicitly construct Shape Dynamics' global Hamiltonian and eliminate second class constraints. This method was completely laid out, and in Gomes 2011 it was used for extending Shape Dynamics (SD) to the non-vacuum case, showing how other fields are coupled to the theory. In the latter paper it was noticed that, unlike the vacuum case, the use of such methods yielded puzzling bounds on the density of some types of fields. Here we show that the original SD cannot be extended beyond such bounds, but that a slight modification of the original can withstand any type of coupling. When the bound is broken, the theory does not come equipped with a single Hamiltonian as in vacuum SD, but with a finite set of weakly commuting Hamiltonians, which we describe.
14 pages

http://arxiv.org/abs/1110.6350
Evolution of Primordial Black Holes in Loop Quantum Gravity
Debabrata Dwivedee, Bibekananda Nayak, Mubasher Jamil, Lambodar Prasad Singh
(Submitted on 28 Oct 2011 (v1), last revised 24 Nov 2011 (this version, v2))
In this work, we study the evolution of Primordial Black Holes within the context of Loop Quantum Gravity. First we calculate the scale factor and energy density of the universe for different cosmic era and then taking these as inputs we study evolution of primordial black holes. From our estimation it is found that accretion of radiation does not affect evolution of primordial black holes in loop quantum gravity even though a larger number of primordial black holes may form in early universe in comparison with Einstein's or scalar-tensor theories.
8 pages, 1 figure

brief mention:
http://arxiv.org/abs/1201.4147
Are OPERA neutrinos faster than light because of non-inertial reference frames?
Claudio Germana
(Submitted on 19 Jan 2012)
Recent results from the OPERA experiment reported a neutrino beam traveling faster than light. The experiment measured the neutrino time of flight (TOF) over a baseline from the CERN to the Gran Sasso site. The neutrino beam arrives 60 ns earlier than a light ray would do. Because the result has an enormous impact on science, it might be worth double-checking the time definitions with respect to the non-inertial system in which the neutrino travel time was measured. Potential problems in the OPERA data analysis connected with the definition of the reference frame and time synchronization are emphasized. We aim to investigate the synchronization of non-inertial clocks on Earth by relating this time to the proper time of an inertial observer at Solar System Barycenter(SSB). The Tempo2 software was used to time-stamp events observed on the geoid with respect to the SSB inertial observer time. Neutrino results from OPERA might carry the fingerprint of non-inertial effects. The CERN-Gran Sasso clock synchronization is accomplished by applying corrections that depend on special and general relativistic time dilation effects at the clocks, depending on the position of the clocks in the solar system gravitational well. As a consequence, TOF distributions are centered on values shorter by tens of ns than expected, integrating over a period from April to December, longer if otherwise. It is worth remarking that the OPERA runs have always been carried out from April/May to November. If the analysis by Tempo2 holds for the OPERA experiment, the excellent measurement by the OPERA collaboration will turn into a proof of the General Relativity theory in a weak field approximation. The analysis presented here is falsifiable because it predicts that performing the experiment from January to March/April, the neutrino beam will be detected to arrive 50 ns later than light.
5 pages, 4 figures, accepted for publication in Astronomy and Astrophysics Letters

 

[marcus]

http://arxiv.org/abs/1201.4247
On the relations between gravity and BF theories
Laurent Freidel, Simone Speziale
(Submitted on 20 Jan 2012)
We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell-Mansouri action.
16 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"

http://arxiv.org/abs/1201.4229
Revisiting the quantum scalar field in spherically symmetric quantum gravity
Enrique F. Borja, Iñaki Garay, Eckhard Strobel
(Submitted on 20 Jan 2012)
We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini, Pullin and Rastgoo and a comparison between their result and the one given in this work is made.
16 pages

http://arxiv.org/abs/1201.4226
Gravitational four-fermion interaction on the Planck scale
I.B. Khriplovich
(Submitted on 20 Jan 2012)
The four-fermion gravitational interaction is induced by torsion, and gets essential on the Planck scale. On this scale, the axial-axial contribution dominates strongly in the discussed interaction. The energy-momentum tensor, generated by this contribution, is analyzed, as well as stability of the problem with respect to compression. The trace of this energy-momentum tensor can be negative.
4 pages

 

[marcus]

http://arxiv.org/abs/1201.4598
Introduction to Loop Quantum Gravity
Abhay Ashtekar
(Submitted on 22 Jan 2012)
This article is based on the opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011. The goal of the lecture was to present a broad perspective on loop quantum gravity for young researchers. The first part is addressed to beginning students and the second to young researchers who are already working in quantum gravity.
30 pages, 2 figures.

http://arxiv.org/abs/1201.4853
Effective Dynamics in Bianchi Type II Loop Quantum Cosmology
Alejandro Corichi, Edison Montoya
(Submitted on 23 Jan 2012)
We numerically investigate the solutions to the effective equations of the Bianchi II model within the "improved" Loop Quantum Cosmology (LQC) dynamics. The matter source is a massless scalar field. We perform a systematic study of the space of solutions, and focus on the behavior of several geometrical observables. We show that the big-bang singularity is replaced by a bounce and the point-like singularities do not saturate the energy density bound. There are up to five directional bounces in the scale factors, one global bounce in the expansion, the shear presents up to four local maxima and can be zero at the bounce. This allows for solutions with density larger than the maximal density for the isotropic and Bianchi I cases. The asymptotic behavior is shown to behave like that of a Bianchi I model, and the effective solutions connect anisotropic solutions even when the shear is zero at the bounce. All known facts of Bianchi I are reproduced. In the "vacuum limit", solutions are such that almost all the dynamics is due to the anisotropies. Since Bianchi II plays an important role in the Bianchi IX model and the the Belinskii, Khalatnikov, Lifgarbagez (BKL) conjecture, our results can provide an intuitive understanding of the behavior in the vicinity of general space-like singularities.
23 pages, 26 figures

http://arxiv.org/abs/1201.4543
Aspects of Quantum Gravity in Cosmology
Massimiliano Rinaldi
(Submitted on 22 Jan 2012)
We review some aspects of quantum gravity in the context of cosmology. In particular, we focus on models with a phenomenology accessible to current and near-future observations, as the early Universe might be our only chance to peep through the quantum gravity realm.
15 pages, 1 figure. Invited review for Modern Physics Letter A

 

[marcus]

http://arxiv.org/abs/1201.4874
Divergences in spinfoam quantum gravity
Matteo Smerlak
(Submitted on 23 Jan 2012)
In this thesis we study the flat model, the main buidling block for the spinfoam approach to quantum gravity, with an emphasis on its divergences. Besides a personal introduction to the problem of quantum gravity, the manuscript consists in two part. In the first one, we establish an exact powercounting formula for the bubble divergences of the flat model, using tools from discrete gauge theory and twisted cohomology. In the second one, we address the issue of spinfoam continuum limit, both from the lattice field theory and the group field theory perspectives. In particular, we put forward a new proof of the Borel summability of the Boulatov-Freidel-Louapre model, with an improved control over the large-spin scaling behaviour. We conclude with an outlook of the renormalization program in spinfoam quantum gravity.
113 pages. PhD thesis, introduction and conclusion in French, main text in English.

http://arxiv.org/abs/1201.4996
Gauge symmetries in spinfoam gravity: the case for "cellular quantization"
Valentin Bonzom, Matteo Smerlak
(Submitted on 24 Jan 2012)
The spinfoam approach to quantum gravity rests on a "quantization" of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this "spinfoam quantization" must be amended to be made consistent with the gauge symmetries of discrete BF theory. We discuss a suitable generalization, called "cellular quantization", which (1) is finite, (2) produces a topological invariant, (3) matches with the properties of the continuum BF theory, (4) corresponds to its loop quantization. These results significantly clarify the foundations - and limitations - of the spinfoam formalism, and open the path to understanding, in a discrete setting, the symmetry-breaking which reduces BF theory to gravity.
6 pages

 

[marcus]

http://arxiv.org/abs/1201.5423
Dirac fields and Barbero-Immirzi parameter in Cosmology
G. de Berredo-Peixoto, L. Freidel, I.L. Shapiro, C.A. de Souza
(Submitted on 26 Jan 2012)
We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect fluid with the equation of state p = wρ, with w = 1 which is independent of the BI parameter. The existence of mass imposes a variable w, which creates either an inflationary phase with w=-1, or assumes an ultra hard equation of states w = 1 for very early universe. Both phases relax to a pressureless fluid w = 0 for late universe (corresponding to the limit m→∞).
16 pages

http://arxiv.org/abs/1201.5470
New tools for Loop Quantum Gravity with applications to a simple model
Enrique F. Borja, Jacobo Díaz-Polo, Laurent Freidel, Iñaki Garay, Etera R. Livine
(Submitted on 26 Jan 2012)
Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field at large scales. Here we will review the recent U(N) framework for Loop Quantum Gravity and the new spinor representation (that provides a classical setting for the U(N) framework). Then, we will apply these techniques to a simple model in order to propose a dynamics for a symmetry reduced sector of the theory. Furthermore, we will explore certain analogies of this model with Loop Quantum Cosmology.
4 pages, to appear in Proceedings of Spanish Relativity Meeting 2011 (ERE 2011) held in Madrid, Spain

 

[marcus]

http://arxiv.org/abs/1201.6102
Entropy of quantum black holes
Romesh K. Kaul
(Submitted on 30 Jan 2012)
In the Loop Quantum Gravity, black holes (or even more general Isolated Horizons) are described by a SU(2) Chern-Simons theory. There is an equivalent formulation of the horizon degrees of freedom in terms of a U(1) gauge theory which is just a gauged fixed version of the SU(2) theory. These developments will be surveyed here. Quantum theory based on either formulation can be used to count the horizon micro-states associated with quantum geometry fluctuations and from this the micro-canonical entropy can be obtained. We shall review the computation in SU(2) formulation. Leading term in the entropy is proportional to horizon area with a coefficient depending on the Barbero-Immirzi parameter which is fixed by matching this result with the Bekenstein-Hawking formula. Remarkably there are corrections beyond the area term, the leading one is logarithm of the horizon area with a definite coefficient -3/2, a result which is more than a decade old now. How the same results are obtained in the equivalent U(1) framework will also be indicated. Over years, this entropy formula has also been arrived at from a variety of other perspectives. In particular, entropy of BTZ black holes in three dimensional gravity exhibits the same logarithmic correction. Even in the String Theory, many black hole models are known to possesses such properties. This may suggests a possible universal nature of this logarithmic correction.
42 pages, 1 figure. Invited article for the special issue on Loop Quantum Gravity and Cosmology of SIGMA

brief mention:
http://arxiv.org/abs/1201.6164
Cosmological inflation
K. Enqvist (Univ. Helsinki and Helsinki Inst. Phys.)
(Submitted on 30 Jan 2012)
The very basics of cosmological inflation are discussed. We derive the equations of motion for the inflaton field, introduce the slow-roll parameters, and present the computation of the inflationary perturbations and their connection to the temperature fluctuations of the cosmic microwave background.
9 pages

http://arxiv.org/abs/1201.6094
Gerbert of Aurillac: astronomy and geometry in tenth century Europe
Costantino Sigismondi
5 pages

 

[atyy]

http://arxiv.org/abs/1201.6212
Quantum fermions and quantum field theory from classical statistics
C. Wetterich
(Submitted on 30 Jan 2012)
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory for Dirac particles in an external electromagnetic field. This yields in the non-relativistic one-particle limit the Schrödinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.

 

[marcus]

http://arxiv.org/abs/1201.6505
Geometry and symmetries in lattice spinor gravity
C.Wetterich
(Submitted on 31 Jan 2012)
Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space and time is not put in a priori, and the euclidean and Minkowski quantum field theory are unified in one functional integral. The metric and its signature arise as a result of the dynamics, corresponding to a given ground state or cosmological solution. Geometrical objects as the vierbein, spin connection or the metric are expectation values of collective fields built from an even number of fermions. The quantum effective action for the metric is invariant under general coordinate transformations in the continuum limit. The action of our model is found to be also invariant under gauge transformations. We observe a "geometrical entanglement" of gauge- and Lorentz-transformations due to geometrical objects transforming non-trivially under both types of symmetry transformations.
38 pages

My comment: (He refers to Rovelli's http://arxiv.org/abs/1102.3660 the Zakopane Lectures on Loop Gravity, and also to papers on CDT and Regge QG, as part of clarifying why his approach is different.)

 

[marcus]

http://arxiv.org/abs/1202.0008
Super-renormalizable Higher-Derivative Quantum Gravity
Leonardo Modesto
(Submitted on 31 Jan 2012)
In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but is not unitary because of the presence of a ghost in the theory (pole with negative residue in the propagator). The new theory is instead ghost-free since an entire function (or form factor) is introduced in the model without involving new poles in the propagator. The local high derivative theory is recovered expanding the entire functions to the lowest order in the mass scale of the theory. Any truncation of the entire function gives rise to unitarity violation. The theory is divergent at one loop and finite from two loops upwards: the theory is then super-renormalizable. Using the modified graviton propagator, we demonstrate the regularity of the gravitational potential in r=0.
5 pages, 2 figures, text overlap with arXiv:1107.2403

 

[marcus]

http://arxiv.org/abs/1202.0412
Emission spectra of self-dual black holes
Sabine Hossenfelder, Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 2 Feb 2012)
We calculate the particle spectra of evaporating self-dual black holes that are potential dark matter candidates. We first estimate the relevant mass and temperature range and find that the masses are below the Planck mass, and the temperature of the black holes is small compared to their mass. In this limit, we then derive the number-density of the primary emission particles, and, by studying the wave-equation of a scalar field in the background metric of the black hole, show that we can use the low energy approximation for the greybody factors. We finally arrive at the expression for the spectrum of secondary particle emission from a dark matter halo constituted of self-dual black holes.
15 pages, 6 figures

This excerpt from page 1 helps clarify what the paper is about:

One approach to quantum gravity, Loop Quantum Gravity (LQG) [1–4], has given rise to models that allow to describe the very early universe. Simplified frameworks of LQG using a minisuperspace approximation has been shown to resolve the initial singularity problem [5, 6]. In the present work we will study the properties of black holes in such a minisuperspace model. The metric of black holes in this model was previously derived in [7], where it was shown in particular that the singularity is removed by a self-duality of the metric that replaces the black hole’s usually singular inside by another asymptotically flat region. The thermodynamical properties of these self-dual black holes have been examined in [8], and in [9] the dynamical aspects of the collapse and evaporation were studied...​

http://arxiv.org/abs/1202.0526
Coherent states for quantum gravity: towards collective variables
Daniele Oriti, Roberto Pereira, Lorenzo Sindoni
(Submitted on 2 Feb 2012)
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the diffeomorphism invariance of the theory. Aiming at approximating a continuum geometry in terms of discrete, graph-based data, we focus on coherent states for collective observables characterizing both the intrinsic and extrinsic geometry of the hypersurface, and we argue that one needs to revise accordingly the more local definitions of coherent states considered in the literature so far. In order to clarify the concepts introduced, we work through a concrete example that we hope will be useful to applying coherent state techniques to cosmology.
25 pages, 1 figure

Increasing tendency for LQG papers to simply say "quantum gravity" in the title or not even say it in the title and have "quantum gravity" as a keyword tag for the search engine. So unless it is in the abstract you may have to look at the first page and the leading references cited at the end to see it is Loop.

 

[marcus]

The FGZ paper seems to be turning out to be important. (Freidel Geiller Ziprick).
http://arxiv.org/abs/1110.4833.
Jonathan Z. just gave an excellent PIRSA video presentation, which can aid us in understanding the paper:
http://pirsa.org/12020096/
The title of the video talk is Continuous Formulation of the Loop Quantum Gravity Phase Space
He also gave a more introductory parallel session talk at Loops 2011 Madrid last May:
http://161.111.24.32/loops11/Archives/Parallel-Sessions/Jonathan-Ziprick_Geometry-of-Loop-Gravity.pdf
The talk was titled Geometry of Loop Gravity
The slides PDF is clear and helpful. It augments what one gets from the February 2012 video.

The first idea in this slide set, from which the rest takes off, is
LOOP CLASSICAL GRAVITY and the diagram of this idea is

GR —discretization→ LCG —quantization→ LQGZiprick is a PhD student at Waterloo/PI, Freidel we know, Marc Geiller is at Paris-Diderot.

This same FGZ paper will be presented by Geiller on 28 February at the ILQGS
http://relativity.phys.lsu.edu/ilqgs/schedulesp12.html
http://relativity.phys.lsu.edu/ilqgs/
Audio and slides PDF are normally available online.

This PIRSA presentation by Ziprick is interesting for several reasons, one is that his presentation went smoothly and was over in 25 minutes but was then followed by 40 minutes of discussion! The people in the audience doing the discussing included Laurent Freidel, Lee Smolin, and Bianca Dittrich.
So the total video is 65 minutes.
But if all you want is the straight presentation you just need to watch the first 25 minutes.
It gets extra interesting around 20 minutes where he is summarizing and drawing conclusions.

 

[marcus]

brief mention, not primarily QG but potentially of interest:
http://arxiv.org/abs/1202.1101
On classicalization in nonlinear sigma models
Roberto Percacci, Leslaw Rachwal
(Submitted on 6 Feb 2012)
We consider the phenomenon of classicalization in nonlinear sigma models with both positive and negative target space curvature and with any number of derivatives. We find that the theories with only two derivatives exhibit a weak form of classicalization, and that the quantitative results depend on the sign of the curvature. Nonlinear sigma models with higher derivatives show a strong form of the phenomenon which is independent of the sign of curvature. We argue that weak classicalization may actually be equivalent to asymptotic safety, whereas strong classicalization seems to be a genuinely different phenomenon. We also discuss possible ambiguities in the definition of the classical limit.
14 pages

 

[marcus]

I think this paper will influence how we view the AsymSafe QG approach. It would be reallyi nice to have an explanation for inflation. Easson has been a co-author of Nobelist Smoot.
http://arxiv.org/abs/1202.1285
Higgs Boson in RG running Inflationary Cosmology
Yi-Fu Cai, Damien A. Easson
(Submitted on 6 Feb 2012)
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
5 pages
I put this out for discussion in a separate related thread in case anyone wants to ask or comment about it https://www.physicsforums.com/showthread.php?p=3751800#post3751800

If curious about "curvaton" see:
http://en.wikipedia.org/wiki/Curvaton
"The curvaton is a hypothetical elementary particle which mediates a scalar field in early universe cosmology. It can generate fluctuations during inflation, but does not itself drive inflation, instead it generates curvature perturbations at late times after the inflaton field has decayed and the decay products have redshifted away, when the curvaton is the dominant component of the energy density.
The model was proposed by David Wands and David H. Lyth in 2001."

 

[marcus]

brief mention (though not QG may still be of use in QG):

http://arxiv.org/abs/1202.1818
Measure and Probability in Cosmology
Joshua S. Schiffrin, Robert M. Wald
(Submitted on 8 Feb 2012)
General relativity has a Hamiltonian formulation, which formally provides a canonical (Liouville) measure on the space of solutions. In ordinary statistical physics, the Liouville measure is used to compute probabilities of macrostates, and it would seem natural to use the similar measure arising in general relativity to compute probabilities in cosmology, such as the probability that the universe underwent an era of inflation. Indeed, a number of authors have used the restriction of this measure to the space of homogeneous and isotropic universes with scalar field matter (minisuperspace)---namely, the Gibbons-Hawking-Stewart measure---to make arguments about the likelihood of inflation. We argue here that there are at least four major difficulties with using the measure of general relativity to make probability arguments in cosmology: (1) Equilibration does not occur on cosmological length scales. (2) Even in the minisuperspace case, the measure of phase space is infinite and the computation of probabilities depends very strongly on how the infinity is regulated. (3) The inhomogeneous degrees of freedom must be taken into account (we illustrate how) even if one is interested only in universes that are very nearly homogeneous. The measure depends upon how the infinite number of degrees of freedom are truncated, and how one defines "nearly homogeneous." (4) In a universe where the second law of thermodynamics holds, one cannot make use of our knowledge of the present state of the universe to "retrodict" the likelihood of past conditions.
43 pages, 2 figures

http://arxiv.org/abs/1202.1793
The presence of Primordial Gravitational Waves in the Cosmic Microwave Background
Wytler Cordeiro dos Santos
(Submitted on 8 Feb 2012)
The General Relativity affirms that any field is a source of gravitational field, thus one should affirm that the energy of Cosmic Microwave Background (CMB) generated primordial gravitational waves. The present article shows that a gravitational wave with dimensionless amplitude ~ 10^-5 and large wave length ~ 10 megaparsecs shifts temperature of CMB radiation about of a part in 10⁵
7 pages, 1 figure

 

[marcus]

http://arxiv.org/abs/1202.1846
Effective constrained polymeric theories and their continuum limit
Alejandro Corichi, Tatjana Vukasinac
(Submitted on 8 Feb 2012)
The classical limit of polymer quantum theories yields a one parameter family of 'effective' theories labeled by λ. Here we consider such families for constrained theories and pose the problem of taking the 'continuum limit', λ→0. We put forward criteria for such question to be well posed, and propose a concrete strategy based in the definition of appropriately constructed Dirac observables. We analyze two models in detail, namely a constrained oscillator and a cosmological model arising from loop quantum cosmology. For both these models we show that the program can indeed be completed, provided one makes a particular choice of λ-dependent internal time with respect to which the dynamics is described and compared. We show that the limiting theories exist and discuss the corresponding limit. These results might shed some light in the problem of defining a renormalization group approach, and its associated continuum limit, for quantum constrained systems.
19 pages, 5 figures

http://arxiv.org/abs/1202.1824
The Hidden Quantum Groups Symmetry of Super-renormalizable Gravity
Stephon Alexander, Antonino Marciano, Leonardo Modesto
(Submitted on 8 Feb 2012)
In this paper we consider the relation between the super-renormalizable theories of quantum gravity (SRQG) studied in [arXiv:1110.5249v2, arXiv:1202.0008] and an underlying non-commutativity of spacetime. For one particular super-renormalizable theory we show that at linear level (quadratic in the Lagrangian) the propagator of the theory is the same we obtain starting from a theory of gravity endowed with θ-Poincaré quantum groups of symmetry. Such a theory is over the so called θ-Minkowski non-commuative spacetime. We shed new light on this link and show that among the theories considered in [arXiv:1110.5249v2, arXiv:1202.0008], there exist only one non-local and Lorentz invariant super-renormalizable theory of quantum gravity that can be described in terms of a quantum group symmetry structure. We also emphasize contact with pre-existent works in the literature and discuss preservation of the equivalence principle in our framework.
10 pages

 

[marcus]

http://arxiv.org/abs/1202.2274
Quantum Einstein Gravity
Martin Reuter, Frank Saueressig
(Submitted on 10 Feb 2012)
We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a particular focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the Causal Dynamical Triangulation approach.
87 pages, 13 figures, review article prepared for the New Journal of Physics focus issue on Quantum Einstein Gravity

http://arxiv.org/abs/1202.2301
Canonical Partition function of Loop Black Holes
Kinjalk Lochan, Cenalo Vaz
(Submitted on 10 Feb 2012)
We compute the canonical partition for quantum black holes in the approach of Loop Quantum Gravity (LQG). We argue that any quantum theory of gravity in which the horizon area is built of non-interacting constituents cannot yield qualitative corrections to the Bekenstein-Hawking (B-H) area law, but corrections to the area law can arise as a consequence additional constraints inducing interactions between the constituents. In LQG this is implemented by requiring spherical horizons. The canonical approach for LQG favours a logarithmic correction to the B-H law with a coefficient of -1/2, independently of the area spectrum. Our initial calculation of the partition function uses certain approximations that, we show, do not qualitatively affect the expression for the black hole entropy. We later discuss the quantitative corrections to these results when the simplifying approximations are relaxed and the full LQG spectrum is dealt with. We show how these corrections can be recovered to all orders in perturbation theory. However, the convergence properties of the perturbative series remains unknown.
16 pages, 1 figure

brief mention (a sweet bit of history, possibly of general interest)
http://arxiv.org/abs/1202.2347
A Sommerfeld Explanation
Jeremy Bernstein
(Submitted on 10 Feb 2012)
Sommerfeld shows that the Wien displacement formula implies the existence of Planck's constant.

 

[marcus]

http://arxiv.org/abs/1202.2710
Dynamical dimensional reduction in toy models of 4D causal quantum gravity
Georgios Giasemidis, John F. Wheater, Stefan Zohren
(Submitted on 13 Feb 2012)
In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came from numerical results of four-dimensional causal dynamical triangulations (CDT) [Ambj{\o}rn et al., Phys. Rev. Lett. 95 (2005) 171]. Since then little progress has been made in analytically understanding the numerical results coming from the CDT approach and showing that they remain valid when taking the continuum limit. In this letter we propose a new toy model of "radially reduced" four-dimensional CDT in which we can take the continuum limit analytically and obtain a scale dependent spectral dimension varying from four to two with scale. Furthermore, the functional behaviour of the spectral dimension is exactly of the form which was conjectured on the basis of the numerical results.
5 pages, 2 figures

brief mention:
http://arxiv.org/abs/1202.2539
Quantum Time Crystals
Frank Wilczek
(Submitted on 12 Feb 2012)
Difficulties around the idea of spontaneous breaking of time translation symmetry in a closed quantum mechanical system are identified, and then overcome in a simple model. The possibility of ordering in imaginary time is also discussed.
6 pages,

 

[marcus]

brief mention (may be of general interest though not directly QG-related):
http://arxiv.org/abs/1202.3324
On the inertia of heat
Matteo Smerlak
(Submitted on 15 Feb 2012)
Does heat have inertia? This question is at the core of a long-standing controversy on Eckart's dissipative relativistic hydrodynamics. Here I show that the troublesome inertial term in Eckart's heat flux arises only if one insists on defining thermal diffusivity as a spacetime constant. I argue that this is the most natural definition, and that all confusion disappears if one considers instead the space-dependent comoving diffusivity, in line with the fact that, in the presence of gravity, space is an inhomogeneous medium.
3 pages

 

[marcus]

Great talk by Frank Saueressig on Asym Safe QG. Perimeter video here:
http://pirsa.org/12020088/
Part of the talk explains the basics--a clear introduction. Part goes into advanced topics.
He's an excellent presenter IMO. He's worked with Martin Reuter for around 10 years and is now at Mainz as junior faculty, so about as authoritative as anyone concerning AS.

http://arxiv.org/abs/1202.3637
Random tensor models in the large N limit: Uncoloring the colored tensor models
Valentin Bonzom, Razvan Gurau, Vincent Rivasseau
(Submitted on 16 Feb 2012)
Tensor models generalize random matrix models in yielding a theory of dynamical triangulations in arbitrary dimensions. Colored tensor models have been shown to admit a 1/N expansion and a continuum limit accessible analytically. In this paper we prove that these results extend to the most general tensor model for a single generic, i.e. non-symmetric, complex tensor. Colors appear in this setting as a canonical book-keeping device and not as a fundamental feature. In the large N limit, we exhibit a set of Virasoro constraints satisfied by the free energy and an infinite family of multicritical behaviors with entropy exponents γ_m=1-1/m.
15 pages

extremely brief mention (a reminder about Ingemar Bengtsson):
http://arxiv.org/abs/1202.3559
http://arxiv.org/abs/1202.3561

 

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http://arxiv.org/abs/1202.4066
Comment on arXiv:1104.2019, "Relative locality and the soccer ball problem," by Amelino-Camelia et al
Sabine Hossenfelder
(Submitted on 18 Feb 2012)
It is explained why the argument in arXiv:1104.2019 does not answer the question how to describe multi-particle states in models with a deformed Lorentz-symmetry in momentum space.
3 pages

brief mention:
http://arxiv.org/abs/1202.4435
New multicritical matrix models and multicritical 2d CDT
Jan Ambjorn, Lisa Glaser, Andrzej Gorlich, Yuki Sato
(Submitted on 20 Feb 2012)
We define multicritical CDT models of 2d quantum gravity and show that they are a special case of multicritical generalized CDT models obtained from the new scaling limit, the so-called "classical" scaling limit, of matrix models. The multicritical behavior agrees with the multicritical behavior of the so-called branched polymers.
16 pages, 4 figures

http://arxiv.org/abs/1202.4322
An Analytical Analysis of CDT Coupled to Dimer-like Matter
Max R. Atkin, Stefan Zohren
(Submitted on 20 Feb 2012)
We consider a model of restricted dimers coupled to two-dimensional causal dynamical triangulations (CDT), where the dimer configurations are restricted in the sense that they do not include dimers in regions of high curvature. It is shown how the model can be solved analytically using bijections with decorated trees. At a negative critical value for the dimer fugacity the model undergoes a phase transition at which the critical exponent associated to the geometry changes. This represents the first account of an analytical study of a matter model with two-dimensional interactions coupled to CDT.

http://arxiv.org/abs/1202.4186
http://arxiv.org/abs/1202.4187
Edward Anderson

 

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http://arxiv.org/abs/1202.5039
Degenerate Plebanski Sector and its Spin Foam Quantization
Sergei Alexandrov
(Submitted on 22 Feb 2012)
We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact provides its spin foam quantization and allows to test various approaches of imposing the simplicity constraints. Our analysis suggests a unique method of imposing the constraints which leads to a consistent and well defined spin foam model.
34 pages

 

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http://arxiv.org/abs/1202.6183
A Gauge Theoretic Approach to Gravity
Kirill Krasnov
(Submitted on 28 Feb 2012)
Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full non-linear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an inifnite-parameter class of gravity theories all describing just two propagating polarisations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang-Mills arise as sectors of a general diffeomorphism invariant gauge theory. We finish by outlining a possible scenario of the UV completion of quantum gravity within this approach.
40 pages; invited review to appear in Proceedings of the Royal Society A
[my comment: see page 34, section 4.3, and the next section Conclusions. conjecture about RG flow of theory, tie-in with asym-safe approach]

http://arxiv.org/abs/1202.6322
Multigraph models for causal quantum gravity and scale dependent spectral dimension
Georgios Giasemidis, John F Wheater, Stefan Zohren
(Submitted on 28 Feb 2012)
We study random walks on ensembles of a specific class of random multigraph graphs associated with theories of causal quantum gravity. In particular, we investigate the spectral dimension of the graph ensemble for recurrent as well as transient walks. We investigate the circumstances in which the spectral dimension and Hausdorff dimension are equal and show that this occurs when rho, the exponent for anomalous behaviour of the resistance to infinity, is zero. The concept of scale dependent spectral dimension in these models is introduced. We apply this notion to a multigraph ensemble with a measure induced by a size biased critical Galton-Watson process which has a scale dependent spectral dimension of two at large scales and one at small scales. We conclude by discussing a specific model related to four dimensional quantum gravity which has a spectral dimension of four at large scales and two at small scales.
30 pages, 3 figures
[my comment: most references are to "causal dynamical triangulations" and related qg. they call it "causal QG" but it's a close relative of CDT, more about the interesting running of dimensionality with scale]

 

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http://arxiv.org/abs/1203.0174
Quantum isolated horizons and black hole entropy
J. Fernando Barbero G., Jerzy Lewandowski, Eduardo J. S. Villaseñor
(Submitted on 1 Mar 2012)
We give a short introduction to the approaches currently used to describe black holes in loop quantum gravity. We will concentrate on the classical issues related to the modeling of black holes as isolated horizons, give a short discussion of their canonical quantization by using loop quantum gravity techniques, and a description of the combinatorial methods necessary to solve the counting problems involved in the computation of the entropy.
28 pages. Contribution to the Proceedings of the 3rd Quantum Geometry and Quantum Gravity School in Zakopane (2011)

 

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http://arxiv.org/abs/1203.1040
Cleaning up the cosmological constant
Ian Kimpton, Antonio Padilla
(Submitted on 5 Mar 2012)
We present a novel idea for screening the vacuum energy contribution to the overall value of the cosmological constant, thereby enabling us to choose the bare value of the vacuum curvature empirically, without any need to worry about the zero-point energy contributions of each particle. The trick is to couple matter to a metric that is really a composite of other fields, with the property that the square-root of its determinant is the integrand of a topological invariant, and/or a total derivative. This ensures that the vacuum energy contribution to the Lagrangian is non-dynamical. We then give an explicit example of a theory with this property that is free from Ostrogradski ghosts, and is consistent with solar system physics and cosmological tests.
4 pages
[my comment: depends on prior work http://arxiv.org/abs/1106.2000 published in Physical Review Letters in 2012]

http://arxiv.org/abs/1203.1173
Cosmological particle creation in the lab?
Ralf Schützhold, William G. Unruh
(Submitted on 6 Mar 2012)
One of the most striking examples for the production of particles out of the quantum vacuum due to external conditions is cosmological particle creation, which is caused by the expansion or contraction of the Universe. Already in 1939, Schrödinger understood that the cosmic evolution could lead to a mixing of positive and negative frequencies and that this "would mean production or annihilation of matter, merely by the expansion". Later this phenomenon was derived via more modern techniques of quantum field theory in curved space-times by Parker (who apparently was not aware of Schrödinger's work) and subsequently has been studied in numerous publications. Even though cosmological particle creation typically occurs on extremely large length scales, it is one of the very few examples for such fundamental effects where we actually may have observational evidence: According to the inflationary model of cosmology, the seeds for the anisotropies in the cosmic microwave background (CMB) and basically all large scale structures stem from this effect. In this Chapter, we shall provide a brief discussion of this phenomenon and sketch a possibility for an experimental realization via an analogue in the laboratory.
13 pages

 

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http://arxiv.org/abs/1203.1530
One vertex spin-foams with the Dipole Cosmology boundary
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta
(Submitted on 7 Mar 2012)
We find all the spin-foams contributing in the first order of the vertex expansion to the transition amplitude of the Bianchi-Rovelli-Vidotto Dipole Cosmology model. Our algorithm is general and provides spin-foams of arbitrarily given, fixed: boundary and, respectively, a number of internal vertices. We use the recently introduced Operator Spin-Network Diagrams framework.
23 pages, 30 figures

 

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http://arxiv.org/abs/1203.2161
Highlights of Noncommutative Spectral Geometry
Mairi Sakellariadou
(Submitted on 9 Mar 2012)
A summary of noncommutative spectral geometry as an approach to unification is presented. The role of the doubling of the algebra, the seeds of quantization and some cosmological implications are briefly discussed.
4 pages, to be published in the Journal of Physics Conference Series under the title "Vishwa Mimansa - An Interpretative Exposition of the Universe"; talk given at the 7th International Conference on Gravitation and Cosmology, 14-19 December 2011, Goa, India

http://arxiv.org/abs/1203.1934
Loop Quantization of the Supersymmetric Two-Dimensional BF Model
Clisthenis P. Constantinidis, Ruan Couto, Ivan Morales, Olivier Piguet
(Submitted on 8 Mar 2012)
In this paper we consider the quantization of the 2d BF model coupled to topological matter. Guided by the rigid supersymmetry this system can be viewed as a super-BF model, where the field content is expressed in terms of superfields. A canonical analysis is done and the constraints are then implemented at the quantum level in order to construct the Hilbert space of the theory under the perspective of Loop Quantum Gravity methods.
17 pages

http://arxiv.org/abs/1203.1962
An effective action for asymptotically safe gravity
Alfio Bonanno
(Submitted on 8 Mar 2012)
Asymptotically safe theories of gravitation have received great attention in recent times. In this framework an effective action embodying the basic features of the renormalized flow around the non-gaussian fixed point is derived and its implications for the early universe are discussed. In particular, a "landscape" of a countably infinite number of cosmological inflationary solutions characterized by an unstable de Sitter phase lasting for a large enough number of e-folds is found.
5 pages, to appear as a Rapid Communication in Physical Review D

http://arxiv.org/abs/1203.2158
The "tetrad only" theory space: Nonperturbative renormalization flow and Asymptotic Safety
Ulrich Harst, Martin Reuter
(Submitted on 9 Mar 2012)
We set up a nonperturbative gravitational coarse graining flow and the corresponding functional renormalization group equation on the as to yet unexplored "tetrad only" theory space. It comprises action functionals which depend on the tetrad field (along with the related background and ghost fields) and are invariant under the semi-direct product of spacetime diffeomorphisms and local Lorentz transformations. This theory space differs from that of Quantum Einstein Gravity (QEG) in that the tetrad rather than the metric constitutes the fundamental variable and because of the additional symmetry requirement of local Lorentz invariance. It also differs from "Quantum Einstein Cartan Gravity" (QECG) investigated recently since the spin connection is not an independent field variable now. We explicitly compute the renormalization group flow on this theory space within the tetrad version of the Einstein-Hilbert truncation. A detailed comparison with analog results in QEG and QECG is performed in order to assess the impact the choice of a fundamental field variable has on the renormalization behavior of the gravitational average action, and the possibility of an asymptotically safe infinite cutoff limit is investigated. Implications for nonperturbative studies of fermionic matter coupled to quantum gravity are also discussed. It turns out that, in the context of functional flow equations, the "hybrid calculations" proposed in the literature (using the tetrad for fermionic diagrams only, and the metric in all others) are unlikely to be quantitatively reliable. Moreover we find that, unlike in perturbation theory, the non-propagating Faddeev-Popov ghosts related to the local Lorentz transformations may not be discarded but rather contribute quite significantly to the beta functions of Newton's constant and the cosmological constant.
45 pages, 10 figures

brief mention (not QG but possibly of general interest):
http://arxiv.org/abs/1203.2035
A Noether Theorem for Markov Processes
John C. Baez, Brendan Fong
(Submitted on 9 Mar 2012)
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.
9 pages

 

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http://arxiv.org/abs/1203.2733
From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
Kristina Giesel, Hanno Sahlmann
(Submitted on 13 Mar 2012)
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction is the inclusion of new proposals for coupling matter to gravity that can be used to deparametrize the theory, thus making its dynamics more tractable. The classical and quantum aspects of these new proposals are explained alongside the standard quantization of vacuum general relativity in loop quantum gravity.
55 pages. Contribution to the Proceedings of the 3rd Quantum Geometry and Quantum Gravity School in Zakopane (2011)

brief mention (not directly Loop-related but possibly of general interest):
http://arxiv.org/abs/1203.2622
The Optimal Cosmic Epoch for Precision Cosmology
Abraham Loeb (Harvard)
(Submitted on 12 Mar 2012)
The statistical uncertainty in measuring the primordial density perturbations on a given comoving scale is dictated by the number of independent regions of that scale that are accessible to an observer. This number varies with cosmic time and diminishes per Hubble volume in the distant past or future of the standard cosmological model. We show that the best constraints on the initial power spectrum of linear density perturbations are accessible (e.g. through 21-cm intensity mapping) at redshifts z~10-50, and that the ability to constrain the cosmological initial conditions will deteriorate quickly in our cosmic future.
4 pages, 4 figures

http://arxiv.org/abs/1203.2642
Very special relativity as particle in a gauge field and two-time physics

Juan M. Romero, Eric Escobar, Etelberto Vazquez
(Submitted on 12 Mar 2012)
The action for a particle in very special relativity is studied. It is shown that this system is equivalent to a relativistic particle in a gauge field. A new symmetry for this system is found. A general action with restored Lorentz symmetry is proposed for this system. It is shown that this new action contain very special relativity and two-time physics.
12 pages

http://arxiv.org/abs/1203.2679
Noncommutative Mixmaster Cosmologies
Christopher Estrada, Matilde Marcolli
(Submitted on 13 Mar 2012)
In this paper we investigate a variant of the classical mixmaster universe model of anisotropic cosmology, where the spatial sections are noncommutative 3-tori. We consider ways in which the discrete dynamical system describing the mixmaster dynamics can be extended to act on the noncommutative torus moduli, and how the resulting dynamics differs from the classical one, for example, in the appearance of exotic smooth structures. We discuss properties of the spectral action, focussing on how the slow-roll inflation potential determined by the spectral action affects the mixmaster dynamics. We relate the model to other recent results on spectral action computation and we identify other physical contexts in which this model may be relevant.
24 pages

http://arxiv.org/abs/1203.2641
Internal Relativity
Olaf Dreyer
(Submitted on 12 Mar 2012)
General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential geometry. The connection that comes from a metric is used to glue together the different gravity-free Minkowski spaces. In this article we argue that there is another way to implement the equivalence principle. In this new way it is not different Minkowski spaces that are connected but different vacua of an underlying solid-state like model. One advantage of this approach to gravity is that one can start with a quantum mechanical model so that the question of how to arrive at a quantum theory of gravity does not arise. We show how the gravitational constant can be calculated in this setup.
9 pages

 

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A new ILQGS talk (given 13 March) by Diaz-Polo
Black Hole Evaporation in Loop Quantum Gravity
Slides PDF:
http://relativity.phys.lsu.edu/ilqgs/diazpolo031312.pdf
Audio:
http://relativity.phys.lsu.edu/ilqgs/diazpolo031312.wav
or
http://relativity.phys.lsu.edu/ilqgs/diazpolo031312.aif
based on this paper:
http://arxiv.org/abs/1109.4239
Probing Loop Quantum Gravity with Evaporating Black Holes
Aurelien Barrau, Xiangyu Cao, Jacobo Diaz-Polo, Julien Grain, Thomas Cailleteau
(Submitted on 20 Sep 2011)
This letter aims at showing that the observation of evaporating black holes should allow distinguishing between the usual Hawking behavior and Loop Quantum Gravity (LQG) expectations. We present a full Monte-Carlo simulation of the evaporation in LQG and statistical tests that discriminate between competing models. We conclude that contrarily to what was commonly thought, the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal quantum gravity footprints.
5 pages, 3 figures. Published in Physical Review Letters 107, 251301 (2011)

 

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http://arxiv.org/abs/1203.3449
Non-singular Power-law and Assisted inflation in Loop Quantum Cosmology
Evan Ranken, Parampreet Singh
(Submitted on 15 Mar 2012)
We investigate the dynamics of single and multiple scalar fields with exponential potentials, leading to power-law and assisted inflation, in loop quantum cosmology. Unlike in the classical theory, dynamical trajectories in loop quantum cosmology are generically non-singular, with a big bounce replacing classical big bang in the Planck regime. Post bounce, after a phase of super-inflation, dynamical trajectories evolve towards the classical attractor in the inflationary scenarios. Depending on the initial conditions, bounce is shown to occur in kinetic as well as potential dominated regimes. We analyze the number of e-foldings resulting from the phase of super-inflation, and find the dependence of the maximum possible number of e-foldings on the equation of state at the bounce and on the steepness of the potential. We find that if the potential is not steep, this phase can lead to large number of e-foldings in power-law inflation. For the assisted inflation scenario, an increase in the number of fields can yield a significant increase in the number of e-foldings during super-inflation.
21 pages, 15 figures

 

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http://arxiv.org/abs/1203.3591
Nonperturbative Quantum Gravity
J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll
(Submitted on 15 Mar 2012)
Asymptotic safety describes a scenario in which general relativity can be quantized as a conventional field theory, despite being nonrenormalizable when expanding it around a fixed background geometry. It is formulated in the framework of the Wilsonian renormalization group and relies crucially on the existence of an ultraviolet fixed point, for which evidence has been found using renormalization group equations in the continuum.
"Causal Dynamical Triangulations" (CDT) is a concrete research program to obtain a nonperturbative quantum field theory of gravity via a lattice regularization, and represented as a sum over spacetime histories. In the Wilsonian spirit one can use this formulation to try to locate fixed points of the lattice theory and thereby provide independent, nonperturbative evidence for the existence of a UV fixed point.
We describe the formalism of CDT, its phase diagram, possible fixed points and the "quantum geometries" which emerge in the different phases. We also argue that the formalism may be able to describe a more general class of Horava-Lifgarbagez gravitational models.
146 pages, many figures