Revised listing of third quarter 2012 Loop-and-allied QG papers. Two new ones which just appeared (Ashtekar et al, Dittrich et al). We have 19 paper, which is a lot, may have to drop some and narrow the list down.
http://arxiv.org/abs/1207.0637
New ground state for quantum gravity
Joao Magueijo, Laura Bethke
(Submitted on 3 Jul 2012)
In this paper we conjecture the existence of a new "ground" state in quantum gravity, supplying a wave function for the inflationary Universe. We present its explicit perturbative expression in the connection representation, exhibiting the associated inner product. The state is chiral, dependent on the Immirzi parameter, and is the vacuum of a second quantized theory of graviton particles. We identify the physical and unphysical Hilbert sub-spaces. We then contrast this state with the perturbed Kodama state and explain why the latter can never describe gravitons in a de Sitter background. Instead, it describes self-dual excitations, which are composites of the positive frequencies of the right-handed graviton and the negative frequencies of the left-handed graviton. These excitations are shown to be unphysical under the inner product we have identified. Our rejection of the Kodama state has a moral tale to it: the semi-classical limit of quantum gravity can be the wrong path for making contact with reality (which may sometimes be perturbative but nonetheless fully quantum). Our results point towards a non-perturbative extension, and we present some conjectures on the nature of this hypothetical state.
http://arxiv.org/abs/1207.0505
Emergent perspective of Gravity and Dark Energy
T. Padmanabhan
(Submitted on 2 Jul 2012)
There is sufficient amount of internal evidence in the nature of gravitational theories to indicate that gravity is an emergent phenomenon like, e.g, elasticity. Such an emergent nature is most apparent in the structure of gravitational dynamics. It is, however, possible to go beyond the field equations and study the space itself as emergent in a well-defined manner in (and possibly only in) the context of cosmology. In the first part of this review, I describe various pieces of evidence which show that gravitational field equations are emergent. In the second part, I describe a novel way of studying cosmology in which I interpret the expansion of the universe as equivalent to the emergence of space itself. In such an approach, the dynamics evolves towards a state of holographic equipartition, characterized by the equality of number of bulk and surface degrees of freedom in a region bounded by the Hubble radius. This principle correctly reproduces the standard evolution of a Friedmann universe. Further, (a) it demands the existence of an early inflationary phase as well as late time acceleration for its successful implementation and (b) allows us to link the value of late time cosmological constant to the e-folding factor during inflation.
38 pages; 5 figures
http://arxiv.org/abs/1207.4353
Inflation from non-minimally coupled scalar field in loop quantum cosmology
Michal Artymowski, Andrea Dapor, Tomasz Pawlowski
(Submitted on 18 Jul 2012)
The FRW model with non-minimally coupled massive scalar field has been investigated in LQC framework. Considered form of the potential and coupling allows applications to Higgs driven inflation. The resulting dynamics qualitatively modifies the standard bounce paradigm in LQC in two ways: (i) the bounce point is no longer marked by critical matter energy density, (ii) the Planck scale physics features the "mexican hat" trajectory with two consecutive bounces and rapid expansion and recollapse between them. Furthermore, for physically viable coupling strength and initial data the subsequent inflation exceeds 60 e-foldings.
14 pages, 5 figures
http://arxiv.org/abs/1207.4596
The Construction of Spin Foam Vertex Amplitudes
Eugenio Bianchi, Frank Hellmann
(Submitted on 19 Jul 2012)
Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. They fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4 dimensional generalization of the Ponzano-Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barret and Crane and Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentz-invariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine.
22 Pages. 1 Figure. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"
http://arxiv.org/abs/1207.5156
Divergences and Orientation in Spinfoams
Marios Christodoulou, Miklos Långvik, Aldo Riello, Christian Röken, Carlo Rovelli
(Submitted on 21 Jul 2012)
We suggest that large radiative corrections appearing in the spinfoam framework might be tied to the implicit sum over orientations. Specifically, we show that in a suitably simplified context the characteristic "spike" divergence of the Ponzano-Regge model disappears when restricting the theory to just one of the two orientations appearing in the asymptotic limit of the vertex amplitude.
10 pages, 5 figures
http://arxiv.org/abs/1207.6348
The twistorial structure of loop-gravity transition amplitudes
Simone Speziale, Wolfgang M. Wieland
(Submitted on 26 Jul 2012)
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial description, which brings new light on both classical and quantum aspects of the theory. At the classical level, we clarify the covariant properties of the discrete geometries involved, and the role of the simplicity constraints in leading to SU(2) Ashtekar-Barbero variables. We identify areas and Lorentzian dihedral angles in twistor space, and show that they form a canonical pair. The primary simplicity constraints are solved by simple twistors, parametrized by SU(2) spinors and the dihedral angles. We construct an SU(2) holonomy and prove it to correspond to the Ashtekar-Barbero connection. We argue that the role of secondary constraints is to provide a non trivial embedding of the cotangent bundle of SU(2) in the space of simple twistors. At the quantum level, a Schroedinger representation leads to a spinorial version of simple projected spin networks, where the argument of the wave functions is a spinor instead of a group element. We rewrite the Liouville measure on the cotangent bundle of SL(2,C) as an integral in twistor space. Using these tools, we show that the Engle-Pereira-Rovelli-Livine transition amplitudes can be derived from a path integral in twistor space. We construct a curvature tensor, show that it carries torsion off-shell, and that its Riemann part is of Petrov type D. Finally, we make contact between the semiclassical asymptotic behaviour of the model and our construction, clarifying the relation of the Regge geometries with the original phase space.
39 pages
http://arxiv.org/abs/1208.1030
Resilience of the Spectral Standard Model
Ali H. Chamseddine, Alain Connes
(Submitted on 5 Aug 2012)
We show that the inconsistency between the spectral Standard Model and the experimental value of the Higgs mass is resolved by the presence of a real scalar field strongly coupled to the Higgs field. This scalar field was already present in the spectral model and we wrongly neglected it in our previous computations. It was shown recently by several authors, independently of the spectral approach, that such a strongly coupled scalar field stabilizes the Standard Model up to unification scale in spite of the low value of the Higgs mass. In this letter we show that the noncommutative neutral singlet modifies substantially the RG analysis, invalidates our previous prediction of Higgs mass in the range 160--180 Gev, and restores the consistency of the noncommutative geometric model with the low Higgs mass.
http://arxiv.org/abs/1208.2228
Bohr-Sommerfeld Quantization of Space
Eugenio Bianchi, Hal M. Haggard
(Submitted on 10 Aug 2012)
We introduce semiclassical methods into the study of the volume spectrum in loop gravity. The classical system behind a 4-valent spinnetwork node is a Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase space and apply Bohr-Sommerfeld quantization to find the volume spectrum. The analysis shows a remarkable quantitative agreement with the volume spectrum computed in loop gravity. Moreover, it provides new geometrical insights into the degeneracy of this spectrum and the maximum and minimum eigenvalues of the volume on intertwiner space.
32 pages, 10 figures
http://arxiv.org/abs/1208.3388
Holonomy Spin Foam Models: Definition and Coarse Graining
Benjamin Bahr, Bianca Dittrich, Frank Hellmann, Wojciech Kaminski
(Submitted on 16 Aug 2012)
We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin foam models to arbitrary, in particular finite groups. The similarity with standard lattice gauge theories allows to apply standard coarse graining methods, which for finite groups can now be easily considered numerically. We will summarize other holonomy and spin network formulations of spin foams and group field theories and explain how the different representations arise through variable transformations in the partition function. A companion paper will provide a description of boundary Hilbert spaces as well as a canonical dynamic encoded in transfer operators.
36 pages, 12 figures
http://arxiv.org/abs/1208.5023
Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
Christopher Estrada, Matilde Marcolli
(Submitted on 24 Aug 2012)
We study the renormalization group flow for the Higgs self coupling in the presence of gravitational correction terms. We show that the resulting equation is equivalent to a singular linear ODE, which has explicit solutions in terms of hypergeometric functions. We discuss the implications of this model with gravitational corrections on the Higgs mass estimates in particle physics models based on the spectral action functional.
25 pages
http://arxiv.org/abs/1208.5874
A possibility to solve the problems with quantizing gravity
S. Hossenfelder
(Submitted on 29 Aug 2012)
It is generally believed that quantum gravity is necessary to resolve the known tensions between general relativity and the quantum field theories of the standard model. Since perturbatively quantized gravity is non-renormalizable, the problem how to unify all interactions in a common framework has been open since the 1930s. Here, I propose a possibility to circumvent the known problems with quantizing gravity, as well as the known problems with leaving it unquantized: By changing the prescription for second quantization, a perturbative quantization of gravity is sufficient as an effective theory because matter becomes classical before the perturbative expansion breaks down. This is achieved by considering the vanishing commutator between a field and its conjugated momentum as a symmetry that is broken at low temperatures, and by this generates the quantum phase that we currently live in, while at high temperatures Planck's constant goes to zero.
4 pages, 1 figure
http://arxiv.org/abs/1208.6217
A complete hybrid quantization in inhomogeneous cosmology
Mikel Fernández-Méndez, Guillermo A. Mena Marugán, Javier Olmedo
(Submitted on 30 Aug 2012)
A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on the minimum volume section, and from this we construct the physical Hilbert space. Moreover, a perturbative study allows us to introduce small inhomogeneities. After gauge fixing, the inhomogeneous part of the system is reduced to a linear field theory. We then adopt a standard Fock representation to quantize these degrees of freedom. For the considered case of compact spatial topology, the requirements of: i) invariance under the spatial isometries, and ii) unitary implementation of the quantum dynamics, pick up a unique Fock representation and a particular set of canonical fields (up to unitary equivalence).
6 pages
http://arxiv.org/abs/1209.0065
General relativistic statistical mechanics
Carlo Rovelli
(Submitted on 1 Sep 2012)
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = h dτ/ds, with k the Boltzmann constant, h the Planck constant, ds proper time and dτ the equilibrium thermal time.
9 pages. A tentative second step in the thermal time direction, 10 years after the paper with Connes. The aim is the full thermodynamics of gravity. The language of the paper is a bit technical: look at the Appendix first
http://arxiv.org/abs/1209.0396
Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
Mariano Celada, Merced Montesinos
(Submitted on 3 Sep 2012)
We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian action principles that describe general relativity as a constrained BF theory and that include the Immirzi parameter. The relation between these two Lagrangian actions has been already studied through a map among the fields involved. The main difference between these is the way the Immirzi parameter is included, since in one of them the Immirzi parameter is included explicitly in the BF terms, whereas in the other (the CMPR action) it is in the constraint on the B fields. In this work we continue the analysis of their relationship but at the Hamiltonian level. Particularly, we are interested in seeing how the above difference appears in the constraint structure of both action principles. We find that they both possesses the same number of first-class and second-class constraints and satisfy a very similar (off-shell) Poisson-bracket algebra on account of the type of canonical variables employed. The two algebras can be transformed into each other by making a suitable change of variables
16 pages
http://arxiv.org/abs/1209.0473
Observational effects from quantum cosmology
Gianluca Calcagni
(Submitted on 3 Sep 2012)
The status of quantum cosmologies as testable models of the early universe is assessed in the context of inflation. While traditional Wheeler-DeWitt quantization is unable to produce sizable effects in the cosmic microwave background, the more recent loop quantum cosmology can generate potentially detectable departures from the standard cosmic spectrum. Thus, present observations constrain the parameter space of the model, which could be made falsifiable by near-future experiments.
14 pages, 3 figures. Invited review article also containing original material
http://arxiv.org/abs/1209.1609
A Quantum Gravity Extension of the Inflationary Scenario
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 7 Sep 2012)
Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This pre-inflationary dynamics also opens a small window for novel effects, e.g. a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early universe.
4 pages, 2 figures
http://arxiv.org/abs/1209.3649
Functional renormalization with fermions and tetrads
Pietro Donà, Roberto Percacci
(Submitted on 17 Sep 2012)
We investigate some aspects of the renormalization group flow of gravity in the presence of fermions, which have remained somewhat puzzling so far. The first is the sign of the fermionic contribution to the running of Newton's constant, which depends on details of the cutoff. We argue that only one of the previously used schemes correctly implements the cutoff on eigenvalues of the Dirac operator, and it acts in the sense of screening Newton's constant. We also show that Kähler fermions give the same contribution to the running of the cosmological and Newton constant as four Dirac spinors. We then calculate the graviton contributions to the beta functions by imposing the cutoffs on the irreducible spin components of the tetrad. In this way we can probe the gauge dependence of the off-shell flow. The results resemble closely those of the metric formalism, except for an increased scheme-- and (off shell) gauge--dependence.
28 pages, 4 figures
http://arxiv.org/abs/1209.4374
On the Uniqueness of Kinematics of Loop Quantum Cosmology
Abhay Ashtekar, Miguel Campiglia
(Submitted on 19 Sep 2012)
The holonomy-flux algebra A of loop quantum gravity is known to admit a natural representation that is uniquely singled out by the requirement of covariance under spatial diffeomorphisms. In the cosmological context, the requirement of spatial homogeneity naturally reduces A to a much smaller algebra, A
Red, used in loop quantum cosmology. In Bianchi I models, it is shown that the requirement of covariance under
residual diffeomorphism symmetries again uniquely selects the representation of A
Red that has been commonly used. We discuss the close parallel between the two uniqueness results and also point out a difference.
9 pages
http://arxiv.org/abs/1209.4539
Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
Bianca Dittrich, Frank Hellmann, Wojciech Kaminski
(Submitted on 20 Sep 2012)
In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored. After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert space, on which the imposition of different forms of the simplicity constraints can be studied. We detail under which conditions this Hilbert space can be mapped to a Hilbert space of projected spin networks or an ordinary spin network space.
These considerations allow to derive the general form of the transfer operators which generates discrete time evolution. We will describe the transfer operators for some current models on the different boundary Hilbert spaces and highlight the role of the simplicity constraints determining the concrete form of the time evolution operators.
51 pages, 18 figures
By now the top five may have changed. You can check the current cites numbers (links are provided) if you want.
