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marcus

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## Main Question or Discussion Point

A lot of papers this quarter. I want to sift this preliminary list and narrow down to the 10 or so which appear of most potential value to future research.

http://arxiv.org/abs/1003.5652

Florian Conrady (Perimeter Inst. Theor. Phys.)

22 pages

(Submitted on 29 Mar 2010)

"Spin foams of 4d gravity were recently extended from complexes with purely spacelike surfaces to complexes that also contain timelike surfaces. In this article, we express the associated partition function in terms of vertex amplitudes and integrals over coherent states. The coherent states are characterized by unit 3-vectors which represent normals to surfaces and lie either in the 2--sphere or the 2d hyperboloids. In the case of timelike surfaces, a new type of coherent state is used and the associated completeness relation is derived. It is also shown that the quantum simplicity constraints can be deduced by three different methods: by weak imposition of the constraints, by restriction of coherent state bases and by the master constraint."

http://arxiv.org/abs/1003.4811

Niayesh Afshordi (Perimeter/Waterloo)

4 pages

(Submitted on 25 Mar 2010)

"The two apparently distinct phenomena of dark energy (or late-time cosmic acceleration) and quantum gravity dominate physics on extremely low, and extremely high energies, but do not seem to have any apparent empirical connection. Nevertheless, the two have a theoretical connection, through the cosmological constant problem. I argue that the finite temperature quantum gravitational corrections to black hole entropy yields a pressure for the gravitational vacuum (or gravitational aether). Assuming that the relative corrections are linear in horizon temperature (i.e. are suppressed by one power of Planck energy), the pressure is comparable to that of dark energy for astrophysical black holes. This implies that the observation of late-time cosmic acceleration may have provided us with the first precision

http://arxiv.org/abs/1003.4660

Jakub Mielczarek, Thomas Cailleteau, Julien Grain, Aurelien Barrau

11 pages, 14 figures

(Submitted on 24 Mar 2010)

"Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Due to holonomy corrections, the singularity is replaced by a "bounce". The dynamics of the background is investigated into the details, as a function of the parameters of the model. In particular, the conditions required for inflation to occur are carefully considered and are shown to be generically met. The propagation of gravitational waves is then investigated in this framework. By both numerical and analytical approaches, the primordial tensor power spectrum is computed for a wide range of parameters. Several interesting features could be

http://arxiv.org/abs/1003.3483

Eugenio Bianchi, Carlo Rovelli, Francesca Vidotto

8 pages

(Submitted on 17 Mar 2010)

"We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the

http://arxiv.org/abs/1003.2412

R. Durka, J. Kowalski-Glikman

(Submitted on 11 Mar 2010)

"In this paper we discuss canonical analysis of SO(4,1) constrained BF theory. The action of this theory contains topological terms appended by a term that breaks the gauge symmetry down to the Lorentz subgroup SO(3,1). The equations of motion of this theory turn out to be the vacuum Einstein equations. By solving the B field equations one finds that the action of this theory contains not only the standard Einstein-Cartan term, but also the Holst term proportional to the inverse of the Immirzi parameter, as well as a combination of topological invariants. We show that the structure of the constraints of a SO(4,1) constrained BF theory is exactly that of gravity in Holst formulation. We also briefly discuss quantization of the theory."

http://arxiv.org/abs/1003.1998

Leonardo Modesto, Andrew Randono

(Submitted on 9 Mar 2010)

"It has been known for some time that there is a deep connection between thermodynamics and gravity, with perhaps the most dramatic implication that the Einstein equations can be viewed as a thermodynamic equation of state. Recently Verlinde has proposed a model for gravity with a simple statistical mechanical interpretation that is applicable in the non-relatvistic regime. After critically analyzing the construction, we present a strong consistency check of the model. Specifically, we consider two well-motivated corrections to the area-entropy relation, the log correction and the volume correction, and follow Verlinde's construction to derive corrections to Newton's law of gravitation. We show that the deviations from Newton's law stemming from the log correction have the same form as the lowest order quantum effects of perturbative quantum gravity, and the deviations stemming from the volume correction have the same form as some modified Newtonian gravity models designed to explain the anomalous galactic rotation curves."

http://arxiv.org/abs/1003.1886

John W. Barrett, Richard J. Dowdall, Winston J. Fairbairn, Henrique Gomes, Frank Hellmann, Roberto Pereira

(Submitted on 9 Mar 2010)

"We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary data. For some classes of geometrical boundary data, the asymptotic formulae are given, in all three cases, by simple functions of the Regge action for the four-simplex geometry."

http://arxiv.org/abs/1003.1528

Damien A. Easson, Paul H. Frampton, George F. Smoot

(Submitted on 7 Mar 2010)

"One of the major pillars of modern cosmology is a period of accelerating expansion in the early universe. This accelerating expansion, or inflation, must be sustained for at least 30 e--foldings. One mechanism, used to drive the acceleration, is the addition of a new energy field, called the Inflaton; often this is a scalar field. We propose an alternative mechanism which, like our approach to explain the late-time accelerating universe, uses the entropy and temperature intrinsic to information holographically stored on a screen enclosing the observed space. The acceleration is due in both cases to an emergent entropic force, naturally arising from the information storage on the horizon."

http://arxiv.org/abs/1003.1015

Sabine Hossenfelder

(Submitted on 4 Mar 2010)

"We offer some, hopefully clarifying, comments on Verlinde's recent claim that gravity is an entropic force. A suitable identification of quantities shows that both formulations of Newtonian gravity, the classical and the thermodynamical one, are actually equivalent. It turns out that some additional assumptions made by Verlinde are unnecessary. However, when it comes to General Relativity there remain some gaps in the argument. We comment on whether this identification can be done also for electrostatics. Finally, some thoughts on the use of this reinterpretation are offered."

http://arxiv.org/abs/1002.4278

Damien A. Easson, Paul H. Frampton, George F. Smoot

10 pages, 1 figure

(Submitted on 23 Feb 2010)

"To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann-Lemaître equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the temperature intrinsic to the information holographically stored on the screen which is the surface of the universe.

http://arxiv.org/abs/1002.1959

Florian Conrady (Perimeter Inst. Theor. Phys.), Jeff Hnybida (Perimeter Inst. Theor. Phys. and Waterloo U.)

26 pages, 1 figure

(Submitted on 9 Feb 2010)

"We derive simplicity constraints for the quantization of general Lorentzian 4-geometries. Our method is based on the correspondence between coherent states and classical bivectors and the minimization of associated uncertainties. For spacelike geometries, this scheme agrees with the master constraint method of the model by Engle, Pereira, Rovelli and Livine (EPRL). When it is applied to general Lorentzian geometries, we obtain new constraints that include the EPRL constraints as a special case. They imply a discrete area spectrum for both spacelike and timelike surfaces. We use these constraints to define a spin foam model for general Lorentzian 4-geometries. "

http://arxiv.org/abs/1002.1035

Jerzy Kowalski-Glikman

(Submitted on 4 Feb 2010)

"In this note I argue that the expression for entropic force, used as a starting point in Verlinde's derivation of Newton's law, can be deduced from first principles if one assumes that that the microscopic theory behind his construction is the topological SO(4,1) BF theory coupled to particles."

http://arxiv.org/abs/1001.5147

Abhay Ashtekar, Miguel Campiglia, Adam Henderson

(Submitted on 28 Jan 2010)

"The goal of spin foam models is to provide a viable path integral formulation of quantum gravity. Because of background independence, their underlying framework has certain novel features that are not shared by path integral formulations of familiar field theories in Minkowski space. As a simple viability test, these features were recently examined through the lens of loop quantum cosmology (LQC). Results of that analysis, reported in a brief communication [1], turned out to provide concrete arguments in support of the spin foam paradigm. We now present detailed proofs of those results. Since the quantum theory of LQC models is well understood, this analysis also serves to shed new light on some long standing issues in the spin foam and group field theory literature. In particular, it suggests an intriguing possibility for addressing the question of why the cosmological constant is positive and small."

http://arxiv.org/abs/1001.3668

Lee Smolin

16 pages

(Submitted on 20 Jan 2010)

"We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime."

http://arxiv.org/abs/1001.2748

Laurent Freidel, Simone Speziale

(Submitted on 15 Jan 2010)

"A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph. These are defined by the assignment to each triangle of its area, the two unit normals as seen from the two polyhedra sharing it, and an additional angle related to the extrinsic curvature. These quantities do not define a Regge geometry, since they include extrinsic data, but a looser notion of discrete geometry which is twisted in the sense that it is locally well-defined, but the local patches lack a consistent gluing among each other. We give the Poisson brackets among the new variables, and exhibit a symplectomorphism which maps them into the Poisson brackets of loop gravity. The new parametrization has the advantage of a simple description of the gauge-invariant reduced phase space, which is given by a product of phase spaces associated to edges and vertices, and it also provides an abelianisation of the SU(2) connection. The results are relevant for the construction of coherent states, and as a byproduct, contribute to clarify the connection between loop gravity and its subset corresponding to Regge geometries."

http://arxiv.org/abs/1001.0785

Authors: Erik P. Verlinde

(Submitted on 6 Jan 2010)

"Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic."

http://arxiv.org/abs/1003.5652

**Spin foams with timelike surfaces**Florian Conrady (Perimeter Inst. Theor. Phys.)

22 pages

(Submitted on 29 Mar 2010)

"Spin foams of 4d gravity were recently extended from complexes with purely spacelike surfaces to complexes that also contain timelike surfaces. In this article, we express the associated partition function in terms of vertex amplitudes and integrals over coherent states. The coherent states are characterized by unit 3-vectors which represent normals to surfaces and lie either in the 2--sphere or the 2d hyperboloids. In the case of timelike surfaces, a new type of coherent state is used and the associated completeness relation is derived. It is also shown that the quantum simplicity constraints can be deduced by three different methods: by weak imposition of the constraints, by restriction of coherent state bases and by the master constraint."

http://arxiv.org/abs/1003.4811

**Dark Energy, Black Hole Entropy, and the First Precision Measurement in Quantum Gravity**Niayesh Afshordi (Perimeter/Waterloo)

4 pages

(Submitted on 25 Mar 2010)

"The two apparently distinct phenomena of dark energy (or late-time cosmic acceleration) and quantum gravity dominate physics on extremely low, and extremely high energies, but do not seem to have any apparent empirical connection. Nevertheless, the two have a theoretical connection, through the cosmological constant problem. I argue that the finite temperature quantum gravitational corrections to black hole entropy yields a pressure for the gravitational vacuum (or gravitational aether). Assuming that the relative corrections are linear in horizon temperature (i.e. are suppressed by one power of Planck energy), the pressure is comparable to that of dark energy for astrophysical black holes. This implies that the observation of late-time cosmic acceleration may have provided us with the first precision

**measurement**of quantum gravity, i.e. that of black hole entropy."http://arxiv.org/abs/1003.4660

**Inflation in loop quantum cosmology: dynamics and spectrum of gravitational waves**Jakub Mielczarek, Thomas Cailleteau, Julien Grain, Aurelien Barrau

11 pages, 14 figures

(Submitted on 24 Mar 2010)

"Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Due to holonomy corrections, the singularity is replaced by a "bounce". The dynamics of the background is investigated into the details, as a function of the parameters of the model. In particular, the conditions required for inflation to occur are carefully considered and are shown to be generically met. The propagation of gravitational waves is then investigated in this framework. By both numerical and analytical approaches, the primordial tensor power spectrum is computed for a wide range of parameters. Several interesting features could be

**observationally**probed."http://arxiv.org/abs/1003.3483

**Towards Spinfoam Cosmology**Eugenio Bianchi, Carlo Rovelli, Francesca Vidotto

8 pages

(Submitted on 17 Mar 2010)

"We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the

**Friedmann equation**in the appropriate limit."http://arxiv.org/abs/1003.2412

**Hamiltonian analysis of SO(4,1) constrained BF theory**R. Durka, J. Kowalski-Glikman

(Submitted on 11 Mar 2010)

"In this paper we discuss canonical analysis of SO(4,1) constrained BF theory. The action of this theory contains topological terms appended by a term that breaks the gauge symmetry down to the Lorentz subgroup SO(3,1). The equations of motion of this theory turn out to be the vacuum Einstein equations. By solving the B field equations one finds that the action of this theory contains not only the standard Einstein-Cartan term, but also the Holst term proportional to the inverse of the Immirzi parameter, as well as a combination of topological invariants. We show that the structure of the constraints of a SO(4,1) constrained BF theory is exactly that of gravity in Holst formulation. We also briefly discuss quantization of the theory."

http://arxiv.org/abs/1003.1998

**Entropic corrections to Newton's law**Leonardo Modesto, Andrew Randono

(Submitted on 9 Mar 2010)

"It has been known for some time that there is a deep connection between thermodynamics and gravity, with perhaps the most dramatic implication that the Einstein equations can be viewed as a thermodynamic equation of state. Recently Verlinde has proposed a model for gravity with a simple statistical mechanical interpretation that is applicable in the non-relatvistic regime. After critically analyzing the construction, we present a strong consistency check of the model. Specifically, we consider two well-motivated corrections to the area-entropy relation, the log correction and the volume correction, and follow Verlinde's construction to derive corrections to Newton's law of gravitation. We show that the deviations from Newton's law stemming from the log correction have the same form as the lowest order quantum effects of perturbative quantum gravity, and the deviations stemming from the volume correction have the same form as some modified Newtonian gravity models designed to explain the anomalous galactic rotation curves."

http://arxiv.org/abs/1003.1886

**Asymptotics of 4d spin foam models**John W. Barrett, Richard J. Dowdall, Winston J. Fairbairn, Henrique Gomes, Frank Hellmann, Roberto Pereira

(Submitted on 9 Mar 2010)

"We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary data. For some classes of geometrical boundary data, the asymptotic formulae are given, in all three cases, by simple functions of the Regge action for the four-simplex geometry."

http://arxiv.org/abs/1003.1528

**Entropic Inflation**Damien A. Easson, Paul H. Frampton, George F. Smoot

(Submitted on 7 Mar 2010)

"One of the major pillars of modern cosmology is a period of accelerating expansion in the early universe. This accelerating expansion, or inflation, must be sustained for at least 30 e--foldings. One mechanism, used to drive the acceleration, is the addition of a new energy field, called the Inflaton; often this is a scalar field. We propose an alternative mechanism which, like our approach to explain the late-time accelerating universe, uses the entropy and temperature intrinsic to information holographically stored on a screen enclosing the observed space. The acceleration is due in both cases to an emergent entropic force, naturally arising from the information storage on the horizon."

http://arxiv.org/abs/1003.1015

**Comments on and Comments on Comments on Verlinde's paper "On the Origin of Gravity and the Laws of Newton"**Sabine Hossenfelder

(Submitted on 4 Mar 2010)

"We offer some, hopefully clarifying, comments on Verlinde's recent claim that gravity is an entropic force. A suitable identification of quantities shows that both formulations of Newtonian gravity, the classical and the thermodynamical one, are actually equivalent. It turns out that some additional assumptions made by Verlinde are unnecessary. However, when it comes to General Relativity there remain some gaps in the argument. We comment on whether this identification can be done also for electrostatics. Finally, some thoughts on the use of this reinterpretation are offered."

http://arxiv.org/abs/1002.4278

**Entropic Accelerating Universe**Damien A. Easson, Paul H. Frampton, George F. Smoot

10 pages, 1 figure

(Submitted on 23 Feb 2010)

"To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann-Lemaître equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the temperature intrinsic to the information holographically stored on the screen which is the surface of the universe.

**Dark energy is thereby obviated**and the acceleration is due to an entropic force naturally arising from the information storage on a surface screen. We consider an additional quantitative approach based upon the entropy and surface terms usually neglected in General Relativity and show that this leads to the entropic accelerating universe."http://arxiv.org/abs/1002.1959

**A spin foam model for general Lorentzian 4-geometries**Florian Conrady (Perimeter Inst. Theor. Phys.), Jeff Hnybida (Perimeter Inst. Theor. Phys. and Waterloo U.)

26 pages, 1 figure

(Submitted on 9 Feb 2010)

"We derive simplicity constraints for the quantization of general Lorentzian 4-geometries. Our method is based on the correspondence between coherent states and classical bivectors and the minimization of associated uncertainties. For spacelike geometries, this scheme agrees with the master constraint method of the model by Engle, Pereira, Rovelli and Livine (EPRL). When it is applied to general Lorentzian geometries, we obtain new constraints that include the EPRL constraints as a special case. They imply a discrete area spectrum for both spacelike and timelike surfaces. We use these constraints to define a spin foam model for general Lorentzian 4-geometries. "

http://arxiv.org/abs/1002.1035

**A note on gravity, entropy, and BF topological field theory**Jerzy Kowalski-Glikman

(Submitted on 4 Feb 2010)

"In this note I argue that the expression for entropic force, used as a starting point in Verlinde's derivation of Newton's law, can be deduced from first principles if one assumes that that the microscopic theory behind his construction is the topological SO(4,1) BF theory coupled to particles."

http://arxiv.org/abs/1001.5147

**Casting Loop Quantum Cosmology in the Spin Foam Paradigm**Abhay Ashtekar, Miguel Campiglia, Adam Henderson

(Submitted on 28 Jan 2010)

"The goal of spin foam models is to provide a viable path integral formulation of quantum gravity. Because of background independence, their underlying framework has certain novel features that are not shared by path integral formulations of familiar field theories in Minkowski space. As a simple viability test, these features were recently examined through the lens of loop quantum cosmology (LQC). Results of that analysis, reported in a brief communication [1], turned out to provide concrete arguments in support of the spin foam paradigm. We now present detailed proofs of those results. Since the quantum theory of LQC models is well understood, this analysis also serves to shed new light on some long standing issues in the spin foam and group field theory literature. In particular, it suggests an intriguing possibility for addressing the question of why the cosmological constant is positive and small."

http://arxiv.org/abs/1001.3668

**Newtonian gravity in loop quantum gravity**Lee Smolin

16 pages

(Submitted on 20 Jan 2010)

"We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime."

http://arxiv.org/abs/1001.2748

**Twisted geometries: A geometric parametrisation of SU(2) phase space**Laurent Freidel, Simone Speziale

(Submitted on 15 Jan 2010)

"A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph. These are defined by the assignment to each triangle of its area, the two unit normals as seen from the two polyhedra sharing it, and an additional angle related to the extrinsic curvature. These quantities do not define a Regge geometry, since they include extrinsic data, but a looser notion of discrete geometry which is twisted in the sense that it is locally well-defined, but the local patches lack a consistent gluing among each other. We give the Poisson brackets among the new variables, and exhibit a symplectomorphism which maps them into the Poisson brackets of loop gravity. The new parametrization has the advantage of a simple description of the gauge-invariant reduced phase space, which is given by a product of phase spaces associated to edges and vertices, and it also provides an abelianisation of the SU(2) connection. The results are relevant for the construction of coherent states, and as a byproduct, contribute to clarify the connection between loop gravity and its subset corresponding to Regge geometries."

http://arxiv.org/abs/1001.0785

**On the Origin of Gravity and the Laws of Newton**Authors: Erik P. Verlinde

(Submitted on 6 Jan 2010)

"Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic."

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