Posts Tagged gravitational action

Recent Postings from gravitational action

Entropy function from the gravitational surface action for an extremal near horizon black hole

It is often argued that all the information of a gravitational theory is encoded in the surface term of the action; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. derivation of the Einstein’s equations, surface term calculated on the horizon leads to entropy, etc. Here I investigate the role of it in the context of entropy function and entropy of extremal near horizon black holes. Considering only the Gibbons-Hawking-York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that there exists a "holographic" nature in the gravitational action – surface term contains the information of the bulk.

Entropy function from the gravitational surface action for an extremal near horizon black hole [Cross-Listing]

It is often argued that all the information of a gravitational theory is encoded in the surface term of the action; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. derivation of the Einstein’s equations, surface term calculated on the horizon leads to entropy, etc. Here I investigate the role of it in the context of entropy function and entropy of extremal near horizon black holes. Considering only the Gibbons-Hawking-York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that there exists a "holographic" nature in the gravitational action – surface term contains the information of the bulk.

Gravitational radiation in massless-particle collisions [Cross-Listing]

The angular and frequency characteristics of the gravitational radiation emitted in collisions of massless particles is studied perturbatively in the context of classical General Relativity for small values of the ratio $\alpha\equiv 2 r_S/b$ of the Schwarzschild radius over the impact parameter. The particles are described with their trajectories, while the contribution of the leading nonlinear terms of the gravitational action is also taken into account. The old quantum results are reproduced in the zero frequency limit $\omega\ll 1/b$. The radiation efficiency $\epsilon \equiv E_{\rm rad}/2E$ outside a narrow cone of angle $\alpha$ in the forward and backward directions with respect to the initial particle trajectories is given by $\epsilon \sim \alpha^2$ and is dominated by radiation with characteristic frequency $\omega \sim {\mathcal O}(1/r_S)$.

Gravitational radiation in massless-particle collisions

The angular and frequency characteristics of the gravitational radiation emitted in collisions of massless particles is studied perturbatively in the context of classical General Relativity for small values of the ratio $\alpha\equiv 2 r_S/b$ of the Schwarzschild radius over the impact parameter. The particles are described with their trajectories, while the contribution of the leading nonlinear terms of the gravitational action is also taken into account. The old quantum results are reproduced in the zero frequency limit $\omega\ll 1/b$. The radiation efficiency $\epsilon \equiv E_{\rm rad}/2E$ outside a narrow cone of angle $\alpha$ in the forward and backward directions with respect to the initial particle trajectories is given by $\epsilon \sim \alpha^2$ and is dominated by radiation with characteristic frequency $\omega \sim {\mathcal O}(1/r_S)$.

Constraining the gravitational action with CMB tensor anisotropies [Cross-Listing]

We present a complete analysis of the imprint of tensor anisotropies on the Cosmic Microwave Background for a class of f(R) gravity theories within the PPF-CAMB framework. We derive the equations, both for the cosmological background and gravitational wave perturbations, required to obtain the standard temperature and polarization power spectra, taking care to include all effects which arise from f(R) modifications of both the background and the perturbation equations. For R^n gravity, we show that for n different from 2, the initial conditions in the radiation dominated era are the same as those found in General Relativity. We also find that by doing simulations which involve either modifying the background evolution while keeping the perturbation equations fixed or fixing the background to be the Lambda-CDM model and modifying the perturbation equations, the dominant contribution to deviations from General Relativity in the temperature and polarization spectra can be attributed to modifications in the background. This demonstrates the importance of using the correct background in perturbative studies of f(R) gravity. Finally an enhancement in the B-modes power spectra is observed which may allow for lower inflationary energy scales.

Constraining the gravitational action with CMB tensor anisotropies

We present a complete analysis of the imprint of tensor anisotropies on the Cosmic Microwave Background for a class of f(R) gravity theories within the PPF-CAMB framework. We derive the equations, both for the cosmological background and gravitational wave perturbations, required to obtain the standard temperature and polarization power spectra, taking care to include all effects which arise from f(R) modifications of both the background and the perturbation equations. For R^n gravity, we show that for n different from 2, the initial conditions in the radiation dominated era are the same as those found in General Relativity. We also find that by doing simulations which involve either modifying the background evolution while keeping the perturbation equations fixed or fixing the background to be the Lambda-CDM model and modifying the perturbation equations, the dominant contribution to deviations from General Relativity in the temperature and polarization spectra can be attributed to modifications in the background. This demonstrates the importance of using the correct background in perturbative studies of f(R) gravity. Finally an enhancement in the B-modes power spectra is observed which may allow for lower inflationary energy scales.

Constraining the gravitational action with CMB tensor anisotropies [Cross-Listing]

We present a complete analysis of the imprint of tensor anisotropies on the Cosmic Microwave Background for a class of f(R) gravity theories within the PPF-CAMB framework. We derive the equations, both for the cosmological background and gravitational wave perturbations, required to obtain the standard temperature and polarization power spectra, taking care to include all effects which arise from f(R) modifications of both the background and the perturbation equations. For R^n gravity, we show that for n different from 2, the initial conditions in the radiation dominated era are the same as those found in General Relativity. We also find that by doing simulations which involve either modifying the background evolution while keeping the perturbation equations fixed or fixing the background to be the Lambda-CDM model and modifying the perturbation equations, the dominant contribution to deviations from General Relativity in the temperature and polarization spectra can be attributed to modifications in the background. This demonstrates the importance of using the correct background in perturbative studies of f(R) gravity. Finally an enhancement in the B-modes power spectra is observed which may allow for lower inflationary energy scales.

Entropy vs Gravitational Action: Do Total Derivatives Matter? [Cross-Listing]

The total derivatives in the gravitational action are usually disregarded as non-producing any non-trivial dynamics. In the context of the gravitational entropy, within Wald’s approach, these terms are considered irrelevant as non-contributing to the entropy. On the other hand, the total derivatives are usually present in the trace anomaly in dimensions higher than 2. As the trace anomaly is related to the logarithmic term in the entanglement entropy it is natural to ask whether the total derivatives make any essential contribution to the entropy or they can be totally ignored. In this note we analyze this question for some particular examples of total derivatives. Rather surprisingly, in all cases that we consider the total derivatives produce non-trivial contributions to the entropy. Some of them are non-vanishing even if the extrinsic curvature of the surface is zero. We suggest that this may explain the earlier observed discrepancy between the holographic entanglement entropy and Wald’s entropy.

Entropy vs Gravitational Action: Do Total Derivatives Matter?

The total derivatives in the gravitational action are usually disregarded as non-producing any non-trivial dynamics. In the context of the gravitational entropy, within Wald’s approach, these terms are considered irrelevant as non-contributing to the entropy. On the other hand, the total derivatives are usually present in the trace anomaly in dimensions higher than 2. As the trace anomaly is related to the logarithmic term in the entanglement entropy it is natural to ask whether the total derivatives make any essential contribution to the entropy or they can be totally ignored. In this note we analyze this question for some particular examples of total derivatives. Rather surprisingly, in all cases that we consider the total derivatives produce non-trivial contributions to the entropy. Some of them are non-vanishing even if the extrinsic curvature of the surface is zero. We suggest that this may explain the earlier observed discrepancy between the holographic entanglement entropy and Wald’s entropy.

Entropy vs Gravitational Action: Do Total Derivatives Matter? [Replacement]

The total derivatives in the gravitational action are usually disregarded as non-producing any non-trivial dynamics. In the context of the gravitational entropy, within Wald’s approach, these terms are considered irrelevant as non-contributing to the entropy. On the other hand, the total derivatives are usually present in the trace anomaly in dimensions higher than 2. As the trace anomaly is related to the logarithmic term in the entanglement entropy it is natural to ask whether the total derivatives make any essential contribution to the entropy or they can be totally ignored. In this note we analyze this question for some particular examples of total derivatives. Rather surprisingly, in all cases that we consider the total derivatives produce non-trivial contributions to the entropy. Some of them are non-vanishing even if the extrinsic curvature of the surface is zero. We suggest that this may explain the earlier observed discrepancy between the holographic entanglement entropy and Wald’s entropy.

Entropy vs Gravitational Action: Do Total Derivatives Matter? [Replacement]

The total derivatives in the gravitational action are usually disregarded as non-producing any non-trivial dynamics. In the context of the gravitational entropy, within Wald’s approach, these terms are considered irrelevant as non-contributing to the entropy. On the other hand, the total derivatives are usually present in the trace anomaly in dimensions higher than 2. As the trace anomaly is related to the logarithmic term in the entanglement entropy it is natural to ask whether the total derivatives make any essential contribution to the entropy or they can be totally ignored. In this note we analyze this question for some particular examples of total derivatives. Rather surprisingly, in all cases that we consider the total derivatives produce non-trivial contributions to the entropy. Some of them are non-vanishing even if the extrinsic curvature of the surface is zero. We suggest that this may explain the earlier observed discrepancy between the holographic entanglement entropy and Wald’s entropy.

Entropy vs Gravitational Action: Do Total Derivatives Matter? [Replacement]

The total derivatives in the gravitational action are usually disregarded as non-producing any non-trivial dynamics. In the context of the gravitational entropy, within Wald’s approach, these terms are considered irrelevant as non-contributing to the entropy. On the other hand, the total derivatives are usually present in the trace anomaly in dimensions higher than 2. As the trace anomaly is related to the logarithmic term in the entanglement entropy it is natural to ask whether the total derivatives make any essential contribution to the entropy or they can be totally ignored. In this note we analyze this question for some particular examples of total derivatives. Rather surprisingly, in all cases that we consider the total derivatives produce non-trivial contributions to the entropy. Some of them are non-vanishing even if the extrinsic curvature of the surface is zero. We suggest that this may explain the earlier observed discrepancy between the holographic entanglement entropy and Wald’s entropy.

Entropy vs Gravitational Action: Do Total Derivatives Matter? [Replacement]

The total derivatives in the gravitational action are usually disregarded as non-producing any non-trivial dynamics. In the context of the gravitational entropy, within Wald’s approach, these terms are considered irrelevant as non-contributing to the entropy. On the other hand, the total derivatives are usually present in the trace anomaly in dimensions higher than 2. As the trace anomaly is related to the logarithmic term in the entanglement entropy it is natural to ask whether the total derivatives make any essential contribution to the entropy or they can be totally ignored. In this note we analyze this question for some particular examples of total derivatives. Rather surprisingly, in all cases that we consider the total derivatives produce non-trivial contributions to the entropy. Some of them are non-vanishing even if the extrinsic curvature of the surface is zero. We suggest that this may explain the earlier observed discrepancy between the holographic entanglement entropy and Wald’s entropy.

Entropy vs Gravitational Action: Do Total Derivatives Matter? [Replacement]

The total derivatives in the gravitational action are usually disregarded as non-producing any non-trivial dynamics. In the context of the gravitational entropy, within Wald’s approach, these terms are considered irrelevant as non-contributing to the entropy. On the other hand, the total derivatives are usually present in the trace anomaly in dimensions higher than 2. As the trace anomaly is related to the logarithmic term in the entanglement entropy it is natural to ask whether the total derivatives make any essential contribution to the entropy or they can be totally ignored. In this note we analyze this question for some particular examples of total derivatives. Rather surprisingly, in all cases that we consider the total derivatives produce non-trivial contributions to the entropy. Some of them are non-vanishing even if the extrinsic curvature of the surface is zero. We suggest that this may explain the earlier observed discrepancy between the holographic entanglement entropy and Wald’s entropy.

Friedmann model with viscous cosmology in modified $f(R,T)$ gravity theory [Replacement]

In this paper, we introduce bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function $f(R,T)$, where $R$ and $T$ denote the curvature scalar and the trace of the energy-momentum tensor, respectively within the framework of a flat Friedmann-Robertson-Walker model. As an equation of state for prefect fluid, we take $p=(\gamma-1)\rho$, where $0 \leq \gamma \leq 2$ and viscous term as a bulk viscosity due to isotropic model, of the form $\zeta =\zeta_{0}+\zeta_{1}H$, where $\zeta_{0}$ and $\zeta_{1}$ are constants, and $H$ is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non- viscous and viscous fluids, respectively by assuming a simplest particular model of the form of $f(R,T) = R+2f(T)$, where $f(T)=\alpha T$ ( $\alpha$ is a constant). A big-rip singularity is also observed for $\gamma<0$ at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of $\alpha$ to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits transition from decelerated phase to accelerated phase under certain constraints of $\zeta_0$ and $\zeta_1$. We compare the viscous models with the non-viscous one through the graph plotted between scale factor and cosmic time and find that bulk viscosity plays the major role in the expansion of the universe. A similar graph is plotted for deceleration parameter with non-viscous and viscous fluids and find a transition from decelerated to accelerated phase with some form of bulk viscosity.

Superluminal Gravitational Waves

The quantum gravity effects of vacuum polarization of gravitons propagating in a curved spacetime cause the quantum vacuum to act as a dispersive medium with a refractive index. Due to this dispersive medium gravitons acquire superluminal velocities. The dispersive medium is produced by higher derivative curvature contributions to the effective gravitational action. It is shown that in a Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the early universe near the Planck time $t_{\rm PL}\gtrsim 10^{-43}\,{\rm sec}$, the speed of gravitational waves $c_g\gg c_{g0}=c_0$, where $c_{g0}$ and $c_0$ are the speeds of gravitational waves and light today. The large speed of gravitational waves stretches their wavelengths to super-horizon sizes, allowing them to be observed in B-polarization experiments.

$R^2\log R$ quantum corrections and the inflationary observables [Cross-Listing]

We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+\alpha R^2+\beta R^2 \ln R$. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index $n_s$ and the tensor to scalar ratio yield $10^{-4}\lesssim r\lesssim0.03$ and $0.94\lesssim n_s \lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary observables are $d n_s/d\ln k \gtrsim -5.2 \times 10^{-4},\, \mu \lesssim 2.1 \times 10^{-8} ,\, y \lesssim 2.6 \times 10^{-9}$. Despite the enhancement in $r$, if the recent BICEP2 measurement stands, this model is disfavoured.

$R^2\log R$ quantum corrections and the inflationary observables [Cross-Listing]

We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+\alpha R^2+\beta R^2 \ln R$. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index $n_s$ and the tensor to scalar ratio yield $10^{-4}\lesssim r\lesssim0.03$ and $0.94\lesssim n_s \lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary observables are $d n_s/d\ln k \gtrsim -5.2 \times 10^{-4},\, \mu \lesssim 2.1 \times 10^{-8} ,\, y \lesssim 2.6 \times 10^{-9}$. Despite the enhancement in $r$, if the recent BICEP2 measurement stands, this model is disfavoured.

$R^2\log R$ quantum corrections and the inflationary observables

We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+\alpha R^2+\beta R^2 \ln R$. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index $n_s$ and the tensor to scalar ratio yield $10^{-4}\lesssim r\lesssim0.03$ and $0.94\lesssim n_s \lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary observables are $d n_s/d\ln k \gtrsim -5.2 \times 10^{-4},\, \mu \lesssim 2.1 \times 10^{-8} ,\, y \lesssim 2.6 \times 10^{-9}$. Despite the enhancement in $r$, if the recent BICEP2 measurement stands, this model is disfavoured.

Marginally Deformed Starobinsky Gravity [Replacement]

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Marginally Deformed Starobinsky Gravity [Replacement]

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Marginally Deformed Starobinsky Gravity [Cross-Listing]

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Marginally Deformed Starobinsky Gravity [Replacement]

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Marginally Deformed Starobinsky Gravity

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Marginally Deformed Starobinsky Gravity [Replacement]

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Marginally Deformed Starobinsky Gravity [Cross-Listing]

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Marginally Deformed Starobinsky Gravity [Replacement]

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Marginally Deformed Starobinsky Gravity [Replacement]

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive $\alpha$. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Entropy of isolated horizon from surface term of gravitational action

Starting from the surface term of gravitational action, one can construct a Virasoro algebra with central extension, with which the horizon entropy can be derived by using Cardy formula. This approach gives a new routine to calculate and interpret the horizon entropy. In this paper, we generalize this approach to a more general case, the isolated horizon, which contains non-stationary spacetimes beyond stationary ones. By imposing appropriate boundary conditions near the horizon, the full set of diffeomorphism is restricted to a subset where the corresponding Noether charges form a Virasoro algebra with central extension. Then by using the Cardy formula, we can derive the entropy of the isolated horizon.

Entropy of isolated horizon from surface term of gravitational action [Cross-Listing]

Starting from the surface term of gravitational action, one can construct a Virasoro algebra with central extension, with which the horizon entropy can be derived by using Cardy formula. This approach gives a new routine to calculate and interpret the horizon entropy. In this paper, we generalize this approach to a more general case, the isolated horizon, which contains non-stationary spacetimes beyond stationary ones. By imposing appropriate boundary conditions near the horizon, the full set of diffeomorphism is restricted to a subset where the corresponding Noether charges form a Virasoro algebra with central extension. Then by using the Cardy formula, we can derive the entropy of the isolated horizon.

Determination of Gravitational Counterterms Near Four Dimensions from RG Equations

The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell’s RG equations for massless QED in curved space, we determine the gravitational counterterms and conformal anomalies near four dimensions. As conjectured for conformal couplings in 1970s, we show at all orders of the perturbation that they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and \begin{eqnarray*} E_D=G_4 +(D-4)\chi(D)H^2 -4\chi(D) \nabla^2 H, \end{eqnarray*} where $G_4$ is the usual Euler density, $H=R/(D-1)$ is the rescaled scalar curvature and $\chi(D)$ is a finite function of $D$ only. The number of the dimensionless gravitational couplings is also reduced to two. $\chi(D)$ can be determined order by order in series of $D-4$, whose first several coefficients are calculated. It has a universal value of $1/2$ at $D=4$. The familiar ambiguous $\nabla^2 R$ term is fixed. At the $D \to 4$ limit, the conformal anomaly $E_D$ just yields the combination $E_4=G_4-2\nabla^2 R/3$, which induces Riegert’s effective action.

Determination of Gravitational Counterterms Near Four Dimensions from RG Equations [Replacement]

The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell’s RG equations for massless QED in curved space, we determine the gravitational counterterms and the conformal anomalies as well near four dimensions. As conjectured for conformal couplings in 1970s, we show that at all orders of the perturbation they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and \begin{eqnarray*} E_D=G_4 +(D-4)\chi(D)H^2 -4\chi(D) \nabla^2 H, \end{eqnarray*} where $G_4$ is the usual Euler density, $H=R/(D-1)$ is the rescaled scalar curvature and $\chi(D)$ is a finite function of $D$ only. The number of the dimensionless gravitational couplings is also reduced to two. $\chi(D)$ can be determined order by order in series of $D-4$, whose first several coefficients are calculated. It has a universal value of $1/2$ at $D=4$. The familiar ambiguous $\nabla^2 R$ term is fixed. At the $D \to 4$ limit, the conformal anomaly $E_D$ just yields the combination $E_4=G_4-2\nabla^2 R/3$, which induces Riegert’s effective action.

Determination of Gravitational Counterterms Near Four Dimensions from RG Equations [Replacement]

The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell’s RG equations for massless QED in curved space, we determine the gravitational counterterms and the conformal anomalies as well near four dimensions. As conjectured for conformal couplings in 1970s, we show that at all orders of the perturbation they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and $E_D=G_4 +(D-4)\chi(D)H^2 -4\chi(D) \nabla^2 H$, where $G_4$ is the usual Euler density, $H=R/(D-1)$ is the rescaled scalar curvature and $\chi(D)$ is a finite function of $D$ only. The number of the dimensionless gravitational couplings is also reduced to two. $\chi(D)$ can be determined order by order in series of $D-4$, whose first several coefficients are calculated. It has a universal value of $1/2$ at $D=4$. The familiar ambiguous $\nabla^2 R$ term is fixed. At the $D \to 4$ limit, the conformal anomaly $E_D$ just yields the combination $E_4=G_4-2\nabla^2 R/3$, which induces Riegert’s effective action.

Determination of Gravitational Counterterms Near Four Dimensions from RG Equations [Replacement]

The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell’s RG equations for massless QED in curved space, we determine the gravitational counterterms and the conformal anomalies as well near four dimensions. As conjectured for conformal couplings in 1970s, we show that at all orders of the perturbation they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and $E_D=G_4 +(D-4)\chi(D)H^2 -4\chi(D) \nabla^2 H$, where $G_4$ is the usual Euler density, $H=R/(D-1)$ is the rescaled scalar curvature and $\chi(D)$ is a finite function of $D$ only. The number of the dimensionless gravitational couplings is also reduced to two. $\chi(D)$ can be determined order by order in series of $D-4$, whose first several coefficients are calculated. It has a universal value of $1/2$ at $D=4$. The familiar ambiguous $\nabla^2 R$ term is fixed. At the $D \to 4$ limit, the conformal anomaly $E_D$ just yields the combination $E_4=G_4-2\nabla^2 R/3$, which induces Riegert’s effective action.

Determination of Gravitational Counterterms Near Four Dimensions from RG Equations [Replacement]

The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell’s RG equations for massless QED in curved space, we determine the gravitational counterterms and the conformal anomalies as well near four dimensions. As conjectured for conformal couplings in 1970s, we show that at all orders of the perturbation they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and $E_D=G_4 +(D-4)\chi(D)H^2 -4\chi(D) \nabla^2 H$, where $G_4$ is the usual Euler density, $H=R/(D-1)$ is the rescaled scalar curvature and $\chi(D)$ is a finite function of $D$ only. The number of the dimensionless gravitational couplings is also reduced to two. $\chi(D)$ can be determined order by order in series of $D-4$, whose first several coefficients are calculated. It has a universal value of $1/2$ at $D=4$. The familiar ambiguous $\nabla^2 R$ term is fixed. At the $D \to 4$ limit, the conformal anomaly $E_D$ just yields the combination $E_4=G_4-2\nabla^2 R/3$, which induces Riegert’s effective action.

Dynamics of Linear Perturbations in the hybrid metric-Palatini gravity [Replacement]

In this work we focus on the evolution of the linear perturbations in the novel hybrid metric-Palatini theory achieved by adding a $f(\mathcal{R})$ function to the gravitational action. Working in the Jordan frame, we derive the full set of linearized evolution equations for the perturbed potentials and present them in the Newtonian and synchronous gauges. We also derive the Poisson equation, and perform the evolution of the lensing potential, $\Phi_{+}$, for a model with a background evolution indistinguishable from $\Lambda$CDM. In order to do so, we introduce a designer approach that allows to retrieve a family of functions $f(\mathcal{R})$ for which the effective equation of state is exactly $w_{\textrm{eff}} = -1$. We conclude, for this particular model, that the main deviations from standard General Relativity and the Cosmological Constant model arise in the distant past, with an oscillatory signature in the ratio between the Newtonian potentials, $\Phi$ and $\Psi$.

Dynamics of Linear Perturbations in the hybrid metric-Palatini gravity [Replacement]

In this work we focus on the evolution of the linear perturbations in the novel hybrid metric-Palatini theory achieved by adding a $f(\mathcal{R})$ function to the gravitational action. Working in the Jordan frame, we derive the full set of linearized evolution equations for the perturbed potentials and present them in the Newtonian and synchronous gauges. We also derive the Poisson equation, and perform the evolution of the lensing potential, $\Phi_{+}$, for a model with a background evolution indistinguishable from $\Lambda$CDM. In order to do so, we introduce a designer approach that allows to retrieve a family of functions $f(\mathcal{R})$ for which the effective equation of state is exactly $w_{\textrm{eff}} = -1$. We conclude, for this particular model, that the main deviations from standard General Relativity and the Cosmological Constant model arise in the distant past, with an oscillatory signature in the ratio between the Newtonian potentials, $\Phi$ and $\Psi$.

Free energy of a Lovelock holographic superconductor [Replacement]

We study thermodynamics of black hole solutions in Lanczos-Lovelock AdS gravity in d+1 dimensions coupled to nonlinear electrodynamics and a Stueckelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a high-temperature superconductor in d dimensions. Larger number of coupling constants in the gravitational side is necessary to widen a domain of validity of physical quantities in a dual QFT. We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and obtain the exact formula for the free energy of the superconductor in the holographic quantum field theory. Our result is analytic and it includes the effects of backreaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, in order to classify holographic superconductors in terms of the parameters in the theory.

Free energy of a Lovelock holographic superconductor [Replacement]

We study thermodynamics of black hole solutions in Lanczos-Lovelock AdS gravity in d+1 dimensions coupled to nonlinear electrodynamics and a Stueckelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a high-temperature superconductor in d dimensions. Larger number of coupling constants in the gravitational side is necessary to widen a domain of validity of physical quantities in a dual QFT. We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and obtain the exact formula for the free energy of the superconductor in the holographic quantum field theory. Our result is analytic and it includes the effects of backreaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, in order to classify holographic superconductors in terms of the parameters in the theory.

On the renormalization of the Gibbons-Hawking boundary term [Replacement]

The bulk (Einstein-Hilbert) and boundary (Gibbons-Hawking) terms in the gravitational action are generally renormalized differently when integrating out quantum fluctuations. The former is affected by nonminimal couplings, while the latter is affected by boundary conditions. We use the heat kernel method to analyze this behavior for a nonminimally coupled scalar field, the Maxwell field, and the graviton field. Allowing for Robin boundary conditions, we examine in which cases the renormalization preserves the ratio of boundary and bulk terms required for the effective action to possess a stationary point. The implications for field theory and black hole entropy computations are discussed.

Weyl-Cartan-Weitzenb\"ock gravity through Lagrange multiplier [Cross-Listing]

We consider an extension of the Weyl-Cartan-Weitzenb\"{o}ck (WCW) and teleparallel gravity, in which the Weitzenb\"{o}ck condition of the exact cancellation of curvature and torsion in a Weyl-Cartan geometry is inserted into the gravitational action via a Lagrange multiplier. In the standard metric formulation of the WCW model, the flatness of the space-time is removed by imposing the Weitzenb\"{o}ck condition in the Weyl-Cartan geometry, where the dynamical variables are the space-time metric, the Weyl vector and the torsion tensor, respectively. However, once the Weitzenb\"{o}ck condition is imposed on the Weyl-Cartan space-time, the metric is not dynamical, and the gravitational dynamics and evolution is completely determined by the torsion tensor. We show how to resolve this difficulty, and generalize the WCW model, by imposing the Weitzenb\"{o}ck condition on the action of the gravitational field through a Lagrange multiplier. The gravitational field equations are obtained from the variational principle, and they explicitly depend on the Lagrange multiplier. As a particular model we consider the case of the Riemann-Cartan space-times with zero non-metricity, which mimics the teleparallel theory of gravity. The Newtonian limit of the model is investigated, and a generalized Poisson equation is obtained, with the weak field gravitational potential explicitly depending on the Lagrange multiplier and on the Weyl vector. The cosmological implications of the theory are also studied, and three classes of exact cosmological models are considered.

Weyl-Cartan-Weitzenb\"ock gravity through Lagrange multiplier [Replacement]

We consider an extension of the Weyl-Cartan-Weitzenb\"{o}ck (WCW) and teleparallel gravity, in which the Weitzenb\"{o}ck condition of the exact cancellation of curvature and torsion in a Weyl-Cartan geometry is inserted into the gravitational action via a Lagrange multiplier. In the standard metric formulation of the WCW model, the flatness of the space-time is removed by imposing the Weitzenb\"{o}ck condition in the Weyl-Cartan geometry, where the dynamical variables are the space-time metric, the Weyl vector and the torsion tensor, respectively. However, once the Weitzenb\"{o}ck condition is imposed on the Weyl-Cartan space-time, the metric is not dynamical, and the gravitational dynamics and evolution is completely determined by the torsion tensor. We show how to resolve this difficulty, and generalize the WCW model, by imposing the Weitzenb\"{o}ck condition on the action of the gravitational field through a Lagrange multiplier. The gravitational field equations are obtained from the variational principle, and they explicitly depend on the Lagrange multiplier. As a particular model we consider the case of the Riemann-Cartan space-times with zero non-metricity, which mimics the teleparallel theory of gravity. The Newtonian limit of the model is investigated, and a generalized Poisson equation is obtained, with the weak field gravitational potential explicitly depending on the Lagrange multiplier and on the Weyl vector. The cosmological implications of the theory are also studied, and three classes of exact cosmological models are considered.

Incorporating gravity into trace dynamics: the induced gravitational action [Replacement]

We study the incorporation of gravity into the trace dynamics framework for classical matrix-valued fields, from which we have proposed that quantum field theory is the emergent thermodynamics, with state vector reduction arising from fluctuation corrections to this thermodynamics. We show that the metric must be incorporated as a classical, not a matrix-valued, field, with the source for gravity the exactly covariantly conserved trace stress-energy tensor of the matter fields. We then study corrections to the classical gravitational action induced by the dynamics of the matrix-valued matter fields, by examining the average over the trace dynamics canonical ensemble of the matter field action, in the presence of a general background metric. Using constraints from global Weyl scaling and three-space general coordinate transformations, we show that to zeroth order in derivatives of the metric, the induced gravitational action in the preferred rest frame of the trace dynamics canonical ensemble must have the form $$ \Delta S=\int d^4x (^{(4)}g)^{1/2}(g_{00})^{-2} A\big(g_{0i} g_{0j} g^{ij}/g_{00}, D^ig_{ij}D^j/g_{00}, g_{0i}D^i/g_{00}\big), $$ with $D^i$ is defined through the co-factor expansion of $^{(4)}g$ by $^{(4)}g/{^{(3)}g}=g_{00}+g_{0i}D^i$, and with $A(x,y,z)$ a general function of its three arguments. This action has "chameleon-like" properties: For the Robertson-Walker cosmological metric, it {\it exactly} reduces to a cosmological constant, but for the Schwarzschild metric it diverges as $(1-2M/r)^{-2}$ near the Schwarzschild radius, indicating that it will substantially affect the horizon structure.

Incorporating gravity into trace dynamics: the induced gravitational action [Replacement]

We study the incorporation of gravity into the trace dynamics framework for classical matrix-valued fields, from which we have proposed that quantum field theory is the emergent thermodynamics, with state vector reduction arising from fluctuation corrections to this thermodynamics. We show that the metric must be incorporated as a classical, not a matrix-valued, field, with the source for gravity the exactly covariantly conserved trace stress-energy tensor of the matter fields. We then study corrections to the classical gravitational action induced by the dynamics of the matrix-valued matter fields, by examining the average over the trace dynamics canonical ensemble of the matter field action, in the presence of a general background metric. Using constraints from global Weyl scaling and three-space general coordinate transformations, we show that to zeroth order in derivatives of the metric, the induced gravitational action in the preferred rest frame of the trace dynamics canonical ensemble must have the form $$ \Delta S=\int d^4x (^{(4)}g)^{1/2}(g_{00})^{-2} A\big(g_{0i} g_{0j} g^{ij}/g_{00}, D^ig_{ij}D^j/g_{00}, g_{0i}D^i/g_{00}\big), $$ with $D^i$ is defined through the co-factor expansion of $^{(4)}g$ by $^{(4)}g/{^{(3)}g}=g_{00}+g_{0i}D^i$, and with $A(x,y,z)$ a general function of its three arguments. This action has "chameleon-like" properties: For the Robertson-Walker cosmological metric, it {\it exactly} reduces to a cosmological constant, but for the Schwarzschild metric it diverges as $(1-2M/r)^{-2}$ near the Schwarzschild radius, indicating that it will substantially affect the horizon structure.

Incorporating gravity into trace dynamics: the induced gravitational action [Replacement]

We study the incorporation of gravity into the trace dynamics framework for classical matrix-valued fields, from which we have proposed that quantum field theory is the emergent thermodynamics, with state vector reduction arising from fluctuation corrections to this thermodynamics. We show that the metric must be incorporated as a classical, not a matrix-valued, field, with the source for gravity the exactly covariantly conserved trace stress-energy tensor of the matter fields. We then study corrections to the classical gravitational action induced by the dynamics of the matrix-valued matter fields, by examining the average over the trace dynamics canonical ensemble of the matter field action, in the presence of a general background metric. Using constraints from global Weyl scaling and three-space general coordinate transformations, we show that to zeroth order in derivatives of the metric, the induced gravitational action in the preferred rest frame of the trace dynamics canonical ensemble must have the form $$ \Delta S=\int d^4x (^{(4)}g)^{1/2}(g_{00})^{-2} A\big(g_{0i} g_{0j} g^{ij}/g_{00}, D^ig_{ij}D^j/g_{00}, g_{0i}D^i/g_{00}\big), $$ with $D^i$ is defined through the co-factor expansion of $^{(4)}g$ by $^{(4)}g/{^{(3)}g}=g_{00}+g_{0i}D^i$, and with $A(x,y,z)$ a general function of its three arguments. This action has "chameleon-like" properties: For the Robertson-Walker cosmological metric, it {\it exactly} reduces to a cosmological constant, but for the Schwarzschild metric it diverges as $(1-2M/r)^{-2}$ near the Schwarzschild radius, indicating that it will substantially affect the horizon structure.

Incorporating gravity into trace dynamics: the induced gravitational action [Replacement]

We study the incorporation of gravity into the trace dynamics framework for classical matrix-valued fields, from which we have proposed that quantum field theory is the emergent thermodynamics, with state vector reduction arising from fluctuation corrections to this thermodynamics. We show that the metric must be incorporated as a classical, not a matrix-valued, field, with the source for gravity the exactly covariantly conserved trace stress-energy tensor of the matter fields. We then study corrections to the classical gravitational action induced by the dynamics of the matrix-valued matter fields, by examining the average over the trace dynamics canonical ensemble of the matter field action, in the presence of a general background metric. Using constraints from global Weyl scaling and three-space general coordinate transformations, we show that to zeroth order in derivatives of the metric, the induced gravitational action in the preferred rest frame of the trace dynamics canonical ensemble must have the form $$ \Delta S=\int d^4x (^{(4)}g)^{1/2}(g_{00})^{-2} A\big(g_{0i} g_{0j} g^{ij}/g_{00}, D^ig_{ij}D^j/g_{00}, g_{0i}D^i/g_{00}\big), $$ with $D^i$ defined through the co-factor expansion of $^{(4)}g$ by $^{(4)}g/{^{(3)}g}=g_{00}+g_{0i}D^i$, and with $A(x,y,z)$ a general function of its three arguments. This action has "chameleon-like" properties: For the Robertson-Walker cosmological metric, it {\it exactly} reduces to a cosmological constant, but for the Schwarzschild metric it diverges as $(1-2M/r)^{-2}$ near the Schwarzschild radius, indicating that it will substantially affect the horizon structure.

Incorporating gravity into trace dynamics: the induced gravitational action [Replacement]

We study the incorporation of gravity into the trace dynamics framework for classical matrix-valued fields, from which we have proposed that quantum field theory is the emergent thermodynamics, with state vector reduction arising from fluctuation corrections to this thermodynamics. We show that the metric must be incorporated as a classical, not a matrix-valued, field, with the source for gravity the exactly covariantly conserved trace stress-energy tensor of the matter fields. We then study corrections to the classical gravitational action induced by the dynamics of the matrix-valued matter fields, by examining the average over the trace dynamics canonical ensemble of the matter field action, in the presence of a general background metric. Using constraints from global Weyl scaling and three-space general coordinate transformations, we show that to zeroth order in derivatives of the metric, the induced gravitational action in the preferred rest frame of the trace dynamics canonical ensemble must have the form $$ \Delta S=\int d^4x (^{(4)}g)^{1/2}(g_{00})^{-2} A\big(g_{0i} g_{0j} g^{ij}/g_{00}, D^ig_{ij}D^j/g_{00}, g_{0i}D^i/g_{00}\big), $$ with $D^i$ defined through the co-factor expansion of $^{(4)}g$ by $^{(4)}g/{^{(3)}g}=g_{00}+g_{0i}D^i$, and with $A(x,y,z)$ a general function of its three arguments. This action has "chameleon-like" properties: For the Robertson-Walker cosmological metric, it {\it exactly} reduces to a cosmological constant, but for the Schwarzschild metric it diverges as $(1-2M/r)^{-2}$ near the Schwarzschild radius, indicating that it will substantially affect the horizon structure.

Further matters in space-time geometry: $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity [Replacement]

We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor with the matter energy-momentum tensor. The field equations of the model are obtained in the metric formalism, and the equation of motion of a massive test particle is derived. In this type of models the matter energy-momentum tensor is generally not conserved, and this non-conservation determines the appearance of an extra-force acting on the particles in motion in the gravitational field. The Newtonian limit of the model is also considered, and an explicit expression for the extra-acceleration which depends on the matter density is obtained in the small velocity limit for dust particles. We also analyze in detail the so-called Dolgov-Kawasaki instability, and obtain the stability conditions of the model with respect to local perturbations. A particular class of gravitational field equations can be obtained by imposing the conservation of the energy-momentum tensor. We derive the corresponding field equations for the conservative case by using a Lagrange multiplier method, from a gravitational action that explicitly contains an independent parameter multiplying the divergence of the energy-momentum tensor. The cosmological implications of the model are investigated for both the conservative and non-conservative cases, and several classes of analytical solutions are obtained.

Further matters in space-time geometry: $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity [Cross-Listing]

We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor with the matter energy-momentum tensor. The field equations of the model are obtained in the metric formalism, and the equation of motion of a massive test particle is derived. In this type of models the matter energy-momentum tensor is generally not conserved, and this non-conservation determines the appearance of an extra-force acting on the particles in motion in the gravitational field. The Newtonian limit of the model is also considered, and an explicit expression for the extra-acceleration which depends on the matter density is obtained in the small velocity limit for dust particles. We also analyze in detail the so-called Dolgov-Kawasaki instability, and obtain the stability conditions of the model with respect to local perturbations. A particular class of gravitational field equations can be obtained by imposing the conservation of the energy-momentum tensor. We derive the corresponding field equations for the conservative case by using a Lagrange multiplier method, from a gravitational action that explicitly contains an independent parameter multiplying the divergence of the energy-momentum tensor. The cosmological implications of the model are investigated for both the conservative and non-conservative cases, and several classes of analytical solutions are obtained.

Further matters in space-time geometry: $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity [Replacement]

We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor with the matter energy-momentum tensor. The field equations of the model are obtained in the metric formalism, and the equation of motion of a massive test particle is derived. In this type of models the matter energy-momentum tensor is generally not conserved, and this non-conservation determines the appearance of an extra-force acting on the particles in motion in the gravitational field. The Newtonian limit of the model is also considered, and an explicit expression for the extra-acceleration which depends on the matter density is obtained in the small velocity limit for dust particles. We also analyze in detail the so-called Dolgov-Kawasaki instability, and obtain the stability conditions of the model with respect to local perturbations. A particular class of gravitational field equations can be obtained by imposing the conservation of the energy-momentum tensor. We derive the corresponding field equations for the conservative case by using a Lagrange multiplier method, from a gravitational action that explicitly contains an independent parameter multiplying the divergence of the energy-momentum tensor. The cosmological implications of the model are investigated for both the conservative and non-conservative cases, and several classes of analytical solutions are obtained.

 

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