Posts Tagged gravitational action

Recent Postings from gravitational action

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

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.

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.

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 $\Psi$.

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 $D^i$ 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 $D^i$ 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.

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.

The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm [Replacement]

If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study several features of the Einstein-Hilbert action and establish direct connections with horizon thermodynamics. We begin by introducing the concept of holographically conjugate variables (HCVs) in terms of which the surface term in the action has a specific relationship with the bulk term. In addition to g_{ab} and its conjugate momentum \sqrt{-g} M^{cab}, this procedure allows us to (re)discover and motivate strongly the use of f^{ab}=\sqrt{-g}g^{ab} and its conjugate momentum N^c_{ab}. The gravitational action can then be interpreted as a momentum space action for these variables. We also show that many expressions in classical gravity simplify considerably in this approach. For example, the field equations can be written in a form analogous to Hamilton’s equations for a suitable Hamiltonian if we use these variables. More importantly, the variation of the surface term, evaluated on any null surface which acts a local Rindler horizon can be given a direct thermodynamic interpretation. The term involving the variation of the dynamical variable leads to T\delta S while the term involving the variation of the conjugate momentum leads to S\delta T. We have found this correspondence only for the choice of variables (g_{ab}, \sqrt{-g} M^{cab}) or (f^{ab}, N^c_{ab}). We use this result to provide a direct thermodynamical interpretation of the boundary condition in the action principle, when it is formulated in a spacetime region bounded by the null surfaces. We analyse these features from several different perspectives and provide a detailed description, which offers insights about the nature of classical gravity and emergent paradigm.

The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm [Cross-Listing]

If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study several features of the Einstein-Hilbert action and establish direct connections with horizon thermodynamics. We begin by introducing the concept of holographically conjugate variables (HCVs) in terms of which the surface term in the action has a specific relationship with the bulk term. In addition to g_{ab} and its conjugate momentum \sqrt{-g} M^{cab}, this procedure allows us to (re)discover and motivate strongly the use of f^{ab}=\sqrt{-g}g^{ab} and its conjugate momentum N^c_{ab}. The gravitational action can then be interpreted as a momentum space action for these variables. We also show that many expressions in classical gravity simplify considerably in this approach. For example, the field equations can be written in a form analogous to Hamilton’s equations for a suitable Hamiltonian if we use these variables. More importantly, the variation of the surface term, evaluated on any null surface which acts a local Rindler horizon can be given a direct thermodynamic interpretation. The term involving the variation of the dynamical variable leads to T\delta S while the term involving the variation of the conjugate momentum leads to S\delta T. We have found this correspondence only for the choice of variables (g_{ab}, \sqrt{-g} M^{cab}) or (f^{ab}, N^c_{ab}). We use this result to provide a direct thermodynamical interpretation of the boundary condition in the action principle, when it is formulated in a spacetime region bounded by the null surfaces. We analyse these features from several different perspectives and provide a detailed description, which offers insights about the nature of classical gravity and emergent paradigm.

The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm [Replacement]

If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study several features of the Einstein-Hilbert action and establish direct connections with horizon thermodynamics. We begin by introducing the concept of holographically conjugate variables (HCVs) in terms of which the surface term in the action has a specific relationship with the bulk term. In addition to g_{ab} and its conjugate momentum \sqrt{-g} M^{cab}, this procedure allows us to (re)discover and motivate strongly the use of f^{ab}=\sqrt{-g}g^{ab} and its conjugate momentum N^c_{ab}. The gravitational action can then be interpreted as a momentum space action for these variables. We also show that many expressions in classical gravity simplify considerably in this approach. For example, the field equations can be written in a form analogous to Hamilton’s equations for a suitable Hamiltonian if we use these variables. More importantly, the variation of the surface term, evaluated on any null surface which acts a local Rindler horizon can be given a direct thermodynamic interpretation. The term involving the variation of the dynamical variable leads to T\delta S while the term involving the variation of the conjugate momentum leads to S\delta T. We have found this correspondence only for the choice of variables (g_{ab}, \sqrt{-g} M^{cab}) or (f^{ab}, N^c_{ab}). We use this result to provide a direct thermodynamical interpretation of the boundary condition in the action principle, when it is formulated in a spacetime region bounded by the null surfaces. We analyse these features from several different perspectives and provide a detailed description, which offers insights about the nature of classical gravity and emergent paradigm.

Palatini approach to modified f(R) gravity and its bi-metric structure [Cross-Listing]

f(R) gravity theories in the Palatini formalism has been recently used as an alternative way to explain the observed late-time cosmic acceleration with no need of invoking either dark energy or extra spatial dimension. However, its applications have shown that some subtleties of these theories need a more profound examination. Here we are interested in the conformal aspects of the Palatini approach in extended theories of gravity. As is well known, extremization of the gravitational action a la Palatini, naturally "selects" a new metric h related to the metric g of the subjacent manifold by a conformal transformation. The related conformal function is given by the derivative of f(R). In this work we examine the conformal symmetries of the flat (k=0) FLRW spacetime and find that its Conformal Killing Vectors are directly linked to the new metric h and also that each vector yields a different conformal function.

Smoking guns of a bounce in modified theories of gravity through the spectrum of the gravitational waves

We present an inflationary model preceded by a bounce in a metric theory a l\’{a} $f(R)$ where $R$ is the scalar curvature of the space-time. The model is asymptotically de Sitter such that the gravitational action tends asymptotically to a Hilbert-Einstein action, therefore modified gravity affects only the early stages of the universe. We then analyse the spectrum of the gravitational waves through the method of the Bogoliubov coefficients by two means: taking into account the gravitational perturbations due to the modified gravitational action in the $f(R)$ setup and by simply considering those perturbations inherent to the standard Hilbert-Einstein action. We show that there are distinctive (oscillatory) signals on the spectrum for very low frequencies; i.e. corresponding to modes that are currently entering the horizon.

Smoking guns of a bounce in modified theories of gravity through the spectrum of the gravitational waves [Replacement]

We present an inflationary model preceded by a bounce in a metric theory a l\’{a} $f(R)$ where $R$ is the scalar curvature of the space-time. The model is asymptotically de Sitter such that the gravitational action tends asymptotically to a Hilbert-Einstein action, therefore modified gravity affects only the early stages of the universe. We then analyse the spectrum of the gravitational waves through the method of the Bogoliubov coefficients by two means: taking into account the gravitational perturbations due to the modified gravitational action in the $f(R)$ setup and by simply considering those perturbations inherent to the standard Hilbert-Einstein action. We show that there are distinctive (oscillatory) signals on the spectrum for very low frequencies; i.e. corresponding to modes that are currently entering the horizon.

Unimodular Constraint on global scale Invariance [Replacement]

We study global scale invariance along with the unimodular gravity in the vacuum. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar field. This is generalization of conformal theory described in the Ref. \cite{Mannheim}. The possible solutions for the gravitational potential under static linear field approximation are discussed. The new modified solution has additional corrections to the Schwarzschild solution which describe the galactic rotational curve. A comparative study of unimodular theory with conformal theory is also presented. Furthermore, the cosmological solution is studied and it is shown that the unimodular constraint preserve the de Sitter solution explaining the dark energy of the universe.

Unimodular Constraint on global scale Invariance

The global scale invariance along with the unimodular gravity in the vacuum is studied in this paper. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar field. The possible solutions for the gravitational potential under linear field approximation for the allowed values of the introduced parameters of the theory are discussed. The modified solution has additional corrections along with the Schwarzschild solution. A comparative study of unimodular theory with conformal theory is also presented. Furthermore, the cosmological solution is studied and it is shown that the unimodular constraint preserve the de Sitter solution.

A tensor instability in the Eddington inspired Born-Infeld Theory of Gravity [Cross-Listing]

In this paper we consider an extension to Eddington’s proposal for the gravitational action. We study tensor perturbations of a homogeneous and isotropic space-time in the Eddington regime, where modifications to Einstein gravity are strong. We find that the tensor mode is linearly unstable deep in the Eddington regime and discuss its cosmological implications.

A tensor instability in the Eddington inspired Born-Infeld Theory of Gravity [Replacement]

In this paper we consider an extension to Eddington’s proposal for the gravitational action. We study tensor perturbations of a homogeneous and isotropic space-time in the Eddington regime, where modifications to Einstein gravity are strong. We find that the tensor mode is linearly unstable deep in the Eddington regime and discuss its cosmological implications.

Renormalization group scale-setting from the action - a road to modified gravity theories [Replacement]

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the renormalization group is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton’s coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG corrected gravitational theories yields the effective $f(R)$ modified gravity theories with negative powers of the Ricci scalar $R$. The scale-setting at the level of the action at the non-gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in Ricci tensor.

Renormalization group scale-setting from the action - a road to modified gravity theories [Cross-Listing]

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the renormalization group is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton’s coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG corrected gravitational theories yields the effective $f(R)$ modified gravity theories with negative powers of the Ricci scalar $R$. The scale-setting at the level of the action at the non-gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in Ricci tensor. Recently obtained analytical solutions for the quadratic action in $R$ are summarized as an illustration of the dynamics at the non-gaussian fixed point.

Quantum corrections to gravity and their implications for cosmology and astrophysics

The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the post-inflationary cosmology and astrophysics require the corrections to the Einstein-Hilbert action and to the cosmological constant, and those we can not derive yet in a consistent and safe way. At the same time, if we assume that these quantum terms are covariant and that they have relevant magnitude, their functional form can be defined up to a single free parameter, which can be defined on the phenomenological basis. It turns out that the quantum correction may lead, in principle, to surprisingly strong and interesting effects in astrophysics and cosmology.

Weyl-Cartan-Weitzenb\"{o}ck gravity as a generalization of teleparallel gravity [Replacement]

We consider a gravitational model in a Weyl-Cartan space-time, in which the Weitzenb\"{o}ck condition of the vanishing of the sum of the curvature and torsion scalar is also imposed. Moreover, a kinetic term for the torsion is also included in the gravitational action. The field equations of the model are obtained from a Hilbert-Einstein type variational principle, and they lead to a complete description of the gravitational field in terms of two fields, the Weyl vector and the torsion, respectively, defined in a curved background. The cosmological applications of the model are investigated for a particular choice of the free parameters in which the torsion vector is proportional to the Weyl vector. Depending on the numerical values of the parameters of the cosmological model, a large variety of dynamic evolutions can be obtained, ranging from inflationary/accelerated expansions to non-inflationary behaviors. In particular we show that a de Sitter type late time evolution can be naturally obtained from the field equations of the model. Therefore the present model leads to the possibility of a purely geometrical description of the dark energy, in which the late time acceleration of the Universe is determined by the intrinsic geometry of the space-time.

Weyl-Cartan-Weitzenb\"{o}ck gravity [Cross-Listing]

We consider a gravitational model in a Weyl-Cartan space-time, in which the Weitzenb\”{o}ck condition of the vanishing of the sum of the curvature and torsion scalar is also imposed. Moreover, a kinetic term for the torsion is also included in the gravitational action. The field equations of the model are obtained from a Hilbert-Einstein type variational principle, and they lead to a complete description of the gravitational field in terms of two fields, the Weyl vector and the torsion, respectively, defined in a curved background. The cosmological applications of the model are investigated for a particular choice of the free parameters in which the torsion vector is proportional to the Weyl vector. Depending on the numerical values of the parameters of the cosmological model, a large variety of dynamic evolutions can be obtained, ranging from inflationary/accelerated expansions to non-inflationary behaviors. In particular we show that a de Sitter type late time evolution can be naturally obtained from the field equations of the model. Therefore the present model leads to the possibility of a purely geometrical description of the dark energy, in which the late time acceleration of the Universe is determined by the intrinsic geometry of the space-time.

On the stability of the cosmological solutions in f(R,G) gravity [Replacement]

Modified gravity is one of the most promising candidates for explaining the current accelerating expansion of the Universe, and even its unification with the inflationary epoch. Nevertheless, the wide range of models capable to explain the phenomena of dark energy, imposes that current research focuses on a more precise study of the possible effects of modified gravity may have on both cosmological and local levels. In this paper, we focus on the analysis of a type of modified gravity, the so-called f(R,G) gravity and we perform a deep analysis on the stability of important cosmological solutions. This not only can help to constrain the form of the gravitational action, but also facilitate a better understanding of the behavior of the perturbations in this class of higher order theories of gravity, which will lead to a more precise analysis of the full spectrum of cosmological perturbations in future.

On the stability of the cosmological solutions in $f(R,G)$ gravity [Cross-Listing]

Modified gravity is one of the most promising candidates for explaining the current accelerating expansion of the Universe, and even its unification with the inflationary epoch. Nevertheless, the wide range of models capable to explain the phenomena of dark energy, imposes that current research focuses on a more precise study of the possible effects of modified gravity may have on both cosmological and local levels. In this paper, we focus on the analysis of a type of modified gravity, the so-called $f(R,G)$ gravity and we perform a deep analysis on the stability of important cosmological solutions. This not only can help to constrain the form of the gravitational action, but also facilitate a better understanding of the behavior of the perturbations in this class of higher order theories of gravity, which will lead to a more precise analysis of the full spectrum of cosmological perturbations in future.

Gravitational effects of the faraway matter on the rotation curves of spiral galaxies

It was recently shown that in cosmology the gravitational action of faraway matter has quite relevant effects, if retardation of the forces and discreteness of matter (with its spatial correlation) are taken into account. Indeed, far matter was found to exert, on a test particle, a force per unit mass of the order of 0.2 cH0 . It is shown here that such a force can account for the observed rotational velocity curves in spiral galaxies, if the force is assumed to be decorrelated beyond a sufficiently large distance, of the order of 1 kpc. In particular we fit the rotation curves of the galaxies NGC 3198, NGC 2403, UGC 2885 and NGC 4725 without any need of introducing dark matter at all. Two cases of galaxies presenting faster than keplerian decay are also considered.

Towards singularity and ghost free theories of gravity [Replacement]

We present the most general covariant ghost-free gravitational action in a Minkowski vacuum. Apart from the much studied f(R) models, this includes a large class of non-local actions with improved UV behavior, which nevertheless recover Einstein’s general relativity in the IR.

Towards singularity and ghost free theories of gravity [Cross-Listing]

We present the most general ghost-free gravitational action in a Minkowski vacuum. Apart from the much studied f(R) models, this includes a large class of non-local actions with improved UV behavior, which nevertheless recover Einstein’s general relativity in the IR.

The Bispectrum of f(R) Cosmologies [Replacement]

In this paper we analyze a suite of cosmological simulations of modified gravitational action f(R) models, where cosmic acceleration is induced by a scalar field that acts as a fifth force on all forms of matter. In particular, we focus on the bispectrum of the dark matter density field on mildly non-linear scales. For models with the same initial power spectrum, the dark matter bispectrum shows significant differences for cases where the final dark matter power spectrum also differs. Given the different dependence on bias of the galaxy power spectrum and bispectrum, bispectrum measurements can close the loophole of galaxy bias hiding differences in the power spectrum. Alternatively, changes in the initial power spectrum can also hide differences. By constructing LCDM models with very similar final non-linear power spectra, we show that the differences in the bispectrum are reduced (<4%) and are comparable with differences in the imperfectly matched power spectra. These results indicate that the bispectrum depends mainly on the power spectrum and less sensitively on the gravitational signatures of the f(R) model. This weak dependence of the matter bispectrum on gravity makes it useful for breaking degeneracies associated with galaxy bias, even for models beyond general relativity.

The Bispectrum of f(R) Cosmologies

In this paper we analyze a suite of cosmological simulations of modified gravitational action f(R) models, where cosmic acceleration is induced by a scalar field that acts as a fifth force on all forms of matter. In particular, we focus on the bispectrum of the dark matter density field on mildly non-linear scales. For models with the same initial power spectrum, the dark matter bispectrum shows significant differences for cases where the final dark matter power spectrum also differs. Given the different dependence on bias of the galaxy power spectrum and bispectrum, bispectrum measurements can close the loophole of galaxy bias hiding differences in the power spectrum. Alternatively, changes in the initial power spectrum can also hide differences. By constructing LCDM models with very similar final non-linear power spectra, we show that the differences in the bispectrum are reduced (<4%) and are comparable with differences in the imperfectly matched power spectra. These results indicate that the bispectrum depends mainly on the power spectrum and less sensitively on the gravitational signatures of the f(R) model. This weak dependence of the matter bispectrum on gravity makes it useful for breaking degeneracies associated with galaxy bias, even for models beyond general relativity.

Hiding Lorentz Invariance Violation with MOND [Cross-Listing]

Ho\v{r}ava gravity is a attempt to construct a renormalizable theory of gravity by breaking the Lorentz Invariance of the gravitational action at high energies. The underlying principle is that Lorentz Invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low energy limit of Ho\v{r}ava gravity in its non-projectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than $cH_0$; this modification results in the phenomenology of MOND at lower accelerations.

Hiding Lorentz Invariance Violation with MOND [Replacement]

Ho\v{r}ava gravity is a attempt to construct a renormalizable theory of gravity by breaking the Lorentz Invariance of the gravitational action at high energies. The underlying principle is that Lorentz Invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low energy limit of Ho\v{r}ava gravity in its non-projectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than $cH_0$; this modification results in the phenomenology of MOND at lower accelerations.

Hiding Lorentz Invariance Violation with MOND [Replacement]

Ho\v{r}ava gravity is a attempt to construct a renormalizable theory of gravity by breaking the Lorentz Invariance of the gravitational action at high energies. The underlying principle is that Lorentz Invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low energy limit of Ho\v{r}ava gravity in its non-projectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than $cH_0$; this modification results in the phenomenology of MOND at lower accelerations.

Testing dark matter warmness and quantity via the reduced relativistic gas model [Replacement]

We use the framework of a recently proposed model of reduced relativistic gas (RRG) to obtain the bounds for $\Omega$’s of Dark Matter and Dark Energy (in the present case, a cosmological constant), taking into consideration an arbitrary warmness of Dark Matter. An equivalent equation of state has been used by Sakharov to predict the oscillations in the matter power spectrum. Two kind of tests are accounted for in what follows, namely the ones coming from the dynamics of the conformal factor of the homogeneous and isotropic metric and also the ones based on linear cosmic perturbations. The RRG model demonstrated its high effectiveness, permitting to explore a large volume in the space of mentioned parameters in a rather economic way. Taking together the results of such tests as Supernova type Ia (Union2 sample), $H(z)$, CMB ($R$ factor), BAO and LSS (2dfGRS data), we confirm that $\La$CDM is the most favored model. At the same time, for the 2dfGRS data alone we found that an alternative model with a very small quantity of a Dark Matter is also viable. This output is potentially relevant in view of the fact that the LSS is the only test which can not be affected by the possible quantum contributions to the low-energy gravitational action.

Testing DM warmness and quantity via the RRG model

We use the framework of a recently proposed model of reduced relativistic gas (RRG) to obtain the bounds for $\Omega$’s of Dark Matter and Dark Energy (in the present case, a cosmological constant), taking into consideration an arbitrary warmness of Dark Matter. Two kind of tests are accounted for, namely the ones coming from the dynamics of the conformal factor of the homogeneous and isotropic metric and also the ones based on linear cosmic perturbations. The RRG model demonstrated its high effectiveness, permitting to explore a large volume in the space of mentioned parameters in a rather economic way. Taking all the tests together, namely Supernova type Ia (Union2 sample), $H(z)$, CMB ($R$ factor), BAO and LSS (2dfGRS data) into account, we confirm that $\La$CDM is the most favored model. At the same time, for the 2dfGRS data alone we met the possibility of an alternative model with a very small quantity of a Dark Matter. This output is potentially relevant in view of the fact that the LSS is the only test which can not be affected by the possible quantum renormalization-group running in the low-energy gravitational action.

Scale Invariance as a Solution to the Cosmological Constant Problem [Replacement]

We show that scale invariance provides a solution to the fine tuning problem of the cosmological constant. We construct a generalization of the standard model of particle physics which displays exact quantum scale invariance. The matter action is invariant under global scale transformations in arbitrary dimensions. However the gravitational action breaks scale invariance explicitly. The scale symmetry is broken spontaneously in the matter sector of the theory. We show that the contribution to the vacuum energy and hence the cosmological constant is identically zero from the matter sector within the full quantum theory. However the gravitational sector may give non-zero contributions to the cosmological constant at loop orders. No fine tuning may be required at loop orders since the matter sector gives zero contribution to the cosmological constant. We also show that we do not require full scale invariance in order to constrain the vacuum energy from the matter sector. We only require invariance under pseudoscale transformations. Using this idea and motivated by the concept of unimodular gravity we propose an alternative model. In this case also we show that matter sector gives exactly zero contribution to the vacuum energy.

On the $\Lambda$CDM Universe in $f(G)$ gravity [Replacement]

In the context of the so-called Gauss-Bonnet gravity, where the gravitational action includes function of the Gauss-Bonnet invariant, we study cosmological solutions, especially the well-known $\Lambda$CDM model. It is shown that the dark energy contribution and even the inflationary epoch can be explained in the frame of this kind of theories with no need of any other kind of component. Other cosmological solutions are constructed and the rich properties that this kind of theories provide are explored.

 

You need to log in to vote

The blog owner requires users to be logged in to be able to vote for this post.

Alternatively, if you do not have an account yet you can create one here.

Powered by Vote It Up

^ Return to the top of page ^