Generalized Gravity Theories Research Articles

Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories

We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasi-local gravitational energy found recently for $f(R)$ gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the FRW spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for $f(R)$ gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.

Remarks on (super-)accelerating cosmological models in general scalar–tensor gravity

We consider Friedmann-Lemaitre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity (STG) with arbitrary coupling functions, set in the Jordan frame. First we describe the general properties of the phase space in the case of barotropic matter fluid and scalar field potential for any spatial curvature (flat, spherical, hyperbolic). Then we address the question under which conditions epochs of accelerated and super-accelerated expansion are possible in STG. For flat models filled with dust matter (and vanishing potential) we give a necessary condition on the coupling function of the scalar field which must be satisfied to allow acceleration and super-acceleration. This is illustrated by a specific example.

Cosmological evolution in vector-tensor theories of gravity

We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the Universe and carry out a classification of models according to the behavior of the vector field in each cosmological epoch. We also analyze the case in which the Universe is dominated by the vector field, performing a complete analysis of the system phase map and identifying those attracting solutions which give rise to accelerated expansion. Moreover, we consider the evolution in a universe filled with a pressureless fluid in addition to the vector field and study the existence of attractors in which we can have a transition from matter domination to vector domination with accelerated expansion so that the vector field may play the role of dark energy. We find that the existence of solutions with late-time accelerated expansion is a generic prediction of vector-tensor theories and that such solutions typically lead to the presence of future singularities. Finally, limits from local gravity tests are used to get constraints on the value of the vector field at small (Solar System) scales.

Evolution of curvature perturbation in generalized gravity theories

Using the cosmological perturbation theory in terms of the δN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy–momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Hořava–Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy–momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.

SCALAR-TENSOR COSMOLOGIES: GENERAL RELATIVITY AS A FIXED POINT OF THE JORDAN FRAME SCALAR FIELD

We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential and scrutinize its limit to general relativity. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases: potential domination and matter domination. We present the conditions on the mathematical form of the coupling function and potential which determine the nature of the fixed points (attractor or other). There are two types of fixed points, both are characterized by cosmological evolution mimicking general relativity, but only one of the types is compatible with the Solar System PPN constraints.

Spherical scalar-tensor galaxy model

We build a spherical halo model for galaxies using a general scalar-tensor theory of gravity in its Newtonian limit. The scalar field is described by a time-independent Klein-Gordon equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. Our model, by construction, fits both the observed rotation velocities of stars in spirals and a typical luminosity profile. As a result, the form of the new Newtonian potential, the scalar field, and dark matter distribution in a galaxy are determined. Taking into account the constraints for the fundamental parameters of the theory $(\ensuremath{\lambda},\ensuremath{\alpha})$, we analyze the influence of the scalar field in the dark matter distribution, resulting in shallow density profiles in galactic centers.

Wald’s entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling

The Bekenstein-Hawking entropy of black holes in Einstein's theory of gravity is equal to a quarter of the horizon area in units of Newton's constant. Wald has proposed that in general theories of gravity the entropy of stationary black holes with bifurcate Killing horizons is a Noether charge which is in general different from the Bekenstein-Hawking entropy. We show that the Noether charge entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling on the horizon defined by the coefficient of the kinetic term of specific graviton polarizations on the horizon. We present several explicit examples of static spherically symmetric black holes.

Viability of vector-tensor theories of gravity

We present a detailed study of the viability of general vector-tensor theories of gravity in the presence of an arbitrary temporal background vector field. We find that there are six different classes of theories which are indistinguishable from General Relativity by means of local gravity experiments. We study the propagation speeds of scalar, vector and tensor perturbations and obtain the conditions for classical stability of those models. We compute the energy density of the different modes and find the conditions for the absence of ghosts in the quantum theory. We conclude that the only theories which can pass all the viability conditions for arbitrary values of the background vector field are not only those of the pure Maxwell type, but also Maxwell theories supplemented with a (Lorentz type) gauge fixing term.

Extended slow-roll conditions and primordial fluctuations: multiple scalar fields and generalized gravity

As an extension of our previous study, we derive slow-roll conditionsfor multiple scalar fields which are non-minimally coupled with gravityand for generalized gravity theories of the form f(ϕ, R). We providesimple formulae of the spectral indices of scalar/tensor perturbationsin terms of the slow-roll parameters.

The shear diffusion coefficient for generalized theories of gravity

Near the horizon of a black brane in Anti-de Sitter (AdS) space and near the AdS boundary, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. The gauge–gravity duality then relates the boundary hydrodynamics for generalized gravity to that of gauge theories with large finite values of 't Hooft coupling. We discuss, for this framework, the hydrodynamics of the shear mode in generalized theories of gravity in d+1 dimensions. It is shown that the shear diffusion coefficients of the near-horizon and boundary hydrodynamics are equal and can be expressed in a form that is purely local to the horizon. We find that the Einstein-theory relation between the shear diffusion coefficient and the shear viscosity to entropy ratio is modified for generalized gravity theories: Both can be explicitly written as the ratio of a pair of polarization-specific gravitational couplings but implicate differently polarized gravitons. Our analysis is restricted to the shear-mode fluctuations for simplicity and clarity; however, our methods can be applied to the hydrodynamics of all gravitational and matter fluctuation modes.

The generalized second law of thermodynamics in generalized gravity theories

We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In f(R) gravity and scalar–tensor gravity, the condition to protect the GSL can also hold because the temperature should be positive, gravity is always attractive and the effective Newton constant should be an approximate constant satisfying the experimental bounds.

Scalar-tensor cosmologies: Fixed points of the Jordan frame scalar field

We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe the details of the phase space geometry. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases: potential domination and matter domination. We present the conditions on the mathematical form of the coupling function and potential which determine the nature of the fixed points (attractor or other). There are two types of fixed points, both are characterized by cosmological evolution mimicking general relativity, but only one of the types is compatible with the Solar System parametrized post-Newtonian (PPN) constraints. The phase space structure should also carry over to the Einstein frame as long as the transformation between the frames is regular which however is not the case for the latter (PPN compatible) fixed point.

Breakdown of the initial value formulation of scalar-tensor gravity and its physical meaning

We revisit singularities of two distinct kinds in the Cauchy problem of general scalar-tensor theories of gravity (previously discussed in the literature), and of metric and Palatini f(R) gravity, in both their Jordan and Einstein frame representations. Examples and toy models are used to shed light onto the problem and it is shown that, contrary to common lore, the two conformal frames are equivalent with respect to the initial value problem.

Thin accretion disks inf(R)modified gravity models

We consider the basic physical properties of matter forming a thin accretion disc in the static and spherically symmetric space-time metric of the vacuum f(R) modified gravity models. The Lagrangian of the generalized gravity theory is also obtained in a parametric form, and the conditions of the viability of the model are also discussed. The exact Schwarzschild-type solution of the gravitational field equations in the f(R) gravity contains a linearly increasing term, as well as a logarithmic correction, as compared to the standard Schwarzschild solution of general relativity, and it depends on four arbitrary integration constants. The energy flux and the emission spectrum from the accretion disk around the f(R) gravity black holes are obtained, and they are compared to the general relativistic case. Particular signatures can appear in the electromagnetic spectrum, thus leading to the possibility of directly testing modified gravity models by using astrophysical observations of the emission spectra from accretion disks.

Testing general metric theories of gravity with bursting neutron stars

I show that several observable properties of bursting neutron stars in metric theories of gravity can be calculated using only conservation laws, Killing symmetries, and the Einstein equivalence principle, without requiring the validity of the general relativistic field equations. I calculate, in particular, the gravitational redshift of a surface atomic line, the touchdown luminosity of a radius-expansion burst, which is believed to be equal to the Eddington critical luminosity, and the apparent surface area of a neutron star as measured during the cooling tails of bursts. I show that, for a general metric theory of gravity, the apparent surface area of a neutron star depends on the coordinate radius of the stellar surface and on its gravitational redshift in the exact same way as in general relativity. On the other hand, the Eddington critical luminosity depends also on an additional parameter that measures the degree to which the general relativistic field equations are satisfied. These results can be used in conjunction with current and future high-energy observations of bursting neutron stars to test general relativity in the strong-field regime.

Generalized Israel junction conditions for a fourth-order brane world

We discuss a general fourth-order theory of gravity on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the higher powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, while the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to the field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second-order theory by introducing an extra tensor field. We formulate the appropriate junction conditions on the brane. We prove the equivalence of both theories. In particular, we prove the equivalence of the junction conditions with different assumptions related to the continuity of the metric along the brane.

Thermodynamics on the apparent horizon in generalized gravity theories

We present a general procedure to construct the first law of thermodynamics on the apparent horizon and illustrate its validity by examining it in some extended gravity theories. Applying this procedure, we can describe the thermodynamics on the apparent horizon in Randall–Sundrum braneworld imbedded in a nontrivial bulk. We discuss the mass-like function which was used to link Friedmann equation to the first law of thermodynamics and obtain its special case which gives the generalized Misner–Sharp mass in Lovelock gravity.

Pulsed X‐Ray Emission from Pulsar A in the Double Pulsar System J0737−3039

The double pulsar system J0737-3039 is not only a test bed for general relativity and theories of gravity, but also provides a unique laboratory for probing the relativistic winds of neutron stars. Recent X-ray observations have revealed a point source at the position of the J0737-3039 system, but have failed to detect pulsations or orbital modulation. Here we report on Chandra X-Ray Observatory High Resolution Camera observations of the double pulsar. We detect deeply modulated, double-peaked X-ray pulses at the period of PSR J0737-3039A, similar in appearance to the observed radio pulses. The pulsed fraction is ~70%. Purely nonthermal emission from pulsar A plausibly accounts for our observations. However, the X-ray pulse morphology of A, in combination with previously reported spectral properties of the X-ray emission, allows the existence of both nonthermal magnetospheric emission and a broad sinusoidal thermal emission component from the neutron star surface. No pulsations are detected from pulsar B, and there is no evidence for orbital modulation or extended nebular structure. The absence of orbital modulation is consistent with theoretical expectations of a Poynting-dominated relativistic wind at the termination shock between the magnetosphere of B and the wind from A and with the small fraction of the energy outflow from A intercepted by the termination shock.

Cosmological simulations using a static scalar-tensor theory

We present ΛCDM N-body cosmological simulations in the framework of of a static general scalar-tensor theory of gravity. Due to the influence of the non-minimally coupled scalar field, the gravitational potential is modified by a Yukawa type term, yielding a new structure formation dynamics. We present some preliminary results and, in particular, we compute the density and velocity profiles of the most massive group.

Propagation equations for deformable test bodies with microstructure in extended theories of gravity

We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energy-momentum current and the hypermomentum current. In particular, the propagation equations allow for a derivation of the equations of motion of test particles in this generalized gravity theory, and allow for direct identification of the couplings between the matter currents and the gauge gravitational field strengths of the theory, namely, the curvature, the torsion, and the nonmetricity. We demonstrate that the possible non-Riemannian spacetime geometry can only be detected with the help of the test bodies that are formed of matter with microstructure. Ordinary gravitating matter, i.e., matter without microscopic internal degrees of freedom, can probe only the Riemannian spacetime geometry. Thereby, we generalize previous results of general relativity and Poincare gauge theory.