Generalized Gravity Theories Research Articles

Pulsar timing sensitivities to gravitational waves from relativistic metric theories of gravity

Pulsar timing experiments aimed at the detection of gravitational radiation have been performed for decades now. With the forthcoming construction of large arrays capable of tracking multiple millisecond pulsars, it is very likely we will be able to make the first detection of gravitational radiation in the nano-Hertz band, and test Einstein's theory of relativity by measuring the polarization components of the detected signals. Since a gravitational wave predicted by the most general relativistic metric theory of gravity accounts for {\it six} polarization modes (the usual two Einstein's tensor polarizations as well as two vector and two scalar wave components), we have estimated the single-antenna sensitivities to these six polarizations. We find pulsar timing experiments to be significantly more sensitive, over their entire observational frequency band ($\approx 10^{-9} - 10^{-6}$ Hz), to scalar-longitudinal and vector waves than to scalar-transverse and tensor waves. At $10^{-7}$ Hz and with pulsars at a distance of $1$ kpc, for instance, we estimate an average sensitivity to scalar-longitudinal waves that is more than two orders of magnitude better than the sensitivity to tensor waves. Our results imply that a direct detection of gravitational radiation by pulsar timing will result into a test of the theory of general relativity that is more stringent than that based on monitoring the decay of the orbital period of a binary system.

EMERGENT UNIVERSE IN THE CHAMELEON, f(R) AND f(T) GRAVITY THEORIES

In this work, we consider an emergent Universe in generalized gravity theories like the chameleon, f(R) and f(T) gravities. We reconstruct the potential of the chameleon field under the emergent scenario of the Universe and observe its increasing nature with the evolution of the Universe. We reveal that in the emergent Universe scenario, the equation-of-state parameter behaves like quintessence in the case of f(R) gravity and like phantom in the case of f(T) gravity.

Stability, ghost, and strong coupling in nonrelativistic general covariant theory of gravity withλ≠1

In this paper, we investigate three important issues: stability, ghost, and strong coupling, in the Horava--Melby-Thompson setup of the Horava-Lifshitz theory with $\ensuremath{\lambda}\ensuremath{\ne}1$, generalized recently by da Silva. We first develop the general linear scalar perturbations of the Friedmann-Robertson-Walker (FRW) universe with arbitrary spatial curvature and find that an immediate by-product of the setup is that, in all the inflationary models described by a scalar field, the FRW universe is necessarily flat. Applying them to the case of the Minkowski background, we find that it is stable, and, similar to the case $\ensuremath{\lambda}=1$, the spin-0 graviton is eliminated. The vector perturbations vanish identically in the Minkowski background. Thus, similar to general relativity, a free gravitational field in this setup is completely described by a spin-2 massless graviton, even with $\ensuremath{\lambda}\ensuremath{\ne}1$. We also study the ghost problem in the FRW background and find explicitly the ghost-free conditions. To study the strong coupling problem, we consider two different kinds of spacetimes, all with the presence of matter: one is cosmological, and the other is static. We find that the coupling becomes strong for a process with energy higher than ${M}_{\mathrm{pl}}|{c}_{\ensuremath{\psi}}{|}^{5/2}$ in the flat FRW background and ${M}_{\mathrm{pl}}|{c}_{\ensuremath{\psi}}{|}^{3}$ in a static weak gravitational field, where $|{c}_{\ensuremath{\psi}}|\ensuremath{\equiv}|(1\ensuremath{-}\ensuremath{\lambda})/(3\ensuremath{\lambda}\ensuremath{-}1){|}^{1/2}$.

Cosmology in nonrelativistic general covariant theory of gravity

Horava and Melby-Thompson recently proposed a new version of the Horava-Lifshitz theory of gravity, in which the spin-0 graviton is eliminated by introducing a Newtonian prepotential $\ensuremath{\varphi}$ and a local $U(1)$ gauge field $A$. In this paper, we first derive the corresponding Hamiltonian, supermomentum constraints, the dynamical equations, and the equations for $\ensuremath{\varphi}$ and $A$, in the presence of matter fields. Then, we apply the theory to cosmology and obtain the modified Friedmann equation and the conservation law of energy, in addition to the equations for $\ensuremath{\varphi}$ and $A$. When the spatial curvature is different from zero, terms behaving like dark radiation and stiff-fluid exist, from which, among other possibilities, a bouncing universe can be constructed. We also study linear perturbations of the Friedmann-Robertson-Walker universe with any given spatial curvature $k$, and we derive the most general formulas for scalar perturbations. The vector and tensor perturbations are the same as those recently given by one of the present authors [A. Wang, Phys. Rev. D 82, 124063 (2010).] in the setup of Sotiriou, Visser, and Weinfurtner. Applying these formulas to the Minkowski background, we have shown explicitly that the scalar and vector perturbations of the metric indeed vanish, and the only remaining modes are the massless spin-2 gravitons.

Structure of Lanczos-Lovelock Lagrangians in critical dimensions

The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general co-variance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension $D = 2m$ and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in $D = 2m$. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, $R \sqrt{-g} = \partial_j R^j$ for a doublet of functions $R^j = (R^0,R^1)$ which depends only on the metric and its first derivatives. We explicitly construct families of such R^j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in $D = 4$. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.

Scalar-tensor cosmologies with a potential in the general relativity limit

We consider Friedmann-Lemaître-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions, in the era when the energy density of the scalar potential dominates over the energy density of ordinary matter. To study the regime suggested by the local weak field tests (i.e. close to the so-called limit of general relativity) we propose a nonlinear approximation scheme, solve for the phase trajectories, and provide a complete classification of possible solutions. We argue that the topology of phase trajectories in the nonlinear approximation is representative of those of the full system, and thus can tell for which scalar-tensor models general relativity functions as an attractor. To the classes of models which asymptotically approach general relativity we give the solutions also in cosmological time and conclude with some observational implications.

TIME EVOLUTION OF SCALAR-TENSOR COSMOLOGIES IN THE GENERAL RELATIVITY LIMIT

We consider Friedmann-Lemaître-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity in two different cases: in the dust matter dominated era and in the potential dominated era. Motivated by the local weak field constraints and by cosmological observations, we develop and use an approximation scheme for the regime close to the so-called limit of general relativity. The ensuing nonlinear approximate equations for the scalar field can be solved analytically in cosmological time in both cases. We find criteria for the functions ω and V characterizing a scalar-tensor theory, to determine whether the theory does or does not possess solutions converging to general relativity asymptotically in time. The converging solutions can be subsumed under two principal classes: exponentional or polynomial convergence, and damped oscillations around general relativity. The classes of scalar-tensor theories of gravity which contain these types of solutions and satisfy observational constraints, are candidates to explain possible deviations from the standard ΛCDM model. Finally, the effective equation of state parameter w eff is used to illustrate possible asymptotic cosmological dynamics.

LISA sensitivities to gravitational waves from relativistic metric theories of gravity

The direct observation of gravitational waves will provide a unique tool for probing the dynamical properties of highly compact astrophysical objects, mapping ultra-relativistic regions of space-time, and testing Einstein's general theory of relativity. LISA (Laser Interferometer Space Antenna), a joint NASA-ESA mission to be launched in the next decade, will perform these scientific tasks by detecting and studying low-frequency cosmic gravitational waves through their influence on the phases of six modulated laser beams exchanged between three remote spacecraft. By directly measuring the polarization components of the waves LISA will detect, we will be able to test Einstein's theory of relativity with good sensitivity. Since a gravitational wave signal predicted by the most general relativistic metric theory of gravity accounts for {\it six} polarization modes (the usual two Einstein's tensor polarizations as well as two vector and two scalar wave components), we have derived the LISA Time-Delay Interferometric responses and estimated their sensitivities to vector- and scalar-type waves. We find that (i) at frequencies larger than roughly the inverse of the one-way light time ($\approx 6 \times 10^{-2} $ Hz.) LISA is more than ten times sensitive to scalar-longitudinal and vector signals than to tensor and scalar-transverse waves, and (ii) in the low part of its frequency band is equally sensitive to tensor and vector waves and somewhat less sensitive to scalar signals.

Most general fourth-order theory of gravity at low energy

The Newtonian limit of the most general fourth order gravity is performed with metric approach in the Jordan frame with no gauge condition. The most general theory with fourth order differential equations is obtained by generalizing the $f(R)$ term in the action with a generic function containing other two curvature invariants: \emph{Ricci square} ($R_{\alpha\beta}R^{\alpha\beta}$) and \emph{Riemann square} ($R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}$). The spherically symmetric solutions of metric tensor yet present Yukawa-like spatial behavior, but now one has two characteristic lengths. At Newtonian order any function of curvature invariants gives us the same outcome like the so-called \emph{Quadratic Lagrangian} of Gravity. From Gauss - Bonnet invariant one have the complete interpretation of solutions and the absence of a possible third characteristic length linked to Riemann square contribution. From analysis of metric potentials, generated by point-like source, one has a constraint condition on the derivatives of $f$ with respect to scalar invariants.

Unitarity analysis of general Born-Infeld gravity theories

We develop techniques of analyzing the unitarity of general Born-Infeld gravity actions in $D$-dimensional spacetimes. The determinantal form of the action allows us to find a compact expression quadratic in the metric fluctuations around constant curvature backgrounds. This is highly nontrivial since for the Born-Infeld actions, in principle, infinitely many terms in the curvature expansion should contribute to the quadratic action in the metric fluctuations around constant curvature backgrounds, which would render the unitarity analysis intractable. Moreover in even dimensions, unitarity of the theory depends only on finite number of terms built from the powers of the curvature tensor. We apply our techniques to some four-dimensional examples.

Black holes, compact objects and solar system tests in non-relativistic general covariant theory of gravity

We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in terms of the U(1) gauge field A. When solar system tests are considered, severe constraints on A are obtained, which seemingly pick up the Schwarzschild solution uniquely. In contrast to other versions of the Horava-Lifshitz theory, non-singular static stars made of a perfect fluid without heat flow can be constructed, due to the coupling of the fluid with the gauge field. These include the solutions with a constant pressure. We also study the general junction conditions across the surface of a star. In general, the conditions allow the existence of a thin matter shell on the surface. When applying these conditions to the perfect fluid solutions with the vacuum ones as describing their external spacetimes, we find explicitly the matching conditions in terms of the parameters appearing in the solutions. Such matching is possible even without the presence of a thin matter shell.

Scalar-tensor cosmologies with a potential in the general relativity limit: Time evolution

We consider Friedmann–Lemaître–Robertson–Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.

Impact of the WTO Membership, Regional Economic Integration, and Structural Change on China's Trade and Growth

AbstractThe growing economic and political importance of China in the global economy in recent years has been discussed by academic and business economists, trade and investment experts, transnational corporate planners, government advisers, and politicians worldwide. While the discussions have been useful for global knowledge enhancement, and regional and national strategic purposes, they have often been regarded as “hypothetical or with fuzzy outcomes” due to their lack of substantive support. The paper addresses the issue by applying the recent generalized gravity theory to construct a new multi‐equation econometric model of trade–growth causality for China. Using historical trade and growth data and advanced estimation, the model provides substantive evidence for the intertwining impact of China's trade and economic activities, WTO membership, regional economic integration, national, regional and global shocks, and gradual policy reforms on China's trade, growth, and economic relations. Some resulting major strategic trade, development and cooperation issues will also be discussed.

On the new massive gravity and AdS/CFT

Demanding the existence of a simple holographic c-theorem, it is shown that a general (parity preserving) theory of gravity in 2+1 dimensions involving upto four derivative curvature invariants reduces to the new massive gravity theory. We consider extending the theory including upto six derivative curvature invariants. Black hole solutions are presented and consistency with 1+1 CFTs is checked. We present evidence that bulk unitarity is still in conflict with a positive CFT central charge for generic choice of parameters.

Scalar-tensor cosmologies with a potential in the general relativity limit: Phase space view

We consider the potential dominated era of Friedmann-Lemaitre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions, and focus upon the phase space of the scalar field. To study the regime suggested by the local weak field tests (i.e. close to the so-called limit of general relativity) we propose a nonlinear approximation scheme, solve for the phase trajectories, and provide a complete classification of possible phase portraits. We argue that the topology of trajectories in the nonlinear approximation is representative of those of the full system, and thus can tell for which scalar-tensor models general relativity functions as an attractor.

Unifying exact scalar field cosmologies

We present a mechanism that generates the exact solutions of scalar field cosmologies in an unified way. This applies both to standard and phantom scalar fields in the framework of Einsteins General Relativity, and also to extended scenarios based on generalized gravity theories such as Scalar-Tensor theories. We provide a classification of the solutions in terms a single generating function. The existence of form-invariant dualities between the solutions is also discussed.

Fourth-order braneworld gravity

We discuss a general fourth-order theory of gravity and formulate the generalized Israel junction conditions for the theory by application of a generalized Gibbons-Hawking boundary term which is added to the action of the fourth-order gravity theory. Next, we use the generalized Israel junction condition for the construction of a higher-order gravity braneworld model.

Fourth‐order braneworld gravity

We discuss a general fourth-order theory of gravity and formulate the generalized Israel junction conditions for the theory by application of a generalized Gibbons-Hawking boundary term which is added to the action of the fourth-order gravity theory. Next, we use the generalized Israel junction condition for the construction of a higher-order gravity braneworld model.

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.