Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution

We consider $f(R,T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the trace of the stress-energy tensor $T$. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the stress-energy tensor. Generally, the gravitational field equations depend on the nature of the matter source. The field equations of several particular models, corresponding to some explicit forms of the function $f(R,T)$, are also presented. An important case, which is analyzed in detail, is represented by scalar field models. We write down the action and briefly consider the cosmological implications of the $f(R,{T}^{\ensuremath{\phi}})$ models, where ${T}^{\ensuremath{\phi}}$ is the trace of the stress-energy tensor of a self-interacting scalar field. The equations of motion of the test particles are also obtained from a variational principle. The motion of massive test particles is nongeodesic, and takes place in the presence of an extra-force orthogonal to the four velocity. The Newtonian limit of the equation of motion is further analyzed. Finally, we provide a constraint on the magnitude of the extra acceleration by analyzing the perihelion precession of the planet Mercury in the framework of the present model.

$f(R,T)$ gravity

We review different dark energy cosmologies. In particular, we present the ΛCDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the ΛCDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the ΛCDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes F(R) gravity as well as F(R) Hořava-Lifshitz gravity and the teleparallel f(T) gravity. The cosmology of such models representing the ΛCDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.

Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance

We review different dark energy cosmologies. In particular, we present the $\Lambda$CDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the $\Lambda$CDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the $\Lambda$CDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes $F(R)$ gravity as well as $F(R)$ Hořava-Lifshitz gravity and the teleparallel $f(T)$ gravity. The cosmology of such models representing the $\Lambda$CDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.

On etudie des remises a l'echelle conforme du spineur, en se referant a l'approche de Penrose, dans lesquelles le facteur Z, dans H→ZH est complexe. Il n'y a pas de champs de jauge associes a cette retransformation d'echelle. On applique cette approche a la theorie de jauge de Poincare dont le lagrangien est lineaire et quadratique en courbure et torsion

/pdf/conformal-rescalings-applied-to-poincare-gauge-theory-4tzsf8m1zc.pdf

Conformal Rescalings Applied to Poincaré Gauge Theory

Frame-Dragging Precession of Orbiting Gyroscopes in New General Relativity and Possible Violation of Equivalence Principle

The experimental verification of the Aharonov-Bohm proposal suggests that electro­ magnetism can be accounted for in terms of the nonintegrable phase factor. There is, how­ ever, no gravitational analog of such an experiment. In view of the present experimental tests of various gravity theories, we find that gravity can be explained not only by Einstein's General Relativity (1916) in terms of the curvature alone, but also by his New General Relativity (1928) in terms of the torsion alone. For gravity, the concept of motion associated with a closed curve seems much more important than that of the nonintegrable phase factor.

/pdf/gravity-nonintegrable-phase-factor-and-motion-associated-15aesapchm.pdf

Gravity, Nonintegrable Phase Factor and Motion Associated with a Closed Curve

Is Thieberger's Result Inconsistent with Stubbs et al.'s One?

New general relativity predicts a static, isotropic spacetime q\1ite different from the Schwarz­ schild spacetime of general relativity, unless one of the two unknown parameters, c, is exactly zero. In this paper we study its structure as a Riemannian spacetime, paying special attentions to motions of test particles theliein. Recently Kawai and Tomal} have discussed singularities of the static, isotropic spacetime in new general relativity, a gravitational theory based on absolute (or tele-) parallelism. 2 ),*) Here we study structures of the spacetime as probed by spin-1/2 particles and photons. The static, isotropic spacetime of new general relativity is described by the parallel vector fields b={bkl'(x)} with

/pdf/static-isotropic-spacetime-in-new-general-relativity-28f0hzmm6i.pdf

Kenji Hayashi

Papers

Conformal Rescalings Applied to Poincaré Gauge Theory

Frame-Dragging Precession of Orbiting Gyroscopes in New General Relativity and Possible Violation of Equivalence Principle

Gravity, Nonintegrable Phase Factor and Motion Associated with a Closed Curve

Is Thieberger's Result Inconsistent with Stubbs et al.'s One?

Static, Isotropic Spacetime in New General Relativity