Solar System experiments do not yet veto modified gravity models

The dynamical equivalence between modified and scalar-tensor gravity theories is revisited and it is concluded that it breaks down in the limit to general relativity. A gauge-independent analysis of cosmological perturbations in both classes of theories lends independent support to this conclusion. As a consequence, the PPN formalism of scalar-tensor gravity and Solar System experiments do not veto modified gravity, as previously thought.Comment: 7 pages, latex, submitted to Phys. Rev.

Reconstructing the universe history, from inflation to acceleration, with phantom and canonical scalar fields

We consider the reconstruction technique in theories with a single or multiple (phantom and/or canonical) scalar fields. With the help of several examples, it is demonstrated explicitly that the universe expansion history, unifying early-time inflation and late-time acceleration, can be realized in scalar-tensor gravity. This is generalized to the theory of a scalar field coupled non-minimally to the curvature and to a Brans-Dicke-like theory. Different examples of unification of inflation with cosmic acceleration, in which de Sitter, phantom, and quintessence type fields play the fundamental role--in different combinations--are worked out. Specifically, the frame dependence and stability properties of de Sitter space scalar field theory are studied. Finally, for two-scalar theories, the late-time acceleration and early-time inflation epochs are successfully reconstructed, in realistic situations in which the more and more stringent observational bounds are satisfied, using the freedom of choice of the scalar field potential, and of the kinetic factor.Comment: 22 pages, revtex, no figures, version to appear in Phys. Rev.

The final state and thermodynamics of dark energy universe

As it follows from the classical analysis, the typical final state of the dark energy universe where dominant energy condition is violated is finite time, sudden future singularity (Big Rip). For a number of dark energy universes (including scalar phantom and effective phantom theories as well as specific quintessence model) we demonstrate that quantum effects play the dominant role near Big Rip, driving the universe out of future singularity (or, at least, making it milder). As a consequence, the entropy bounds with quantum corrections become well-defined near Big Rip. Similarly, black holes mass loss due to phantom accretion is not so dramatic as it was expected: masses do not vanish to zero due to transient character of phantom evolution stage. Some examples of cosmological evolution for negative, time-dependent equation of state are also considered with the same conclusions. The application of negative entropy (or negative temparature) occurence in the phantom thermodynamics is briefly discussed.Comment: LaTeX file 36 pages, version to appear in PR

Generalization of Einstein-Lovelock theory to higher order dilaton gravity

A higher order theory of dilaton gravity is constructed as a generalization of the Einstein-Lovelock theory of pure gravity. Its Lagrangian contains terms with higher powers of the Riemann tensor and of the first two derivatives of the dilaton. Nevertheless, the resulting equations of motion are quasi-linear in the second derivatives of the metric and of the dilaton. This property is crucial for the existence of brane solutions in the thin wall limit. At each order in derivatives the contribution to the Lagrangian is unique up to an overall normalization. Relations between symmetries of this theory and the O(d,d) symmetry of the string-inspired models are discussed.Comment: 18 pages, references added, version to be publishe

On the way from matter-dominated era to dark energy universe

We develop the general program of the unification of matter-dominated era with acceleration epoch for scalar-tensor theory or dark fluid. The general reconstruction of single scalar-tensor theory is fulfilled. The explicit form of scalar potential for which the theory admits matter-dominated era, transition to acceleration and (asymptotically deSitter) acceleration epoch consistent with WMAP data is found. The interrelation of the epochs of deceleration-acceleration transition and matter dominance-dark energy transition for dark fluids with general EOS is investigated. We give several examples of such models with explicit EOS (using redshift parametrization) where matter-dark energy domination transition may precede the deceleration-acceleration transition. As some by-product, the reconstruction scheme is applied to scalar-tensor theory to define the scalar potentials which may produce the dark matter effect. The obtained modification of Newton potential may explain the rotation curves of galaxies.Comment: LaTeX 12 pages, 1 figure, extended version to appear in PR

Generalized black hole entropy in two dimensions

The Bekenstein-Hawking entropy of a black hole is proportional to its horizon area, hence in $D=2$ spacetime dimensions it is constant because the horizon degenerates into two points. This fact is consistent with Einstein's gravity becoming topological in two dimensions. In $F(R)$ gravity, which is non-trivial even in $D=2$, we find that the entropy is constant, as for Bekenstein-Hawking. As shown in EPL 139 (2022) no.6, 69001 (arXiv:2208.10146), two-dimensional $F(R)$ gravity is equivalent to Jackiw-Teitelboim gravity, in turn equivalent to the Sachdev-Ye-Kitaev model where the entropy becomes constant in the large $N$ limit. Several recently proposed entropies are functions of the Bekenstein-Hawking entropy and become constant in $D=2$, but in two-dimensional dilaton gravity entropies are not always constant. We study general dilaton gravity and obtain arbitrary static black hole solutions for which the non-constant entropies depend on the mass, horizon radius, or Hawking temperature, and constitute new proposals for a generalized entropy.Comment: 12 pages, latex, to appear in Int. J. Geom. Meth. Mod. Phy