We study the thermodynamics of four-dimensional Kerr-Newman-AdS black holes both in the canonical and the grand-canonical ensemble. The stability conditions are investigated, and the complete phase diagrams are obtained, which include the Hawking-Page phase transition in the grand-canonical ensemble. In the canonical case, one has a first order transition between small and large black holes, which disappears for sufficiently large electric charge or angular momentum. This disappearance corresponds to a critical point in the phase diagram. Via the AdS/CFT conjecture, the obtained phase structure is also relevant for the corresponding conformal field theory living in a rotating Einstein universe, in the presence of a global background U (1) current. An interesting limit arises when the black holes preserve some supersymmetry. These BPS black holes correspond to highly degenerate zero temperature states in the dual CFT, which lives in an Einstein universe rotating with the *

A general approach to viable modified f (R) gravity is developed in both the Jordan and the Einstein frames. A class of exponential, realistic modified gravities is introduced and investigated with care. Special focus is made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One-and two-steps models are explicitly considered, but the analysis is extensible to N -step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way. Moreover, it is demonstrated that models in this category easily pass all local tests, including stability of spherical body solution, non-violation of Newton's law, and generation of a very heavy positive mass for the additional scalar degree of freedom. 95.36.+x,

Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, f (G), is added to the General Relativity action. We show that a theory of this kind is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence or phantom cosmic acceleration, with a possibility for the transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with the Solar System constraints. Specific properties of f (G) gravity in a de Sitter universe, such as dS and SdS solutions, their entropy and its explicit one-loop quantization are studied. The issue of a possible solution of the hierarchy problem in modified gravities is addressed too.

Motivated by the dark energy issue, the one-loop quantization approach for a family of relativistic cosmological theories is discussed in some detail. Specifically, general f (R) gravity at the one-loop level in a de Sitter universe is investigated, extending a similar program developed for the case of pure Einstein gravity. Using generalized zeta regularization, the one-loop effective action is explicitly obtained off-shell, what allows to study in detail the possibility of (de)stabilization of the de Sitter background by quantum effects. The one-loop effective action maybe useful also for the study of constant curvature black hole nucleation rate and it provides the plausible way of resolving the cosmological constant problem.

The heat-kernel expansion and ζ-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times with spatial section consisting in manifold with constant curvature are discussed in detail. Several mathematical results, relevant to physical applications are presented, including exact solutions of the heat-kernel equation, a simple exposition of hyperbolic geometry and an elementary derivation of the Selberg trace formula. With regards to the physical applications, the vacuum energy for scalar fields, the one-loop renormalization of a self-interacting scalar field theory on a hyperbolic space-time, with a discussion on the topological symmetry breaking, the finite temperature effects and the Bose-Einstein condensation, are considered. Some attempts to generalize the results to extended objects are also presented, including some remarks on path integral quantization, asymptotic properties of extended objects and a novel representation for the one-loop (super)string free energy.

We consider scalar-Gauss-Bonnet and modified Gauss-Bonnet gravities and reconstruct these theories from the universe expansion history. In particular, we are able to construct versions of those theories (with and without ordinary matter), in which the matter dominated era makes a transition to the cosmic acceleration epoch. In several of the cases under consideration, matter dominance and the deceleration-acceleration transition occur in the presence of matter only. The late-time acceleration epoch is described asymptotically by de Sitter space but may also correspond to an exact ΛCDM cosmology, having in both cases an effective equation of state parameter w close to −1. The one-loop effective action of modified Gauss-Bonnet gravity on the de Sitter background is evaluated and it is used to derive stability criteria for the ensuing de Sitter universe. PACS numbers: 11.25.-w, 95.36.+x, 98.80.-k I. INTRODUCTIONModified gravity is a promising theory that has become a very attractive gravitational alternative for dark energy (for a recent review, see [1,2,3]. It is, to start, a powerful scheme. Indeed, depending on the specific model considered, modified gravity is able to realize any of the proposed scenarios that have been delimited by the observational constrains leading to cosmic acceleration: effective phantom models, cosmological constant theories or quintessence. Also, it can easily account for the different epochs in the evolution of the unverse, that start to emerge clearly from the observational data (for a recent review of these data and their comparison with dark energy models, see [4]). The qualitative understanding of gravitational dark energy (see [3] for a review) is quite simple: some gravitational terms different from the usual General Relativity ones may dominate at the very early or very late universe epochs. Thus, General Relativity seems to be only approximately valid, both at very early as well as at very late times. To have the possibility to explain -in a unified way as modified gravity effects-fundamental cosmological phenomena such as early time inflation and late time acceleration, is very appealing. Moreover, modified gravity has the possibility to solve the coincidence problem, too, and can also clarify the role of dark matter in the formation and evolution of the universe.

A toy model of Einstein gravity with a Gauss-Bonnet classically "entropic" term mimicking a quantum correction is considered. The static black hole solution due to Tomozawa is found and generalized with the inclusion of non trivial horizon topology, and its entropy evaluated deriving the first law by equations of motion. As a result the Bekenstein-Hawking area law turns to be corrected by a logarithmic area term. A Misner-Sharp expression for the mass of black hole is found. Within a Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological setting, the model is used in order to derive modified Friedmann equations. Such new equations are shown to reproduce the first law with the same formal entropy and quasi local energy of the static case, but here within a FLRW space-time interpreted as a dynamical cosmological black hole. A detailed analysis of cosmological solutions is presented, and it is shown that the presence of the correction term provides regular solutions and interesting phases of acceleration and decelerations, as well as, with negligible matter, exact de Sitter solutions.Comment: 11 pages, published versio

We study inflation induced by (power-low) scalar curvature corrections to General Relativity. The class of inflationary scalar potentials V (σ) ∼ exp[n σ], n general parameter, is investigated in the Einsein frame and the corresponding actions in the Jordan frame are derived. We found the conditions for which these potentials are able to reproduce viable inflation according with the last cosmological data and lead to large scalar curvature corrections which emerge only at a mass scale larger than the Planck mass. Cosmological constant may appear or be set equal to zero in the Jordan frame action without changing the behaviour of the model during inflation. Moreover, polynomial corrections to General Relativity are analyzed in detail. When de Sitter space-time emerges as an exact solution of the models, it is necessary to use perturbative equations in the Jordan framework to study their dynamics during the inflation. In this case, we demonstrate that the Ricci scalar decreases after a correct amount of inflation, making the models consistent with the observable evolution of the universe.