Gianluca Allemandi

Dark energy dominance and cosmic acceleration in first order formalism

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen, in particular, in its Palatini formulation. We analyze here a specific nonlinear gravity-scalar system in the first-order Palatini formalism which leads to a Friedmann-Robertson-Walker cosmology different from the purely metric one. It is shown that the emerging Friedmann-Robertson-Walker cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first-order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation.

Accelerated cosmological models in Ricci squared gravity

Alternative gravitational theories described by Lagrangians depending on general functions of the Ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of the Universe at present time. In this paper we proceed further in this analysis of cosmological applications of alternative gravitational theories depending on (other) curvature invariants. We introduce Ricci squared Lagrangians in minimal interaction with matter (perfect fluid); we find modified Einstein equations and consequently modified Friedmann equations in the Palatini formalism. It is striking that both Ricci scalar and Ricci squared theories are described in the same mathematical framework and both the generalized Einstein equations and generalized Friedmann equations have the same structure. In the framework of the cosmological principle, without the introduction of exotic forms of dark energy, we thus obtain modified equations providing values of

Accelerated cosmological models in first-order nonlinear gravity

{w}_{\mathrm{e}\mathrm{f}\mathrm{f}}l\ensuremath{-}1

Post-newtonian parameters from alternative theories of gravity

in accordance with the experimental data. The spacetime bi-metric structure plays a fundamental role in the physical interpretation of results and gives them a clear and very rich geometrical interpretation.

Conformal aspects of the Palatini approach in Extended Theories of Gravity

The evidence of the acceleration of universe at present time has led to investigate modified theories of gravity and alternative theories of gravity, which are able to explain acceleration from a theoretical viewpoint without the need of introducing dark energy. In this paper we study alternative gravitational theories defined by Lagrangians which depend on general functions of the Ricci scalar invariant in minimal interaction with matter, in view of their possible cosmological applications. Structural equations for the spacetimes described by such theories are solved and the corresponding field equations are investigated in the Palatini formalism, which prevents instability problems. Particular examples of these theories are also shown to provide, under suitable hypotheses, a coherent theoretical explanation of earlier results concerning the present acceleration of the universe and cosmological inflation. We suggest moreover a new possible Lagrangian, depending on the inverse of

Charges and energy in Chern–Simons theories and Lovelock gravity

\mathrm{sinh}(R),

Constraining extended theories of gravity using Solar System tests

which gives an explanation to the present acceleration of the universe.

Covariant charges in Chern–Simons AdS3 gravity

Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini formalism) to test these theories at the solar system level and possibly at the galactic scales. We exactly solve field equations in vacuum and find the corresponding corrections to the standard general relativistic gravitational field. On the other hand, approximate solutions are found in matter cases starting from a Lagrangian which depends on a phenomenological parameter. Both in the vacuum case and in the matter case the deviations from General Relativity are controlled by parameters that provide the Post-Newtonian corrections which prove to be in good agreement with solar system experiments.

Energy in Einstein–Maxwell theory and the first law of isolated horizons via the Noether theorem

The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle gravitational and matter degrees of freedom (passing from the Jordan frame to the Einstein frame) but they acquire a physical meaning considering the bi-metric structure of Palatini approach which allows to distinguish between spacetime structure and geodesic structure. These facts are relevant at least at cosmological scales, while at small scale (i.e. in the spacetime regions relevant for observations) the conformal factor is slowly varying and its effects are not relevant. Examples of higher-order and non-minimally coupled theories are worked out and relevant cosmological solutions in Einstein frame and Jordan frame are discussed showing that also the interpretation of cosmological observations can drastically change depending on the adopted frame.

The Variational Approach to Alternative Theories of Gravity

Starting from the SO(2, 2n) Chern–Simons form in (2n + 1) dimensions, we calculate the variation of conserved quantities in Lovelock gravity and Lovelock–Maxwell gravity through the covariant formalism developed in [23]. Despite the technical complexity of the Lovelock Lagrangian, we obtain a remarkably simple expression for the variation of the charges ensuing from the diffeomorphism covariance of the theory. The viability of the result is tested in specific applications and the formal expression for the entropy of Lovelock black holes is recovered.