A. Troisi

Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase

Abstract We show that f ( R ) -gravity can, in general, give rise to cosmological viable models compatible with a matter-dominated epoch evolving into a late accelerated phase. We discuss the various representations of f ( R ) -gravity as an ideal fluid or a scalar–tensor gravity theory, taking into account conformal transformations. We point out that mathematical equivalence does not correspond, in several cases, to the physical equivalence of Jordan frame and Einstein frame. Finally, we show that wide classes of f ( R ) gravity models, including matter and accelerated phases, can be phenomenologically reconstructed by means of observational data. In principle, any popular quintessence models could be “reframed” as an f ( R ) -gravity model.

CURVATURE QUINTESSENCE MATCHED WITH OBSERVATIONAL DATA

Quintessence issues can be achieved by taking into account higher order curvature invariants into the effective action of gravitational field. Such an approach is naturally related to fundamental theories of quantum gravity which predict higher order terms in loop expansion of quantum fields in curved space-times. In this framework, we obtain a class of cosmological solutions which are fitted against cosmological data. We reproduce encouraging results able to fit high redshift supernovae and WMAP observations. The age of the universe and other cosmological parameters are discussed in this context.

Low surface brightness galaxy rotation curves in the low energy limit of Rn gravity: no need for dark matter?

We investigate the possibility that the observed flatness of the rotation curves of spiral galaxies is not evidence for the existence of dark matter haloes, but rather a signal of the breakdown of General Relativity. To this aim, we consider power-law fourth-order theories of gravity obtained by replacing the scalar curvature R with f(R) =f 0 R n in the gravity Lagrangian. We show that, in the low energy limit, the gravitational potential generated by a point-like source may be written as Φ(r) ∝ r -1 [1 + (r/r c ) β ] with β a function of the slope n of the gravity Lagrangian and r c a scalelength depending on the gravitating system properties. In order to apply the model to realistic systems, we compute the modified potential and the rotation curve for spherically symmetric and for thin disc mass distributions. It turns out that the potential is still asymptotically decreasing, but the corrected rotation curve, although not flat, is higher than the Newtonian one, thus offering the possibility to fit rotation curves without dark matter. To test the viability of the model, we consider a sample of 15 low surface brightness galaxies with combined H [I and Ha measurements of the rotation curve extending in the putative dark matter dominated region. We find a very good agreement between the theoretical rotation curve and the data using only stellar disc and interstellar gas when the slope n of the gravity Lagrangian is set to the value n = 3.5 (giving β = 0.817) obtained by fitting the Type Ia supernova Hubble diagram with the assumed power-law f(R) model and no dark matter. The excellent agreement between theoretical and observed rotation curves and the values of the stellar mass-to-light ratios in agreement with the predictions of population synthesis models make us confident that R n gravity may represent a good candidate to solve both the dark energy problem on cosmological scales and the dark matter one on galactic scales with the same value of the slope n of the higher-order gravity Lagrangian.

Spherically symmetric solutions in f(R) gravity via the Noether symmetry approach

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether symmetry approach. A general formalism in the metric framework is developed considering a point-like f(R) Lagrangian where spherical symmetry is required. Examples of exact solutions are given.

Parametrized post-newtonian limit of fourth order gravity inspired by scalar-tensor gravity

Based on the dynamical equivalence between higher order gravity and scalar-tensor gravity the parametrized post-Newtonian (PPN) limit of fourth order gravity is discussed. We exploit this analogy developing a fourth order gravity version of the Eddington PPN parameters. As a result, Solar System experiments can be reconciled with higher order gravity, if physical constraints descending from experiments are fulfilled.

Evolution of density perturbations in f(R) gravity

We give a rigorous and mathematically well defined presentation of the covariant and gauge invariant theory of scalar perturbations of a Friedmann-Lema\^{\i}tre-Robertson-Walker universe for fourth order gravity, where the matter is described by a perfect fluid with a barotropic equation of state. The general perturbations equations are applied to a simple background solution of

Cosmological dynamics of Rn gravity

{R}^{n}

Some remarks on the dynamical systems approach to fourth order gravity

gravity. We obtain exact solutions of the perturbations equations for scales much bigger than the Hubble radius. These solutions have a number of interesting features. In particular, we find that for all values of

Spherical symmetry in f(R)-gravity

n

Cosmological dynamics of R**n gravity

there is always a growing mode for the density contrast, even if the universe undergoes an accelerated expansion. Such behavior does not occur in standard general relativity, where as soon as dark energy dominates, the density contrast experiences an unrelenting decay. This peculiarity is sufficiently novel to warrant further investigation of fourth order gravity models.