Reconciling dark energy models withf(R)theories

Abstract

Higher order theories of gravity have recently attracted a lot of interest as alternative candidates to explain the observed cosmic acceleration without the need of introducing any scalar field. A critical ingredient is the choice of the function f (R) of the Ricci scalar curvature entering the gravity Lagrangian and determining the dynamics of the universe. We describe an efficient procedure to reconstruct f (R) from the Hubble parameter H depending on the redshift z. Using the metric formulation of f (R) theories, we derive a third order linear differential equation for f (R(z)) which can be numerically solved after setting the boundary conditions on the basis of physical considerations. Since H(z) can be reconstructed from the astrophysical data, the method we present makes it possible to determine, in principle, what is the f (R) theory which best reproduces the observed cosmological dynamics. Moreover, the method allows to reconcile dark energy models with f (R) theories finding out what is the expression of f (R) which leads to the same H(z) of the given quintessence model. As interesting examples, we consider "quiessence" (dark energy with constant equation of state) and the Chaplygin gas. PACS numbers: 98.80.-k, 04.50+h, 98.80.Jk, 98.80.Es * Corresponding author, email: winny@na.infn.it dubbed quintessence [ 8,9]. These models typically involve scalar fields with a particular class of potentials, allowing the vacuum energy to become dominant only recently (see [10] for comprehensive reviews). Although quintessence by a scalar field is the most studied candidate for dark energy, it generally does not avoid ad hoc fine tuning to solve the coincidence problem.

f(R) cosmology from Noether’s symmetry

“…It is worthy to note that once the free parameters are constrained by the data (the set of allowed parameters might be empty anyhow), one can select physically interesting f (R) models as in [21].…”

Higher-order gravity and the cosmological background of gravitational waves

“…The main issues of this "inverse " approach is matching consistently observations at different scales and taking into account wide classes of gravitational theories where "ad hoc" hypotheses are avoided. In principle, the most popular dark energy models can be achieved by considering f (R) theories of gravity [29,30] and the same track can be followed, at completely different scales, to match galactic dynamics [31]. This philosophy can be taken into account also for the cosmological stochastic background of gravitational waves (GW) which, together whit cosmic microwave background radiation (CMBR) [32], would carry, if detected, a huge amount of information on the early stages of the Universe evolution.…”

Dark energy exponential potential models as curvature quintessence

“…(12). Given these mathematical difficulties, a different approach has been proposed in [21] (hereafter CCT) where Eq. (12) is considered as a way to determine f (R) rather than a(t).…”

“…The method developed in [21] makes it possible to derive the f (R) theory which reproduces a given H(z) and represents therefore a sort of bridge between two physically different scenarios. Here, we apply the method to a quintessence model where the evolution of the scalar field is determined by an exponential potential [23,24].…”