f(R) theories of gravity in the Palatini approach matched with observations

Abstract

We investigate the viability of f (R) theories in the framework of the Palatini approach as solutions to the problem of the observed accelerated expansion of the universe. Two physically motivated popular choices for f (R) are considered : power law, f (R) = βR n , and logarithmic, f (R) = α ln R. Under the Palatini approach, both Lagrangians give rise to cosmological models comprising only standard matter and undergoing a present phase of accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the data on the gas mass fraction in relaxed galaxy clusters to see whether these models are able to reproduce what is observed and to constrain their parameters. It turns out that they are indeed able to fit the data with values of the Hubble constant and of the matter density parameter in agreement with some model independent estimates, but the today deceleration parameter is higher than what is measured in the concordance ΛCDM model. I. INTRODUCTIONThe Hubble diagram of type Ia supernovae (hereafter SNeIa) [1,2], the anisotropy spectrum of the cosmic microwave background radiation (hereafter CMBR) [3,4,5], the matter power spectrum determined by the large scale distribution of galaxies [6,7] and by the data on the Lyα clouds [8] are all convincing evidences in favour of a new picture of the universe, unexpected only few years ago. According to this nowadays standard scenario, the universe is flat and undergoing an accelerated expansion driven by a mysterious fluid with negative pressure nearly homogeneously distributed and making up to ∼ 70% of the energy content. This exotic component is what is called dark energy, while the model we have just depicted is usually referred to as the concordance model.Even if strongly supported by the bulk of the available astrophysical data, this new picture is not free of problems. Actually, while it is clear how dark energy works, its nature remains an unsolved problem. The simplest explanation claims for the cosmological constant Λ thus leading to the so called ΛCDM model 1 [9]. Although being the best fit to most of the available astrophysical data [4,7], the ΛCDM model is also plagued by many problems on different scales. If interpreted as vacuum energy, Λ is up to 120 orders of magnitudes smaller than the predicted value. Furthermore, one should also solve the coincidence problem, i.e. the nearly equivalence of * Electronic address: capozziello@sa.infn.it, winny@na.infn.it, francaviglia@dm.unito.it 1 It is common in literature to make no distinction between the concordance and the ΛCDM model even if, strictly speaking, in the concordance model the dark energy may also be provided by a different mechanism.

Viable Palatini-f(R)cosmologies with generalized dark matter

“…This suggests it worthwhile to seriously reconsider the cosmology of the Palatini-f (R) models. Expansionwise, they can generate a viable sequence of radiation dominated, matter dominated and accelerating era matching with the constraints, as has been shown for various parameterizations of the function f (R), most often with some power-law forms (with one, two or three * Electronic address: tomikoiv@pcu.helsinki.fi powers of R), but also with square-root, logarithmic and exponential forms for the curvature correction terms [26,27,28,29,30]. However, the inhomogeneous evolution present in any realistic universe has not been succesfully reconciled with observations in these models.…”

Uncorrelated measurements of the cosmic expansion history and dark energy from supernovae

“…Although current data seem consistent with a cosmological constant (e.g., Choudhury & Padmanabhan (2004); Chen & Ratra (2004); Daly & Djorgovski (2004); Dicus & Repko (2004); Hannestad & Mortsell (2004); Simon, Verde, & Jimenez (2004); Wang & Tegmark (2004)), the uncertainties are large and more exotic models are not ruled out (e.g., Alam, Sahni, & Starobinsky (2004) ;Capozziello, Cardone, & Francaviglia (2004); Huterer & Cooray (2004) ;Feng et al (2004); Wang et al (2004a)). To uncover the nature of dark energy, and differentiate among various dark energy models, it is important that we extract dark energy constraints in a model-independent manner (Wang & Garnavich 2001;Wang & Lovelace 2001;Wang & Freese 2004).…”

Constraints onf(R)cosmology in the Palatini formalism

“…On the other hand, in the Palatini variation of the action where the metric and connection are treated as indepen- * Email address: B.Li@damtp.cam.ac.uk † Email address: kcchan@phy.cuhk.edu.hk ‡ Email address: mcchu@phy.cuhk.edu.hk dent dynamical variables [11], the resultant equations are second order, which are more tractable and concordant with field equations in other branches of physics. In particular, the typical form f (R) = R + α(−R) β has been discussed extensively in the literature as an alternative dark energy model which fits rather well with the supernovae (SNe) Ia data, and it is also tested using cosmic microwave background (CMB) shift parameter and baryon acoustic oscillation (BAO) in [12,13,14,15]. Possible constraints on other types of Palatini-f (R) model have also been considered using big bang nucleosynthesis (BBN) and the requirements that the success of the inflationary paradigm is not spoiled [16].…”