Conditions for the cosmological viability of f(R) dark energy models

We clarify the conditions under which dark energy models whose Lagrangian densities f are written in terms of the Ricci scalar R are cosmologically viable. The existence of a viable matter dominated epoch prior to a late-time acceleration requires that the variable m=Rf_{,RR}/f_{,R} (where f_{,R}=df/dR) satisfies the conditions m(r) approx +0 and dm/dr>-1 at r approx -1 where r=-Rf_{,R}/f. For the existence of a viable late-time acceleration we require instead either (i) m=-r-1, (sqrt{3}-1)/2 0 and n<-1 and are thus cosmologically unacceptable. Similar conclusions can be reached for many other examples discussed in the text. In most cases the standard matter era is replaced by a cosmic expansion with scale factor a=t^{1/2}. We show that the cosmological behavior of f(R) models can be understood by a geometrical approach consisting in studying the m(r) curve on the (r,m) plane. This allows us to classify the f(R) models into four general classes, depending on the existence of a standard matter epoch and on the final accelerated stage. Among several other results, we find that f(R) models can have a strongly phantom attractor but in this case there is no acceptable matter era

Spherically symmetric solutions in f(R)-gravity via 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.Comment: 17 pages, to appear in Class. Quant. Gra

Expansion history and f(R) modified gravity

We attempt to fit cosmological data using $f(R)$ modified Lagrangians containing inverse powers of the Ricci scalar varied with respect to the metric. While we can fit the supernova data well, we confirm the $a\propto t^{1/2}$ behaviour at medium to high redshifts reported elsewhere and argue that the easiest way to show that this class of models are inconsistent with the data is by considering the thickness of the last scattering surface. For the best fit parameters to the supernova data, the simplest 1/R model gives rise to a last scattering surface of thickness $\Delta z\sim 530$, inconsistent with observations.Comment: accepted in JCAP, presentation clarified, results and conclusions unchange

Scalar-Tensor Models of Normal and Phantom Dark Energy

We consider the viability of dark energy (DE) models in the framework of the scalar-tensor theory of gravity, including the possibility to have a phantom DE at small redshifts $z$ as admitted by supernova luminosity-distance data. For small $z$, the generic solution for these models is constructed in the form of a power series in $z$ without any approximation. Necessary constraints for DE to be phantom today and to cross the phantom divide line $p=-\rho$ at small $z$ are presented. Considering the Solar System constraints, we find for the post-Newtonian parameters that $\gamma_{PN}<1$ and $\gamma_{PN,0}\approx 1$ for the model to be viable, and $\beta_{PN,0}>1$ (but very close to 1) if the model has a significantly phantom DE today. However, prospects to establish the phantom behaviour of DE are much better with cosmological data than with Solar System experiments. Earlier obtained results for a $\Lambda$-dominated universe with the vanishing scalar field potential are extended to a more general DE equation of state confirming that the cosmological evolution of these models rule them out. Models of currently fantom DE which are viable for small $z$ can be easily constructed with a constant potential; however, they generically become singular at some higher $z$. With a growing potential, viable models exist up to an arbitrary high redshift.Comment: 30 pages, 4 figures; Matches the published version containing an expanded discussion of various point

On compatibility of string effective action with an accelerating universe

In this paper, we fully investigate the cosmological effects of the moduli dependent one-loop corrections to the gravitational couplings of the string effective action to explain the cosmic acceleration problem in early (and/or late) universe. These corrections comprise a Gauss-Bonnet (GB) invariant multiplied by universal non-trivial functions of the common modulus $\sigma$ and the dilaton $\phi$. The model exhibits several features of cosmological interest, including the transition between deceleration and acceleration phases. By considering some phenomenologically motivated ansatzs for one of the scalars and/or the scale factor (of the universe), we also construct a number of interesting inflationary potentials. In all examples under consideration, we find that the model leads only to a standard inflation ($w \geq -1$) when the numerical coefficient $\delta$ associated with modulus-GB coupling is positive, while the model can lead also to a non-standard inflation ($w<-1$), if $\delta$ is negative. In the absence of (or trivial) coupling between the GB term and the scalars, there is no crossing between the $w -1$ phases, while this is possible with non-trivial GB couplings, even for constant dilaton phase of the standard picture. Within our model, after a sufficient amount of e-folds of expansion, the rolling of both fields $\phi$ and $\sigma$ can be small. In turn, any possible violation of equivalence principle or deviations from the standard general relativity may be small enough to easily satisfy all astrophysical and cosmological constraints.Comment: 30 pages, 8 figures; v2 significant changes in notations, appendix and refs added; v3 significant revisions, refs added; v4 appendix extended, new refs, published versio

The accelerating universe and a limiting curvature proposal

We consider the hypothesis of a limiting minimal curvature in gravity as a way to construct a class of theories exhibiting late-time cosmic acceleration. Guided by the minimal curvature conjecture (MCC) we are naturally lead to a set of scalar tensor theories in which the scalar is non-minimally coupled both to gravity and to the matter Lagrangian. The model is compared to the Lambda Cold Dark Matter concordance model and to the observational data using the gold SNeIa sample of Riess et. al. (2004). An excellent fit to the data is achieved. We present a toy model designed to demonstrate that such a new, possibly fundamental, principle may be responsible for the recent period of cosmological acceleration. Observational constraints remain to be imposed on these models.Comment: 22 pages, 7 figures; revised version to appear in JCAP; references adde

The growth of matter perturbations in some scalar-tensor DE models

We consider asymptotically stable scalar-tensor dark energy (DE) models for which the equation of state parameter $w_{DE}$ tends to zero in the past. The viable models are of the phantom type today, however this phantomness is milder than in General Relativity if we take into account the varying gravitational constant when dealing with the SNIa data. We study further the growth of matter perturbations and we find a scaling behaviour on large redshifts which could provide an important constraint. In particular the growth of matter perturbations on large redshifts in our scalar-tensor models is close to the standard behaviour $\delta_m \propto a$, while it is substantially different for the best-fit model in General Relativity for the same parametrization of the background expansion. As for the growth of matter perturbations on small redshifts, we show that in these models the parameter $\gamma'_0\equiv \gamma'(z=0)$ can take absolute values much larger than in models inside General Relativity. Assuming a constant $\gamma$ when $\gamma'_0$ is large would lead to a poor fit of the growth function $f$. This provides another characteristic discriminative signature for these models.Comment: 13 pages, 7 figures, matches version published in JCA

The growth factor of matter perturbations in an f(R) gravity

The growth of matter perturbations in the $f(R)$ model proposed by Starobinsky is studied in this paper. Three different parametric forms of the growth index are considered respectively and constraints on the model are obtained at both the $1\sigma$ and $2\sigma$ confidence levels, by using the current observational data for the growth factor. It is found, for all the three parametric forms of the growth index examined, that the Starobinsky model is consistent with the observations only at the $2\sigma$ confidence level.Comment: 15 pages, 5 figure

Crossing the Phantom Divide: Theoretical Implications and Observational Status

If the dark energy equation of state parameter w(z) crosses the phantom divide line w=-1 (or equivalently if the expression d(H^2(z))/dz - 3\Omega_m H_0^2 (1+z)^2 changes sign) at recent redshifts, then there are two possible cosmological implications: Either the dark energy consists of multiple components with at least one non-canonical phantom component or general relativity needs to be extended to a more general theory on cosmological scales. The former possibility requires the existence of a phantom component which has been shown to suffer from serious theoretical problems and instabilities. Therefore, the later possibility is the simplest realistic theoretical framework in which such a crossing can be realized. After providing a pedagogical description of various dark energy observational probes, we use a set of such probes (including the Gold SnIa sample, the first year SNLS dataset, the 3-year WMAP CMB shift parameter, the SDSS baryon acoustic oscillations peak (BAO), the X-ray gas mass fraction in clusters and the linear growth rate of perturbations at z=0.15 as obtained from the 2dF galaxy redshift survey) to investigate the priors required for cosmological observations to favor crossing of the phantom divide. We find that a low \Omega_m prior (0.2<\Omega_m <0.25) leads, for most observational probes (except of the SNLS data), to an increased probability (mild trend) for phantom divide crossing. An interesting degeneracy of the ISW effect in the CMB perturbation spectrum is also pointed out.Comment: Accepted in JCAP (to appear). Comments added, typos corrected. 19 pages (revtex), 8 figures. The numerical analysis files (Mathematica + Fortran) with instructions are available at http://leandros.physics.uoi.gr/pdl-cross/pdl-cross.htm . The ppt file of a relevant talk may be downloaded from http://leandros.physics.uoi.gr/pdl-cross/pdl2006.pp

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom