Modified gravity a la Galileon: Late time cosmic acceleration and observational constraints

In this paper we examine the cosmological consequences of fourth order Galileon gravity. We carry out detailed investigations of the underlying dynamics and demonstrate the stability of one de Sitter phase. The stable de Sitter phase contains a Galileon field $\pi$ which is an increasing function of time (\dot{\pi}>0). Using the required suppression of the fifth force, supernovae, BAO and CMB data, we constrain parameters of the model. We find that the $\pi$ matter coupling parameter $\beta$ is constrained to small numerical values such that $\beta$<0.02. We also show that the parameters of the third and fourth order in the action (c_3,c_4) are not independent and with reasonable assumptions, we obtain constraints on them. We investigate the growth history of the model and find that the sub-horizon approximation is not allowed for this model. We demonstrate strong scale dependence of linear perturbations in the fourth order Galileon gravity.Comment: 9 pages, 10 figures, references added, final version to appear in PR

FLRW cosmology in Weyl-Integrable Space-Time

We investigate the Weyl space-time extension of general relativity (GR) for studying the FLRW cosmology through focusing and defocusing of the geodesic congruences. We have derived the equations of evolution for expansion, shear and rotation in the Weyl space-time. In particular we consider the Starobinsky modification, $f(R)=R+\beta R^2-2\Lambda$, of gravity in the Einstein-Palatini formalism, which turns out to reduce to the Weyl integrable space-time (WIST) with the Weyl vector being a gradient. The modified Raychaudhuri equation takes the form of the Hill-type equation which is then analysed for studying formation of the caustics. In this model, it is possible to have a Big Bang singularity free cyclic Universe but unfortunately the periodicity turns out to be extremely short.Comment: 8 pages, 2 figures, version published in JCA

The dispersion of growth of matter perturbations in f(R) gravity

We study the growth of matter density perturbations delta_m for a number of viable f(R) gravity models that satisfy both cosmological and local gravity constraints, where the Lagrangian density f is a function of the Ricci scalar R. If the parameter m=Rf_{,RR}/f_{,R} today is larger than the order of 10^{-6}, linear perturbations relevant to the matter power spectrum evolve with a growth rate s=d (ln delta_m)/d (ln a) (a is the scale factor) that is larger than in the LCDM model. We find the window in the free parameter space of our models for which spatial dispersion of the growth index gamma_0= gamma(z=0) (z is the redshift) appears in the range of values 0.40< gamma_0<0.55, as well as the region in parameter space for which there is essentially no dispersion and gamma_0 converges to values around 0.40<gamma_0<0.43. These latter values are much lower than in the LCDM model. We show that these unusual dispersed or converged spectra are present in most of the viable f(R) models with m(z=0) larger than the order of 10^{-6}. These properties will be essential in the quest for f(R) modified gravity models using future high-precision observations and they confirm the possibility to distinguish clearly most of these models from the LCDM model.Comment: 11 pages, 7 figure

Dispersion in the growth of matter perturbations

We consider the linear growth of matter perturbations on low redshifts in modified gravity Dark Energy (DE) models where G_eff(z,k) is explicitly scale-dependent. Dispersion in the growth today will only appear for scales of the order the critical scale ~ \lambda_{c,0}, the range of the fifth-force today. We generalize the constraint equation satisfied by the parameters \gamma_0(k) and \gamma'_0(k) \equiv \frac{d\gamma(z,k)}{dz}(z=0) to models with G_{eff,0}(k) \ne G. Measurement of \gamma_0(k) and \gamma'_0(k) on several scales can provide information about \lambda_{c,0}. In the absence of dispersion when \lambda_{c,0} is large compared to the probed scales, measurement of \gamma_0 and \gamma'_0 provides a consistency check independent of \lambda_{c,0}. This applies in particular to results obtained earlier for a viable f(R) model.Comment: 8 pages, 5 figure