The growth of matter perturbations in f(R) models

We consider the linear growth of matter perturbations on low redshifts in some $f(R)$ dark energy (DE) models. We discuss the definition of dark energy (DE) in these models and show the differences with scalar-tensor DE models. For the $f(R)$ model recently proposed by Starobinsky we show that the growth parameter $\gamma_0\equiv \gamma(z=0)$ takes the value $\gamma_0\simeq 0.4$ for $\Omega_{m,0}=0.32$ and $\gamma_0\simeq 0.43$ for $\Omega_{m,0}=0.23$, allowing for a clear distinction from $\Lambda$CDM. Though a scale-dependence appears in the growth of perturbations on higher redshifts, we find no dispersion for $\gamma(z)$ on low redshifts up to $z\sim 0.3$, $\gamma(z)$ is also quasi-linear in this interval. At redshift $z=0.5$, the dispersion is still small with $\Delta \gamma\simeq 0.01$. As for some scalar-tensor models, we find here too a large value for $\gamma'_0\equiv \frac{d\gamma}{dz}(z=0)$, $\gamma'_0\simeq -0.25$ for $\Omega_{m,0}=0.32$ and $\gamma'_0\simeq -0.18$ for $\Omega_{m,0}=0.23$. These values are largely outside the range found for DE models in General Relativity (GR). This clear signature provides a powerful constraint on these models.Comment: 14 pages, 7 figures, improved presentation, references added, results unchanged, final version to be published in JCA

Building analytical three-field cosmological models

A difficult task to deal with is the analytical treatment of models composed by three real scalar fields, once their equations of motion are in general coupled and hard to be integrated. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called "extension method". The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is within inflationary models, where the Einstein-Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.Comment: 11 pages, and 3 figures, updated version published in EPJ