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Abstract: We consider the linear growth of matter perturbations on low redshifts insome $fR$ dark energy DE models. We discuss the definition of dark energyDE in these models and show the differences with scalar-tensor DE models. Forthe $fR$ model recently proposed by Starobinsky we show that the growthparameter $\gamma 0\equiv \gammaz=0$ takes the value $\gamma 0\simeq 0.4$ for$\Omega {m,0}=0.32$ and $\gamma 0\simeq 0.43$ for $\Omega {m,0}=0.23$, allowingfor a clear distinction from $\Lambda$CDM. Though a scale-dependence appears inthe growth of perturbations on higher redshifts, we find no dispersion for$\gammaz$ on low redshifts up to $z\sim 0.3$, $\gammaz$ is alsoquasi-linear in this interval. At redshift $z=0.5$, the dispersion is stillsmall with $\Delta \gamma\simeq 0.01$. As for some scalar-tensor models, wefind 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 DEmodels in General Relativity GR. This clear signature provides a powerfulconstraint on these models.

Autor: R. Gannouji, B. Moraes, D. Polarski


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