Imprint of a Steep Equation of State in the growth of structure

Abstract

We study the cosmological properties of a dynamical of dark energy (DE) component determined by a Steep Equation of State (SEoS) $w(z)=w_0+w_i\frac{(z/z_T)^q}{1+(z/z_T)^q}$. The SEoS has a transition at $z_T$ between two pivotal values ($w_i, w_0$) which can be taken as an early time and present day values of $w$ and the steepness is given by $q$. We describe the impact of this dynamical DE at background and perturbative level. The steepness of the transition has a better cosmological fit than a conventional CPL model with $w=w_0+w_a(1-a)$. Furthermore, we analyze the impact of steepness of the transition in the growth of matter perturbations and structure formation. This is manifest in the linear matter power spectrum, $P(k)$, the logarithmic growth function, $f\sigma_8(z)$, and the differential mass function $dn/d\log M(z=0)$. The differences in these last three quantities is at a percent-level using the same cosmological baseline parameters in our SEoS and a $\Lambda CDM$ model. However, we find an increase in the power spectrum, producing a bump at $k\approx k_T$ with $k_T\equiv a_TH(a_T)$ the mode associated to the time of the steep transition ($a_T = 1/(1+z_T)$). Different dynamics of DE lead to a different amount of DM at present time which has an impact in Power Spectrum and accordingly in structure formation.