Three thermodynamically based parametrizations of the deceleration parameter

Abstract

We propose and constrain with the latest observational data, three model-independent parametrizations of the cosmic deceleration parameter $q(z)$. They are well behaved and stay finite at all redshifts. We construct them by fixing the value of $q$ at high redshift, $q(z\ensuremath{\gg}1)=1/2$ (as demanded by cosmic structure formation), and at the far future $q(z=\ensuremath{-}1)=\ensuremath{-}1$, and smoothly interpolating $q(z)$ between them. The fixed point at $z=\ensuremath{-}1$ is not arbitrarily chosen; it readily follows from the second law of thermodynamics. This fairly reduces the ample latitude in parametrizing $q(z)$.