Deceleration parameter

The deceleration parameter is $q=-a\ddot{a}/{\dot{a}}^2$; negative values describe accelerated expansion.

For radiation in cosmology with zero cosmological constant, $p=\rho /3$. The Friedmann acceleration equation gives $\ddot{a}/a=-8\pi G\rho /3$, so the deceleration parameter equals the cosmological density parameter, regardless of spatial curvature. This is a relation for a pure radiation fluid, not a general identity for a mixture.

An accelerating universe has $\ddot{a}>0$, equivalently $q<0$ while expansion continues.

Accelerated contraction has $H<0$ and $\ddot{a}<0$, so the magnitude $|\dot{a}|$ increases. Since $\ddot{a}/a=H^2(1-ϵ)$, it corresponds to a first Hubble slow-roll parameter $ϵ>1$.