Quintessence: An Analytical Study, With Theoretical and Observational Applications

Abstract

The authors focus on minimally coupled (multi)field quintessence models, of thawing type, and their realistic solutions. In a model-independent manner, these cosmological solutions are described analytically throughout the universe history. Starting with a kination–radiation domination phase, an upper bound on the scalar potential is obtained to guarantee an early kination: $V\left(\phi \right)\ll e^{-\sqrt{6}\phi }$. Turning to the radiation–matter phase, analytic expressions are obtained for the scale factor $a\left(t\right)$ (not $t\left(a\right)$) and the scalar fields ${\phi }^i\left(t\right)$ (usually neglected). These allow us to evaluate analytically the freezing of scalar fields, typically $\Delta \phi \lesssim {10}^{-2}$, as well as the transition moment of the dark energy equation of state parameter $w_{\phi }$ from $+1$ to $-1$, with excellent agreement to the numerics. Comments are made on this freezing in view of string theory model building, and of some cosmological events. Turning to the latest phase of matter–dark energy domination, it is shown that the (multi)field displacement is sub-Planckian: $\Delta \phi \le 1$. For that phase analytic expressions are also provided for $\int (w_{\phi }+1)dN$ in terms of matter evolution; these are related to observational targets that are proposed. Finally, using the CPL parameterization, while discussing a phantom behavior, analytic bounds on $w_0$ and $w_a$ are derived.