Quintessence: an analytical study, with theoretical and observational applications

TL;DR

This paper provides an analytical framework for minimally coupled multi-field quintessence models, offering explicit solutions across cosmic history, with implications for string theory and observational cosmology.

Contribution

It introduces a model-independent analytical approach to describe the evolution of quintessence fields throughout the universe's history, including bounds on potential and field displacement.

Findings

Analytical bounds on scalar potential for early kination phase

Explicit expressions for scale factor and scalar fields during radiation-matter transition

Sub-Planckian field displacement during dark energy domination

Abstract

We focus on minimally coupled (multi)field quintessence models, of thawing type, and their realistic solutions. In a model-independent manner, we describe analytically these cosmological solutions throughout the universe history. Starting with a kination - radiation domination phase, we obtain an upper bound on the scalar potential to guarantee an early kination: $V(\varphi) \ll e^{-\sqrt{6} \varphi}$. Turning to the radiation - matter phase, we obtain analytic expressions for the scale factor $a(t)$ (not $t(a)$) and the scalar fields $\varphi^i(t)$ (usually neglected). These allow us to evaluate analytically the freezing of scalar fields, typically $\Delta \varphi \lesssim 10^{-2}$, as well as the transition moment of the dark energy equation of state parameter $w_{\varphi}$ from $+1$ to $-1$, with excellent agreement to the numerics. We comment 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, we show that the (multi)field displacement is sub-Planckian: $\Delta \varphi \leq 1$. We also provide for that phase analytic expressions for $\int (w_{\varphi}+1)\, d N$ in terms of matter evolution; we relate those to observational targets that we propose. Using finally the CPL parametrisation, while discussing a phantom behaviour, we derive analytic bounds on $w_0$ and $w_a$.