Direct cosmographic reconstruction of the quintessence potential

TL;DR

This paper develops a method to reconstruct the quintessence potential and its derivatives directly from cosmographic parameters and observational data, without relying on the equation of state.

Contribution

It provides explicit expressions for the derivatives of the quintessence potential in terms of cosmographic parameters, enabling model-independent reconstruction.

Findings

Derived formulas for $V'()$ and $V''()$ in terms of $$, $ $, $q$, $j$, $s$.

Reconstructed the potential $V()$ around the current scalar field value using observational data.

Abstract

We derive expressions for the first and second derivatives of the quintessence potential $V(\phi)$, in terms of $\lambda = -V^{\prime}/V$ and $\Gamma = (V^{\prime \prime}/V)/(V^\prime/V)^2$, as functions of the quintessence density fraction $\Omega_\phi$ and the cosmographic parameters $q$, $j$, and $s$. Our mapping is not explicitly a function of the equation of state parameter $w$. We use these results, along with recent observational data, to derive expansions of $V(\phi)$ about the present-day value of the scalar field, $\phi_0$.