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Direct cosmographic reconstruction of the quintessence potential

Saikat Chakraborty, Peter K. S. Dunsby, Robert J. Scherrer

Abstract

We derive expressions for the first and second derivatives of the quintessence potential $V(φ)$, in terms of $λ= -V^{\prime}/V$ and $Γ= (V^{\prime \prime}/V)/(V^\prime/V)^2$, as functions of the quintessence density fraction $Ω_φ$ 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 $V(φ)$ about the present-day value of the scalar field, $φ_0$.

Direct cosmographic reconstruction of the quintessence potential

Abstract

We derive expressions for the first and second derivatives of the quintessence potential , in terms of and , as functions of the quintessence density fraction and the cosmographic parameters , , and . Our mapping is not explicitly a function of the equation of state parameter . We use these results, along with recent observational data, to derive expansions of about the present-day value of the scalar field, .
Paper Structure (6 sections, 21 equations, 2 figures, 2 tables)

This paper contains 6 sections, 21 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Quintessence model
  3. $j=1$ does not necessarily imply a flat potential
  4. A direct cosmographic reconstruction of the quintessence potential
  5. Sensitivity to the cosmographic parameters
  6. Conclusions

Figures (2)

  • Figure 1: Quintessence potential reconstruction with DESI DR1 data
  • Figure 2: Quintessence potential reconstruction with DESI DR2 data