Exponential Quintessence Model: Analytical Quantification of the Fine-Tuning Problem in Dark Energy

TL;DR

This paper analyzes an exponential quintessence model for dark energy, deriving initial condition constraints that significantly reduce fine-tuning compared to a cosmological constant, and discusses future observational tests.

Contribution

It provides an analytical framework for quantifying fine-tuning in exponential quintessence models, relaxing the fine-tuning problem by many orders of magnitude.

Findings

Fine-tuning is relaxed by dozens of orders of magnitude compared to a cosmological constant.

Analytical constraints on initial conditions are derived consistent with BBN and current dark energy density.

Future gravitational wave observations can test the model.

Abstract

In this paper, we investigate a quintessence field with an exponential potential motivated by the suggestion of time-varying dark energy from the DESI galaxy survey. Assuming a kination epoch in the early Universe, we analytically derive constraints on initial conditions that are consistent with Big Bang Nucleosynthesis and the current dark energy density. Compared to the severe 120-digit fine-tuning required for dark energy to be a cosmological constant, our result suggests that the degree of fine-tuning is naturally relaxed by dozens of orders of magnitude. Furthermore, we discuss the method for testing this model through future observations of the gravitational wave background.