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

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.

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