Inflation and Dark Energy from a Covariant Elastic Medium

Abstract

In this article, we propose a unified framework for cosmological expansion and inflation at the level of background dynamics, by modeling both the inflaton field and dark energy as a four-dimensional continuous medium, whose elastic deformation is described by a covariant vector field. Focusing on a homogeneous and isotropic background cosmology, we show that for a bulk modulus $K = 1.64 \times 10^{109}~\text{N}\cdot\text{m}^{-2}$, the dark energy density decreases by a factor of $\sim 10^{122}$ while the scale factor expands $10^{28}$ times over $\sim 10^{-42}$ seconds during primordial inflation. For illustrative parameter values, our analysis suggests three potential new physical phenomena for future investigation, including longitudinal elastic modes, frequency redshifts in early-universe light, and improved fits to supernova curves. At the end of the paper, we discuss the challenges of applying the framework to inflationary perturbations, particularly the need for a consistent theory capable of producing a nearly scale-invariant power spectrum, as well as of addressing reheating, and identify these as key directions for future work.