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In this article, we investigate the mechanism of cosmological expansion andinflation by modeling dark energy as a four-dimensional continuous medium, withits elastic deformation described by a four-dimensional vector field. Wedemonstrate that when the bulk modulus of this cosmological medium is $K = 1.64\times 10^{109} \text{ N}\cdot\text{m}^{-2}$, the dark energy density,corresponding to the stress-energy associated with the deformation of themedium, decreases by a factor of $\sim 10^{122}$ while the scaling factorexpands from $\sim 10^{-60}$ to $\sim 10^{-32}$ over approximately $10^{-42}$seconds during cosmological inflation in the early universe. Our analysissuggests three potential new physical phenomena for future investigation:detecting longitudinal modes of elastic waves, examining discrepancies in theredshift of light from the early universe, and fitting supernova curves usingthe parameters introduced in our model.

A Time-Dependent Model of Dark Energy Based on Four-Dimensional Continuous Deformation Theory