4D Elastic Cosmology: A Framework to Address the Hubble Tension

We propose a 4D elastic extension of spacetime as a framework to address the long-standing Hubble tension. Within this model, hidden-dimensional deformations generate effective energy contributions that can mimic quintessence or early dark energy, providing a natural mechanism for the discrepancy between local and CMB-based determinations of the Hubble constant. The framework unifies elastic stress-energy with gravitational dynamics, offering predictions for structure growth, BAO scales, and CMB perturbations. It also provides a geometric–elastic interpretation of cosmic acceleration, where stress-energy relaxation in higher dimensions projects observable effects in 3+1D cosmology. This work connects with previous research on the DEM–Strings framework (dark energy as residual elastic tension) and serves as a complementary application to the Hubble tension problem. The results highlight both the potential consistency of elastic cosmology with cosmological data and the challenges of embedding such models into a unified “Equation of Everything.”