Abstract
We present a cosmological framework in which spacetime curvature, the arrow of time, and cosmic acceleration arise from a single scalar entropy field \(\mathcal{S}({{x}^{\mu }})\) defined as the logarithm of the local quantum partition function. Within this formulation, observable quantities emerge from derivatives of \(\mathcal{S}\) : first derivatives encode energy flow and temporal directionality, while second derivatives generate spacetime curvature. Residual, non-equilibrium excitations of the entropy field above a renormalized vacuum baseline give rise to an effective curvature that reproduces key phenomenological features commonly attributed to dark energy and dark matter. On cosmological scales, a nearly homogeneous but nonzero second derivative of \(\mathcal{S}\) yields a de Sitter geometry, with the observed cosmological constant arising from dimensional scaling between the Planck length and the asymptotic de Sitter curvature radius. This geometric interpretation naturally accounts for the 10122-order suppression between naive quantum zero-point energy estimates and the measured value of \(\Lambda \) without invoking fine-tuned cancellations. On astrophysical scales, localized variations of the entropy field act as additional effective sources of curvature, reproducing galactic dynamics and gravitational lensing behavior typically modeled with dark matter. Regions of negative entropic curvature correspond to the geometric conditions required for exotic general-relativistic metrics such as warp bubbles and traversable wormholes. At laboratory scales, the Casimir effect emerges as a boundary-induced perturbation of the entropy field, providing an experimentally accessible manifestation of the same underlying mechanism. This work does not seek to invalidate the empirical successes of \(\Lambda \) CDM, but instead proposes an effective geometric interpretation of dark-matter-like gravitational behavior arising from an entropic vacuum residual. In appropriate limits, standard cosmological expansion histories are recovered. In this sense, dark-matter-like gravitational behavior emerges as a coarse-grained geometric response of the entropic vacuum residual. Taken together, these results support a picture in which spacetime geometry, temporal flow, and gravitational phenomena arise as emergent, coarse-grained responses of an underlying entropic field, offering a unified informational perspective on gravity across scales.
