Checking the second law at cosmic scales

TL;DR

This work tests the applicability of the second law of thermodynamics at cosmic scales by deriving a model-independent bound from Robertson–Walker cosmology and reconstructing the Hubble history $H(z)$ using a Gaussian process approach on CC, BAO, and Pantheon+ SN data. The key bound $H'(z) \ge \Omega_{k0} H_0^2 (1+z)/H(z)$ (equivalently $\zeta(z) \ge 0$) is evaluated without assuming a specific parametric form for $H(z)$, via non-parametric reconstructions of $d_C(z)$ and its derivative. The analysis finds $\tilde{\zeta} = \zeta/H_0 > 0$ for $0<z\le 2$ across curvature choices and data sets, supporting the second law on the largest observable scales and placing constraints on phantom dark energy models. The results, robust across GP kernels (notably the Matérn $\nu=5/2$ kernel), strengthen the view that cosmic expansion is thermodynamically consistent and align with prior independent studies.

Abstract

Based on recent data about the history of the Hubble factor, it is argued that the second law of thermodynamics holds at the largest scales accessible to observation. This is consistent with previous studies of the same question.

Figures (23)

• Figure 2: Contour plots for $M$ and $\Omega_{k0} h^2$ using different GP kernels.
• Figure : (a) CC
• Figure : (a) Reconstructed $H(z)$
• Figure : (a) Reconstructed $H(z)$
• Figure : (a) Reconstructed $d_C(z)$