Observational constraints on Diffusion Cosmologies in Unimodular Gravity from DESI DR2

Abstract

Diffusion functions in unimodular gravity induce a dynamical effective cosmological constant, providing an appealing framework in light of recent DESI observations. In this work, we investigate the observational viability of a general class of diffusion models using baryon acoustic oscillation measurements from DESI DR2, Type Ia supernova compilations (Pantheon+, DES-Dovekie, and DESY5), and Cosmic Chronometer data. We find that diffusion models systematically achieve lower best-fit $\chi^{2}$ values than $\Lambda$CDM across all dataset combinations considered, indicating a modest but persistent improvement in goodness of fit. Nevertheless, the reduction in $\chi^{2}$ is insufficient to offset the larger parameter space, leading standard information criteria to favor the simpler $\Lambda$CDM model. Despite this result, all dataset combinations consistently prefer a nonvanishing diffusion contribution corresponding to approximately $20\%$ of the present dark-energy budget, with a posterior probability $P(f_Q>0.05) =96.78\%$. From an observational perspective, diffusion models therefore remain a viable extension of the standard cosmological scenario and motivate the exploration of simpler diffusion parameterizations, particularly in light of upcoming high-precision cosmological surveys.