Constraints on the Phenomenology of Dissipative Cosmological Memory from BAO (BOSS + DESI 2024) and Pantheon+ Data

Abstract

We propose and test a phenomenological model of ``dissipative memory'' in the gravitational field, where early quantum gravitational processes leave a relic signature in the cosmic expansion rate. The model is parameterized by an additional fluid with amplitude $\epsilon$, decay scale $z_{\ast }$, and a steepness index $\beta$, decaying according to a Debye law $f(z)=\exp [-(z/z_{\ast }{)}^{\beta }]$. We perform a joint Bayesian analysis using baryon acoustic oscillation data from BOSS DR12 and DESI 2024, photometric distances from Pantheon$+$, and $H_0$ measurements (SHOES and Planck). A global optimization reveals that the best fit is identical to $\Lambda$CDM: the memory correction vanishes across the entire observable range $z\in [0.3,2.3]$ ($\Delta {\chi }^2<0.01$ with three extra parameters, $\Delta \mathrm{AIC}=+6.0$, $\Delta \mathrm{BIC}=+9.9$). This establishes an upper bound on the memory amplitude: $\epsilon <0.05$ for $z_{\ast }<2$ (95% CL). We discuss the physical interpretation of this constraint and point out observational channels where the memory effect could potentially manifest.