Little Ado about Everything: ηCDM, a Cosmological Model with Fluctuation-driven Acceleration at Late Times

We propose a model of the Universe (dubbed eta CDM) featuring a controlled stochastic evolution of the cosmological quantities that is meant to render the effects of small deviations from homogeneity/isotropy on scales of 30-50 h( -1) Mpc at late cosmic times associated with the emergence of the cosmic web. Specifically, we prescribe that the behavior of the matter/radiation energy densities in different patches of the Universe with such a size can be effectively described by a stochastic version of the mass-energy evolution equation. The latter includes, besides the usual dilution due to cosmic expansion, an appropriate noise term that statistically accounts for local fluctuations due to inhomogeneities, anisotropic stresses, and matter flows induced by complex gravitational processes. The evolution of the different patches as a function of cosmic time is rendered via the diverse realizations of the noise term; meanwhile, at any given cosmic time, sampling the ensemble of patches will create a nontrivial spatial distribution of the various cosmological quantities. Finally, the overall behavior of the Universe will be obtained by averaging over the patch ensemble. We assume a simple and physically reasonable parameterization of the noise term, gauging it against a wealth of cosmological data sets in the local and high-redshift Universe. We find that, with respect to standard Lambda CDM, the ensemble-averaged cosmic dynamics in the eta CDM model is substantially altered by the stochasticity in three main respects: (i) an accelerated expansion is enforced at late cosmic times without the need for any additional exotic component (e.g., dark energy), (ii) the spatial curvature can stay small even in a low-density Universe constituted solely by matter and radiation, (iii) matter can acquire an effective negative pressure at late times. The eta CDM model is Hubble tension-free, meaning that the estimates of the Hubble constant from early- and late-time measurements do not show marked disagreement as in Lambda CDM. We also provide specific predictions for the variance of the cosmological quantities among the different patches of the Universe at late cosmic times. Finally, the fate of the Universe in the eta CDM model is investigated to show that the cosmic coincidence problem is relieved without invoking the anthropic principle.