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[abridged] We propose a model of the Universe (dubbed $\eta$CDM) featuring astochastic evolution of the cosmological quantities, that is meant to rendersmall deviations from homogeneity/isotropy on scales of $30-50\, h^{-1}$ Mpc atlate cosmic times, associated to the emergence of the cosmic web. Specifically,we prescribe that the behavior of the matter/radiation energy densities indifferent patches of the Universe with such a size can be effectively describedby a stochastic version of the mass-energy evolution equation. The latterincludes an appropriate noise term that statistically accounts for localfluctuations due to inhomogeneities, anisotropic stresses and matter flows. Theevolution of the different patches as a function of cosmic time is rendered viathe diverse realizations of the noise term; meanwhile, at any given cosmictime, sampling the ensemble of patches will originate a nontrivial spatialdistribution of the cosmological quantities. The overall behavior of theUniverse will be obtained by averaging over the patch ensemble. We assume aphysically reasonable parameterization of the noise term, gauging it against awealth of cosmological datasets. We find that, with respect to standard$\Lambda$CDM, the ensemble-averaged cosmic dynamics in the $\eta$CDM model issubstantially altered in three main respects: (i) an accelerated expansion isenforced at late cosmic times without the need for any additional exoticcomponent (e.g., dark energy); (ii) the spatial curvature can stay small evenin a low-density Universe; (iii) matter can acquire an effective negativepressure at late times. We provide predictions for the variance of thecosmological quantities among different patches of the Universe at late cosmictimes. Finally, we show that in $\eta$CDM the Hubble-tension is solved, and thecosmic coincidence problem is relieved without invoking the anthropicprinciple.

Little Ado about Everything: $\eta$CDM, a Cosmological Model with Fluctuation-driven Acceleration at Late Times