The ηCDM framework by [1] is a new cosmological model aimed to cure some drawbacks of the standard ΛCDM scenario, such as the origin of the accelerated expansion at late times, the cosmic tensions, and the violation of the cosmological principle due to the progressive development of inhomogeneous/anisotropic conditions in the Universe during structure formation. To this purpose, the model adopts a statistical perspective envisaging a stochastic evolution of large-scale patches in the Universe with typical sizes 10-50h -1 Mpc, which is meant to describe the complex gravitational processes leading to the formation of the cosmic web. The stochasticity among different patches is technically rendered via the diverse realizations of a multiplicative noise term ('a little ado') in the cosmological equations, and the overall background evolution of the Universe is then operationally defined as an average over the patch ensemble. In this paper we show that such an ensemble-averaged evolution in ηCDM can be described in terms of a spatially flat cosmology and of an 'emergent' dark energy with a time-dependent equation of state, able to originate the cosmic acceleration with the right timing and to solve the coincidence problem. Moreover, we provide a cosmographic study of the ηCDM model, suitable for quick implementation in the analysis of future observations. Then we test the ηCDM model against the most recent supernova type-Ia, baryon acoustic oscillations and structure growth rate datasets, finding an excellent agreement. Remarkably, we demonstrate that ηCDM is able to alleviate simultaneously both the H 0 and the fσ 8 tensions. Finally, we discuss that the Linders' diagnostic test could be helpful to better distinguish ηCDM from the standard scenario in the near future via upcoming galaxy redshift surveys at intermediate redshifts such as those being conducted by the Euclid mission.
