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In [arXiv:2204.13980], we proposed and motivated a modification of theEinstein equation as a function of the topology of the Universe in the form ofa bi-connection theory. The new equation features an additional "topologicalterm" related to a second non-dynamical reference connection and chosen as afunction of the spacetime topology. In the present paper, we analyse theconsequences for cosmology of this modification. First, we show that expansionbecomes blind to the spatial curvature in this new theory, i.e. the expansionlaws do not feature the spatial curvature parameter anymore (i.e.$\Omega_{\not= K} = 1, \ \forall \, \Omega_K$), while this curvature is stillpresent in the evaluation of distances. Second, we derive the first orderperturbations of this homogeneous solution. Two additional gauge invariantvariables coming from the reference connection are present compared withgeneral relativity: a scalar and a vector mode, both sourced by the shear ofthe cosmic fluid. Finally, we confront this model with observations. Thedifferences with the $\Lambda$CDM model are negligible, in particular, theHubble and curvature tensions are still present. Nevertheless, since the maindifference between the two models is the influence of the background spatialcurvature on the dynamics, an increased precision on the measure of thatparameter might allow us to observationally distinguish them.

Is expansion blind to the spatial curvature?