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A first linear cosmological structure formation scenario under extended gravity

The inability of primordial baryonic density fluctuations, as observed in the cosmic microwave background (CMB), to grow into the present day astronomical structures is well established, under Newtonian and Einsteinian gravity. It is hence customary to assume the existence of an underlying dark matter component with density fluctuations, $Δ(M)$, having amplitudes much larger than what CMB observations imply for the baryons. This is in fact one of the recurrent arguments used in support of the dark matter hypothesis. In this letter we prove that the same extended theory of gravity which has been recently shown to accurately reproduce gravitational lensing observations, in absence of any dark matter, and which in the low velocity regime converges to a MONDian force law, implies a sufficiently amplified self-gravity to allow purely baryonic fluctuations with amplitudes in accordance with CMB constraints to naturally grow into the $z=0$ astrophysical structures detected. The linear structure formation scenario which emerges closely resembles the standard concordance cosmology one, as abundantly calibrated over the last decade to match multiple observational constraints at various redshifts. However, in contrast with what occurs in the concordance cosmology, this follows not from a critical dependence on initial conditions and the fine tuning of model parameters, but from the rapid convergence of highly arbitrary initial conditions onto a well defined $Δ(M,z)$ attractor solution.