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The inability of primordial baryonic density fluctuations, as observed in thecosmic microwave background (CMB), to grow into the present day astronomicalstructures is well established, under Newtonian and Einsteinian gravity. It ishence customary to assume the existence of an underlying dark matter componentwith density fluctuations, $\Delta(M)$, having amplitudes much larger than whatCMB observations imply for the baryons. This is in fact one of the recurrentarguments used in support of the dark matter hypothesis. In this letter weprove that the same extended theory of gravity which has been recently shown toaccurately reproduce gravitational lensing observations, in absence of any darkmatter, and which in the low velocity regime converges to a MONDian force law,implies a sufficiently amplified self-gravity to allow purely baryonicfluctuations with amplitudes in accordance with CMB constraints to naturallygrow into the $z=0$ astrophysical structures detected. The linear structureformation scenario which emerges closely resembles the standard concordancecosmology one, as abundantly calibrated over the last decade to match multipleobservational constraints at various redshifts. However, in contrast with whatoccurs in the concordance cosmology, this follows not from a criticaldependence on initial conditions and the fine tuning of model parameters, butfrom the rapid convergence of highly arbitrary initial conditions onto a welldefined $\Delta(M,z)$ attractor solution.

A first linear cosmological structure formation scenario under extended gravity