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, $\Delta(M)$, 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 $\Delta(M,z)$ attractor solution.
