The formation of the first cosmic structures in hybrid Milgromian cosmology

Tackling cosmology with Milgromian Dynamics (MOND) has been a challenge ever since its theoretical inception. In a hybrid MOND scheme, a hypothesized light sterile neutrino of $\approx$ 11 eV/$c^2$ rest-mass is able to provide realistic initial conditions, fitting the third peak of the Planck CMB power spectrum as a Hot Dark Matter (HDM) component. At the same time, MOND governs the gravitational dynamics of density perturbations, while the background expansion follows the standard FLRW metric. We conduct and analyze hydrodynamical simulations of the fiducial $Λ$CDM model ($H_0 = 67.8$ km/s/Mpc, $Ω_m \approx 0.31$, $Ω_{\text{CDM}} \approx 0.26$), the progenitor $ν$HDM model ($H_0 = 67.64$ km/s/Mpc, $Ω_m = 0.3, Ω_ν\approx 0.26$), and its optimized version (opt-$ν$HDM model, $H_0 \approx 55.6$ km/s/Mpc, $Ω_m \approx 0.49$, $Ω_ν \approx 0.42$), utilizing the publicly available codes RAMSES and Phantom of RAMSES. We compare for the first time the total matter power spectrum $P(k)$ of the hydrodynamical simulations at various redshifts, examining the systematic differences of the three investigated cosmologies. The redshift evolution of the power spectrum of the $Λ$CDM model compared to the $ν$HDM variants' counterpart offers important insight about the onset of structure formation. The combination of a light sterile neutrino and MOND gravity exceeds the $Λ$CDM model's matter $P(k)$ over all collapsing scales at late times ($z\lesssim 1$). The density and velocity fields reveal a distinct difference between the underlying laws of gravity. Regardless of the modeled dependence in the jointly estimated data from Planck, DES Y1, SDSS, and eBOSS, the $ν$HDM hybrid models seem to produce an excess of power at associated resolution scales due to their cosmological design.