CMB Acoustic Power Spectra in STVG-MOG

Abstract

We present a cosmological realization of Scalar--Tensor--Vector Gravity (STVG--MOG) in which the pre-recombination scalar perturbation dynamics become degenerate with those of $Λ$CDM without invoking particle dark matter. In the early universe, nonrelativistic excitations of the massive STVG vector field $ϕ_μ$ behave as a collisionless, pressureless component with vanishing sound speed and background density $ρ_ϕ\propto a^{-3}$. On the Fourier scales relevant for the acoustic peaks, the effective gravitational coupling satisfies $G_{\rm eff}(k,a)\simeq G_N$, so that the metric potentials governing baryon--photon oscillations evolve in the same way as in the standard cosmological model. The gravitational wells remain sufficiently deep at horizon entry to preserve the observed height of the third acoustic peak, the most sensitive indicator of a clustering pressureless component prior to recombination. Since Thomson scattering, recombination, baryon loading, and photon diffusion are unchanged, the temperature and polarization spectra can coincide with the standard $Λ$CDM predictions once the vector sector supplies the effective dust component. In this framework, the dynamical role usually attributed to cold dark matter is carried instead by a degree of freedom belonging to the gravitational sector itself. We explain why this vector-sector dust, although dynamically degenerate with cold dark matter in the early universe, is not equivalent to a particle dark matter fluid. The Boltzmann code CLASS is used to obtain a MOG fit to the acoustical power spectrum data.