Cosmic structure formation in massive conformal gravity

TL;DR

Massive conformal gravity (MCG) is proposed as an alternative to $\Lambda$CDM to address tensions in structure formation and the cosmological constant problem. The authors derive relativistic hydrodynamics for a conformal perfect fluid, and linear perturbation equations in MCG, then obtain a Newtonian limit and a growth equation for matter density perturbations. They find that density fluctuations grow as $\delta \propto a^{2.3}$ at early times and transition to a slow, logarithmic growth $\delta \propto \ln a$ at late times, yielding an early halo-collapse scenario and a $\sigma_8(0) \approx 0.74$ that aligns with large-scale-structure and weak-lensing constraints. Overall, the work shows MCG can reproduce key structure-formation observables without a cosmological constant and motivates further non-linear and observational tests.

Abstract

We study the evolution of matter density perturbations in the framework of massive conformal gravity (MCG). Starting from the conservation of the energy-momentum tensor, we find the continuity and Euler equations for the conformal perfect fluid that fills the MCG universe. We then obtain the perturbed MCG cosmological equations, from which we derive the equation that determines the linear growth of matter fluctuations in the MCG universe. The resulting growth equation shows that MCG enhances cosmic structure formation at high redshifts and suppresses it at low redshifts when compared to the $Λ$CDM cosmological model.