Cosmic structure formation in massive conformal gravity

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.

💡 Research Summary

The paper investigates the evolution of matter density perturbations within the framework of massive conformal gravity (MCG), a conformally invariant modification of general relativity that includes a massive spin‑2 ghost field. Starting from the action S = ∫√−g(φ²R + 6∂μφ∂^μφ − ½α²C²)+∫L_m, where φ is a dilaton, α a dimensionless coupling, and C² the Weyl‑tensor squared, the authors derive the field equations Gμν − m²Bμν = 16πGTμν together with the scalar curvature constraint R = 0. Here m = αφ₀ is the mass of the ghost field, and Bμν is the Bach tensor.

A conformal perfect fluid with equation‑of‑state parameter w = p/ρ fills the universe. Conservation of the energy‑momentum tensor yields the continuity equation ρ′ + 4Hρ = 0 and the relativistic Euler equation v′ = −¼∇δ − ∇Φ, where primes denote derivatives with respect to conformal time and H is the conformal Hubble parameter.

Perturbations are introduced in the Newtonian gauge metric ds² = a²(η)