Cosmological perturbations on the Phantom brane

TL;DR

This paper develops a comprehensive model for scalar perturbations in a multi-component braneworld with phantom-like late-time behavior, analyzing their evolution and implications for structure formation and observational tests.

Contribution

It introduces a closed system of equations for perturbations in a phantom brane, including the Weyl fluid, and compares exact results with the quasi-static approximation, highlighting distinctive observational signatures.

Findings

Weyl fluid perturbations diminish after Hubble-radius crossing.

Matter perturbations grow faster than in ΛCDM at late times.

Gravitational potentials Φ and Ψ evolve differently, with Φ/Ψ > 1 during late matter domination.

Abstract

We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, $w_{\rm eff} < -1$, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom - the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which results in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on the brane proceeds at a faster rate than in $\Lambda$CDM. Additionally, the gravitational potentials $\Phi$ and $\Psi$ evolve differently on the brane than in $\Lambda$CDM, for which $\Phi = \Psi$. On the brane, by contrast, the ratio $\Phi/\Psi$ exceeds unity during the late matter-dominated epoch ($z \lesssim 50$). These features emerge as "smoking gun" tests of phantom brane cosmology and allow predictions of this scenario to be tested against observations of galaxy clustering and large-scale structure.