Scalar perturbations in braneworld cosmology

Abstract

We study the behaviour of scalar perturbations in the radiation-dominated era of RandallSundrum braneworld cosmology by numerically solving the coupled bulk and brane master wave equations. We find that density perturbations with wavelengths less than a critical value (set by the bulk curvature length) are amplified during horizon re-entry. This means that the radiation era matter power spectrum will be at least an order of magnitude larger than the predictions of general relativity (GR) on small scales. Conversely, we explicitly confirm from simulations that the spectrum is identical to GR on large scales. Although this magnification is not relevant for the cosmic microwave background or measurements of large scale structure, it will have some bearing on the formation of primordial black holes in Randall-Sundrum models.

Density perturbations in braneworld cosmology and primordial black holes

“…Following [22] we define the factors that show the degree of enhancement of the perturbation amplitudes:…”

“…The solution of the perturbed equations (29) is a generalization of the results of standard 4D cosmological perturbation theory. The corresponding formulas are derived in [22] (in the approximation δπ = 0). These formulas express gauge invariants Φ, Ψ in terms of the gauge invariant matter perturbation variables ∆ (which is a density contrast in the comoving gauge) and V (which is a peculiar velocity in the longitudinal gauge), as in the 4D perturbation theory.…”

“…Using the results of [22] and Eqs. (34) one can easily obtain the ordinary differential equation for the gauge invariant ∆.…”

“…THE HIGH ENERGY REGIME Studying, in the high energy regime of radiation dominated era (when, in particular, H ≈ ρ σℓ , ∂ y ≈ −∂ t ), the dependence of ∆ and Ω on time before horizon crossing, by power series methods, and taking into account only the dominant growing mode, one can obtain (at leading order in kη) the result [22]:…”

“…For an extraction of this information one must know the evolution of these perturbations in radiation era. In the recent work by Cardoso et al [22] it had been shown that the density perturbations with short wavelengths are amplified during horizon re-entry. The magnitude of this enhancement depends, clearly, on a scale of the density perturbations.…”