Cosmological perturbations in the 5D Big Bang

TL;DR

This paper develops a formalism to calculate cosmological perturbations resulting from bubble collisions in a 5D Big Bang scenario, finding a highly tilted spectrum with specific amplitude and scale characteristics.

Contribution

It introduces a simple method to compute the spectrum of perturbations from bubble collisions in a 5D brane-world cosmology, highlighting the spectral tilt and amplitude.

Findings

The perturbation spectrum has a spectral index of n_s=3.

Fluctuation amplitude at horizon crossing scales as (R_0/d)^2 S_E^{-1} k^2.

The spectrum peaks at the smallest relevant scale, k ~ d/R_0.

Abstract

Bucher [Bucher2001] has recently proposed an interesting brane-world cosmological scenario where the ``Big Bang'' hypersurface is the locus of collision of two vacuum bubbles which nucleate in a five dimensional flat space. This gives rise to an open universe, where the curvature can be very small provided that $d/R_0$ is sufficiently large. Here, d is the distance between bubbles and $R_0$ is their size at the time of nucleation. Quantum fluctuations develop on the bubbles as they expand towards each other, and these in turn imprint cosmological perturbations on the initial hypersurface. We present a simple formalism for calculating the spectrum of such perturbations and their subsequent evolution. We conclude that, unfortunately, the spectrum is very tilted, with spectral index $n_s=3$. The amplitude of fluctuations at horizon crossing is given by $<(\delta \rho/\rho)^2> \sim (R_0/d)^2 S_E^{-1} k^2$, where $S_E\gg 1$ is the Euclidean action of the instanton describing the nucleation of a bubble and k is the wavenumber in units of the curvature scale. The spectrum peaks on the smallest possible relevant scale, whose wave-number is given by $k\sim d/R_0$. We comment on the possible extension of our formalism to more general situations where a Big Bang is ignited through the collision of 4D extended objects.