Cosmological structure problem of the ekpyrotic scenario

TL;DR

The paper investigates whether the ekpyrotic scenario can generate a scale-invariant scalar spectrum by analyzing quantum generation and subsequent classical evolution through a nonsingular bounce for a power-law background $a \propto |t|^p$ with $p \ll 1$. It uses two gauges and Mukhanov-variable formalisms to show that the physically surviving final spectrum is blue with $n_S - 1 \simeq 2 \simeq n_T$, and that the scalar amplitude is suppressed relative to tensors by a factor of ${\sqrt{p}}/2$; the apparent scale-invariant result found in some gauges does not survive the bounce. The authors argue that ad hoc matching conditions used in prior work are inadequate, and conclude that achieving scale-invariance requires either $p \gg 1$ (and thus a different equation of state) or alternative mechanisms such as isocurvature perturbations, while noting the analysis hinges on a nonsingular bounce and linear perturbation theory. The work highlights the need for a fuller string-theory-based treatment of the bounce and possible multi-component perturbations to assess the ekpyrotic scenario’s viability for structure formation.

Abstract

We address the perturbation power spectrum generated in the recently proposed ekpyrotic scenario by Khoury et al. The issue has been raised recently by Lyth who used the conventional method based on a conserved variable in the large-scale limit, and derived different results from Khoury et al. The calculation is straightforward in the uniform-curvature gauge where the generated blue spectrum with suppressed amplitude survives as the final spectrum. Whereas, although the metric fluctuations become unimportant and a scale-invariant spectrum is generated in the zero-shear gauge the mode does not survive the bounce, thus with the same final result. Therefore, an exponential potential leads to a power-law expansion/contraction $a \propto |t|^p$, and the power $p$ dictates the final power spectra of both the scalar and tensor structures. If $p \ll 1$ as one realization of the ekpyrotic scenario suggests, the results are $n_S -1 \simeq 2 \simeq n_T$ and the amplitude of the scalar perturbation is suppressed relative to the one of the gravitational wave by a factor $\sqrt{p}/2$. Both results confirm Lyth's. An observation is made on the constraint on the dynamics of the seed generating stage from the requirement of scale-invariant spectrum.