Tilted Ekpyrosis

TL;DR

This paper extends the two-field ekpyrotic collapse model by introducing tilted potentials, showing they can produce a red-tilted, scale-invariant spectrum of fluctuations consistent with observations, but with finite duration and specific initial conditions.

Contribution

It generalizes the ekpyrotic collapse model to include tilted potentials and derives conditions for scale-invariant, red-tilted spectra of isocurvature fluctuations.

Findings

Tilted potentials enable a red-tilted, scale-invariant spectrum.

Finite duration of the ekpyrotic phase is required for a red spectrum.

Preceding phase sets initial conditions, addressing fine-tuning issues.

Abstract

We consider a simple model of cosmological collapse driven by canonical fields with exponential potentials. We generalise the two-field ekpyrotic collapse to consider non-orthogonal or tilted potentials and give the general condition for isocurvature field fluctuations to have a scale-invariant spectrum in this model. In particular we show that tilted potentials allow for a slightly red spectrum of perturbations as required by current observations. However a red spectrum of fluctuations implies that the two-field ekpyrotic phase must have a finite duration and requires a preceding phase which sets the initial conditions for what otherwise appears to be a fine-tuned trajectory in the phase space.