On the Initial Conditions in New Ekpyrotic Cosmology

TL;DR

This work advances New Ekpyrotic Cosmology by addressing the tachyonic instability that feeds scale-invariant entropy perturbations with a natural pre-ekpyrotic stabilization of χ, ensuring robust initial conditions across a wide range. It reframes the dynamics in terms a single steep φ-direction and a tachyonic χ-direction, broadening the allowed potentials beyond two exponentials and enabling tunable spectral tilt via parameters ε, η, and δ. The model predicts substantial non-Gaussianity and, with a ghost-condensate–driven bounce, provides a non-singular transition to the hot big bang, offering a viable alternative to inflation for solving flatness and homogeneity problems. Overall, it articulates a flexible, testable ekpyrotic framework with distinctive signatures in the spectral tilt and non-Gaussianity that can be probed by current and near-future observations.

Abstract

New Ekpyrotic Cosmology is an alternative scenario of early universe cosmology in which the universe existed before the big bang. The simplest model relies on two scalar fields, whose entropy perturbation leads to a scale-invariant spectrum of density fluctuations. The ekpyrotic solution has a tachyonic instability along the entropy field direction which, a priori, appears to require fine-tuning of the initial conditions. In this paper, we show that these can be achieved naturally by adding a small positive mass term for the tachyonic field and coupling to light fermions. Then, for a wide range of initial conditions, the tachyonic field gets stabilized with the appropriate values well before the onset of the ekpyrotic phase. Furthermore, we show that ekpyrotic theory is successful in solving the flatness, horizon and homogeneity problems of standard big bang cosmology. Motivated by the analysis of the tachyonic instability, we propose a simplification of the model in terms of new field variables. Instead of requiring two exponential potentials, one for each scalar field, it suffices to consider a single nearly exponential potential for one of the fields and a tachyonic mass term along the orthogonal direction in field space. All other terms in the potential are essentially arbitrary. This greatly widens the class of ekpyrotic potentials and allows substantial freedom in determining the spectral index and possible non-Gaussianity. We present a generalized expression for the spectral index which is easily consistent with the observed red tilt. We also argue that for a wide range of potentials non-Gaussianity can be substantial, within the reach of current observations.

Figures (9)

• Figure 1: General shape of the potential during the ekpyrotic phase. The arrow indicates the desired solution, corresponding to rolling down a steep, negative and quasi-exponential potential along $\phi$, while remaining perched on top of a tachyonic ridge along $\chi$.
• Figure 2: A pre-ekpyrotic mechanism sets up the desired initial conditions for the ekpyrotic phase. With the addition of a positive mass-squared term, the field is initially stable in the $\chi$ direction. By introducing couplings to light fermions, the field settles down to the minimum for a wide range of initial conditions by the onset of the ekpyrotic phase.
• Figure 3: The end of the ekpyrotic phase is triggered by a term in the potential which is small at early times but eventually pushes the field away from the tachyonic ridge. The field rolls down to a minimum in the $\chi$ direction and starts oscillating around it. Meanwhile the field keeps rolling along the $\phi$ direction.
• Figure 4: Sequence of events in New Ekpyrotic Cosmology.
• Figure 5: Adiabatic ($\sigma$) and entropy ($s$) directions at a given point along the field trajectory in $(\phi,\chi)$ space.