Towards a Cosmological Dual to Inflation
Justin Khoury, Godfrey E. J. Miller
TL;DR
The paper addresses whether inflation is unique among single-field cosmologies with unit sound speed that generate a scale-invariant curvature perturbation $\zeta$. By enforcing $c_s=1$ and a dynamical attractor, the authors derive $\frac{z''}{z}=\frac{2}{\tau^2}$ with $z\equiv a\sqrt{2\epsilon}$, leading to $\epsilon=\frac{1}{a^2 m^2 \tau^2}$ and a coupled system for $|h^{-1}|$ and $\epsilon$, which reveals three attractor branches: inflation, adiabatic-ekpyrotic contraction ($\epsilon\sim 1/\tau^2$ on a contracting background), and a novel adiabatic-ekpyrotic expansion. All three produce the same scale-invariant two-point spectrum, but the degeneracy is broken at the three-point level, where the contracting/expanding ekpyrotic phases yield strongly scale-dependent non-Gaussianities with leading amplitude ${\cal A}_{\epsilon^3}$ giving $f_{\rm NL}^{\rm equil.} \simeq -\frac{5}{144}\frac{K^2}{H_0^2}$. This implies that Planck-style gaussian observations would favor inflation as the unique single-field, unit-sound-speed mechanism for broad scale-invariant perturbations, while the ekpyrotic branches remain viable only with suppressed non-Gaussianity or extra degrees of freedom; future work will extend the analysis to a general $c_s(\tau)$.
Abstract
We derive all single-field cosmologies with unit sound speed that generate scale invariant curvature perturbations on a dynamical attractor background. We identify three distinct phases: slow-roll inflation; a slowly contracting adiabatic ekpyrotic phase, described by a rapidly-varying equation of state; and a novel adiabatic ekpyrotic phase on a slowly expanding background. All of these yield identical power spectra. The degeneracy is broken at the 3-point level: unlike the nearly gaussian spectrum of slow-roll inflation, adiabatic ekpyrosis predicts large non-gaussianities on small scales.