Towards a cosmological dual to inflation

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.The observational evidence for primordial density perturbations with nearly scale invariant and gaussian statistics is compatible with the simplest inflationary scenarios. But is inflation unique? Are there dual cosmologies with indistinguishable predictions? Such questions are critical to our understanding of the very early universe.Inflation not only generates scale invariant and gaussian density perturbations, it does so on an attractor background. On super-horizon scales, the curvature perturbation on comoving hypersurfaces [1, 2], denoted by ζ, measures differences in the expansion history of distant Hubble patches [2]. In single-field inflation, ζ approaches a constant at long wavelengths. In the strict k → 0 limit, ζ → δa/a, so the perturbation simply renormalizes the scale factor of the background solution; such a perturbation can be removed by an appropriate rescaling of global coordinates. For finite k, the perturbation cannot be completely removed, but different Hubble patches experience the same cosmological evolution, up to a shift of local time coordinates and a rescaling of local spatial coordinates. See [3] for a detailed discussion.Achieving both scale invariance and dynamical attraction in alternative scenarios has proven challenging. The ζ equation of a contracting, matter-dominated universe is identical to that of inflation [4], but ζ grows outside the horizon, indicating an unstable background. The contracting phase in the original ekpyrotic scenario [5-10], with V (φ) = −V 0 e −φ/M , is an attractor [11,12], but the resulting spectrum is strongly blue [11][12][13]. A scale invariant spectrum can be obtained through entropy perturbations [14,15], as in the New Ekpyrotic scenario [14], but this requires two scalar fields.The adiabatic ekpyrotic mechanism [16][17][18][19][20] proposed recently offers a counterexample: a single-field model for which the background is a dynamical attractor and generates a scale invariant ζ. The mechanism

Preinflationary genesis with CMB B-mode polarization

“…Initially |t| ≫ |t * | and M b (t * − t) b ≫ 1, the universe is slowly expanding [20], [21], [22], see [31], [32] for alternatives. Here,…”

The slow expansion with nonminimal derivative coupling and its conformal dual

“…The similar idea was also proposed by Wetterich [14,15] for different motivation. The scale-invariant curvature perturbations can also be obtained during the slow contraction (ǫ ≫ 1), i.e., in ekpyrotic universe [16,17], by applying adiabatic ekpyrosis mechanism [18,19], though for ekpyrotic universe the entropic mechanism is actually better to explain the observation [20][21][22].…”

The four fixed points of scale invariant single field cosmological models

“…In this model the universe slowly transitions from expansion to contraction. But unlike in [9], here we describe the apex model as a distinct mechanism that is independent from the adiabatic ekpyrotic slow expansion. When the universe gradually stops expansion to reach an apex, the scale factor a slowly comes to a halt, and the Hubble parameter H has to drop from positive to zero.…”

“…We have shown that the adiabatic ekpyrotic mechanism takes place near the point (0, 0) on the p > 0 side. Notably, this fixed point may also be approached from the p < 0 side, which corresponds to a slow expansion [9,18] that produces scale invariant perturations in a similar way.…”

“…In addition to inflation and adiabatic ekpyrosis, there is a third type of solution in which the universe goes through an "apex" [9], a slow transition from expansion to contraction. Similar to adiabatic ekpyrosis, this scenario also depends on a rapidly changing while the scale factor a is nearly constant.…”