The Pseudo-Conformal Universe: Scale Invariance from Spontaneous Breaking of Conformal Symmetry

TL;DR

The paper introduces the pseudo-conformal universe, a non-inflationary scenario where a conformal field theory in near-flat space develops a time-dependent background that breaks so(4,2) to so(4,1). Gravity is negligible early on, and weight-0 fields acquire scale-invariant perturbations, while the background undergoes slow contraction that flattens and homogenizes the universe. Including gravity, the model yields a blue adiabatic spectrum with scale-invariant entropy perturbations that require conversion to observed curvature perturbations; it also predicts a negligible primordial gravitational-wave signal and potentially detectable non-Gaussianities. The framework is broad, encompassing known examples (Rubakov’s U(1), Galileon Genesis) and extensible via DBI-like non-linear realizations, with observational signatures that can distinguish it from inflation and insights into possible AdS/CFT dual descriptions.

Abstract

We present a novel theory of the very early universe which addresses the traditional horizon and flatness problems of big bang cosmology and predicts a scale invariant spectrum of perturbations. Unlike inflation, this scenario requires no exponential accelerated expansion of space-time. Instead, the early universe is described by a conformal field theory minimally coupled to gravity. The conformal fields develop a time-dependent expectation value which breaks the flat space so(4,2) conformal symmetry down to so(4,1), the symmetries of de Sitter, giving perturbations a scale invariant spectrum. The solution is an attractor, at least in the case of a single time-dependent field. Meanwhile, the metric background remains approximately flat but slowly contracts, which makes the universe increasingly flat, homogeneous and isotropic, akin to the smoothing mechanism of ekpyrotic cosmology. Our scenario is very general, requiring only a conformal field theory capable of developing the appropriate time-dependent expectation values, and encompasses existing incarnations of this idea, specifically the U(1) model of Rubakov and the Galileon Genesis scenario. Its essential features depend only on the symmetry breaking pattern and not on the details of the underlying lagrangian. It makes generic observational predictions that make it potentially distinguishable from standard inflation, in particular significant non-gaussianities and the absence of primordial gravitational waves.

Figures (3)

• Figure 1: Sketch of the scalar potential for the simplest realization of our mechanism. The potential is well approximated by a negative quartic form along the solid curve. Higher-dimensional operators such as ${\cal O}(\phi^6/M_{\rm Pl}^2)$ become important along the dotted curve, stabilizing the potential.
• Figure 2: Loop contributions to the $\varphi$ sector, with $\hat{\chi}$ running in the loops. Solid lines are $\varphi$ and dotted lines are $\hat{\chi}$. These graphs are potentially the most dangerous, since they do not involve $\lambda$ vertices.
• Figure 3: Dominant loop corrections to $\varphi-\hat{\chi}$ operators. Solid lines are $\varphi$ and dotted lines are $\hat{\chi}$.