Cosmic Acceleration from Nothing

TL;DR

The paper investigates whether a universe born from a vacuum fluctuation about empty spacetime (a Milne state) must exhibit late-time cosmic acceleration. By leveraging a cosmological sum rule based on the Schwarzian derivative of the scale factor, it links early-universe boundary conditions to late-time dynamics and highlights symmetry connections with conformal and Möbius transformations. The main result is that the Schwarzian must cross zero during evolution, implying the presence of a component with $-5/3<w<-1/3$ that drives acceleration; in the standard $\Lambda$CDM case this crossing occurs at a finite $\Omega_w$ (e.g., $\Omega_w^{\rm cross}=0.878$ for $w=-1$), a condition that may be compatible with current data. The framework provides a predictive constraint on dark-energy behavior and suggests possible multiple acceleration epochs tied to fundamental symmetry structures.

Abstract

We demonstrate that if the universe started as a vacuum fluctuation rather than from a singular Big Bang state, the universe must have a late-time cosmic acceleration. This is required by a ``cosmological sum rule'' derived using the Schwarzian form of the Friedmann equations. We discuss possible connections to conformal and Möbius transformations, and also compute that the best fit present cosmic data is consistent with the necessary crossing of the Schwarzian through zero having occurred (while it would not yet have happened in a $Λ$CDM cosmology).

Figures (2)

• Figure 1: The sum rule requires the Schwarzian to cross zero, hence the presence of a component with $-5/3 < w < -1/3$. We plot the value of $\Omega_w^{\rm cross}$, i.e. when in the expansion history this occurs, for each $w$, from \ref{['cross']}. For $\Lambda$CDM ($w=-1$), for example, the crossing will occur when $\Omega_w=0.878$.
• Figure 2: The Schwarzian, actually $8\{a, t\}/H^2$, is plotted for $\Lambda$CDM cosmology, showing the required zero crossing.