Power-law Inflation Satisfies Penrose's Weyl Curvature Hypothesis

TL;DR

This paper demonstrates that power-law inflation can be consistent with Penrose's Weyl curvature hypothesis, showing that the initial singularity can have vanishing Weyl curvature and align with the universe's arrow of time.

Contribution

It shows that inflation can start from a null singularity with zero Weyl curvature, aligning Penrose's conditions with inflationary models, especially power-law inflation.

Findings

Inflation begins with a null singularity where Weyl curvature vanishes.

The initial state obeys Penrose's conditions and breaks T-reversal spontaneously.

Predicted observables are marginally in tension with data but can be reconciled with small corrections.

Abstract

Based on entropy considerations and the arrow of time Penrose argued that the universe must have started in a special initial singularity with vanishing Weyl curvature. This is often interpreted to be at odds with inflation. Here we argue just the opposite, that Penrose's persuasions are in fact consistent with inflation. Using the example of power law inflation, we show that inflation begins with a past null singularity, where Weyl tensor vanishes when the metric is initially exactly conformally flat. This initial state precisely obeys Penrose's conditions. The initial null singularity breaks $T$-reversal spontaneously and picks the arrow of time. It can be regulated and interpreted as a creation of a universe from nothing, initially fitting in a bubble of Planckian size when it materializes. Penrose's initial conditions are favored by the initial $O(4)$ symmetry of the bubble, selected by extremality of the regulated Euclidean action. The predicted observables are marginally in tension with the data, but they can fit if small corrections to power law inflation kick in during the last 60 efolds.