Inflation from a Weyl-flat null origin

TL;DR

This paper demonstrates that Weyl-flat null origins of inflation can align with observations, presenting a minimal deformation model that yields realistic cosmological parameters and offers a viable, testable inflationary scenario.

Contribution

It introduces a minimal deformation of Weyl-flat null inflation models that maintains asymptotic geometry and produces realistic phenomenology consistent with observations.

Findings

Viable range of spectral index n_s within Planck data

Tensor-to-scalar ratio r approximately 10^{-3} to 10^{-2}

Smooth exit from inflation with reheating-compatible benchmarks

Abstract

We show that a Weyl-flat null origin of inflation need not be in tension with present observations. For canonical single-field inflation, any background with $\epsilon(N)\to \epsilon_\infty\in(0,1)$ as $N\to\infty$ is asymptotically power-law, inherits the same Weyl-flat null past boundary, and reconstructs an exponential tail in field space. This identifies the origin as an asymptotic universality class rather than a rigid exact solution. We study a minimal deformation, $\epsilon(N)=\epsilon_\infty+(1-\epsilon_\infty)\left(\frac{N_0}{N+N_0}\right)^p$ with $p>1$, which preserves the asymptotic geometry, yields a smooth exit, and produces realistic finite-$N$ phenomenology. Solving the scalar and tensor mode equations directly in e-fold time, we find a viable corridor with $n_s$ in the Planck-preferred range and $r\sim10^{-3}-10^{-2}$, including reheating-compatible benchmarks. The result is a calculable single-field framework in which a Penrose-compatible Weyl-flat inflationary origin survives as a realistic and testable possibility.