On the Three Primordial Numbers

TL;DR

This paper explores the relationships among three key cosmological parameters to distinguish inflationary models, revealing two viable scenarios and predicting a lower bound on the tensor-to-scalar ratio.

Contribution

It identifies two mutually exclusive inflationary scenarios based on relations among three primordial numbers, offering new insights into the early universe.

Findings

Two viable inflationary scenarios identified

A new relation between $1-n_s$ and $ ext{ln}\Delta_R^2$ proposed

Predicts a lower bound on tensor-to-scalar ratio $r > 0.006$

Abstract

Cosmological observations have provided us with the measurement of just three numbers that characterize the very early universe: $ 1-n_{s} $, $ N $ and $\ln\Delta_R^2$. Although each of the three numbers individually carries limited information about the physics of inflation, one may hope to extract non-trivial information from relations among them. Invoking minimality, namely the absence of ad hoc large numbers, we find two viable and mutually exclusive inflationary scenarios. The first is the well-known inverse relation between $1- n_{s} $ and $ N $. The second implies a new relation between $ 1-n_{s} $ and $\ln\Delta_R^2$, which might provide us with a handle on the beginning of inflation and predicts the intriguing $\textit{lower}$ bound on the tensor-to-scalar ratio $ r> 0.006 $ ($ 95\% $ CL).