On the Three Primordial Numbers

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 $\text{lower}$ bound on the tensor-to-scalar ratio $r>0.006$ ($95\%$ CL).

5 pages, 3 figures

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• The Effective Field Theory of Inflation
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• Constraints on the spectral index for the inflation models in string landscape
• Effects of the speed of sound at large-N
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• Inflationary attractors from nonminimal coupling