Inflationary predictions of double-well, Coleman-Weinberg, and hilltop potentials with non-minimal coupling

Abstract

We discuss how the non-minimal coupling $\xi {\varphi }^{2}R$ between the inflaton and the Ricci scalar affects the predictions of single field inflation models where the inflaton has a non-zero vacuum expectation value (VEV) $v$ after inflation. We show that, for inflaton values both above the VEV and below the VEV during inflation, under certain conditions the inflationary predictions become approximately the same as the predictions of the Starobinsky model. We then analyze inflation with double-well and Coleman-Weinberg potentials in detail, displaying the regions in the $v$-$\xi$ plane for which the spectral index $n_s$ and the tensor-to-scalar ratio $r$ values are compatible with the current observations. $r$ is always larger than 0.002 in these regions. Finally, we consider the effect of $\xi$ on small field inflation (hilltop) potentials.

1+21 pages, 9 figures. v2: added references and a few clarifications, matches published version

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• A case for kinetically dominated initial conditions for inflation
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• A Predictive $SO(10)$ Model
• On the Trans-Planckian Censorship Conjecture and the Generalized Non-Minimal Coupling
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• Gravitino Dark matter, Non Thermal Leptogenesis and Low reheating temperature in No-scale Higgs Inflation
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• Realistic Inflation in No-Scale $U(1{)}_R$ Symmetric Flipped $SU(5)$
• Palatini Higgs and Coleman-Weinberg inflation with non-minimal coupling
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• Constraints on the non-minimally coupled Witten-O'Raifeartaigh inflation
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• Reheating study of Mexican-Hat-type Potentials