Year: 2018
Type: article
Abstract: Higgs inflation and ${R}^{2}$ inflation (Starobinsky model) are two limits of the same quantum model, hereafter called Starobinsky-Higgs. We analyze the two-loop action of the Higgs-like scalar $\ensuremath{\phi}$ in the presence of (1) nonminimal coupling ($\ensuremath{\xi}$) and (2) quadratic curvature terms. The latter are generated at the quantum level with $\ensuremath{\phi}$-dependent couplings ($\stackrel{\texttildelow{}}{\ensuremath{\alpha}}$) even if their tree-level couplings ($\ensuremath{\alpha}$) are tuned to zero. Therefore, the potential always depends on both Higgs field $\ensuremath{\phi}$ and scalaron $\ensuremath{\rho}$; hence, multifield inflation is a quantum consequence. The effects of the quantum (one- and two-loop) corrections on the potential $\stackrel{^}{W}(\ensuremath{\phi},\ensuremath{\rho})$ and on the spectral index are discussed, showing that the Starobinsky-Higgs model is, in general, stable in their presence. Two special cases are also considered: first, for a large $\ensuremath{\xi}$ in the quantum action, one can integrate $\ensuremath{\phi}$ and generate a ``refined'' Starobinsky model which contains additional terms ${\ensuremath{\xi}}^{2}{R}^{2}{\mathrm{ln}}^{p}(\ensuremath{\xi}|R|/{\ensuremath{\mu}}^{2})$, $p=1$, 2 ($\ensuremath{\mu}$ is the subtraction scale). These generate corrections linear in the scalaron to the ``usual'' Starobinsky potential and a ``running'' scalaron mass. Second, for a small fixed Higgs field ${\ensuremath{\phi}}^{2}\ensuremath{\ll}{M}_{p}^{2}/\ensuremath{\xi}$ and a vanishing classical coefficient of the ${R}^{2}$ term, we show that ``usual'' Starobinsky inflation is generated by quantum corrections alone, for a suitable nonminimal coupling ($\ensuremath{\xi}$).
Author: D. M. Ghilencea
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2949465725