Inflation with Derivative Self-interaction and Coupling to Gravity

Abstract

We consider a subclass of Horndeski theories for studying cosmic inflation. In particular, we investigate models of inflation in which the derivative self-interaction of the scalar field and the non-minimal derivative coupling to gravity are present in the action and equally important during inflation. In order to control contributions of each term as well as to approach the single-term limit, we introduce a special relation between the derivative interaction and the coupling to gravity. By calculating observable quantities including the power spectra and spectral tilts of scalar and tensor perturbation modes, and the tensor-to-scalar ratio, we found that the tensor-to-scalar ratio is suppressed by a factor of $(1+1/\gamma )$, where $\gamma$ reflects the strength of the derivative self-interaction of the inflaton field with respect to the derivative coupling gravity. We placed observational constraints on the chaotic and natural inflation models and showed that the models are consistent with the current observational data mainly due to the suppressed tensor-to-scalar ratio.

14 pages and 4 figures. v2: Typos corrected, references updated, and added a new subsection, new figures in Section IV

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Cited by in corpus (8)

• Palatini-Higgs inflation with non-minimal derivative coupling
• Primordial black holes and induced gravitational waves in $k$-inflation
• Primordial black holes formation in the inflationary model with field-dependent kinetic term for quartic and natural potentials
• Constraints on dark energy models from the Horndeski theory
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• General Einstein-Cartan quadratic gravity with derivative couplings
• Understanding large scale CMB anomalies with the generalized non-minimal derivative coupling during inflation
• The reheating constraints to natural inflation in Horndeski gravity