Inflation with Derivative Self-interaction and Coupling to Gravity

Understand

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.