Inflation with mixed helicities and its observational imprint on CMB
  In the framework of effective field theories with prominent helicity-0 and
helicity-1 fields coupled to each other via a dimension-3 operator, we study
the dynamics of inflation driven by the helicity-0 mode, with a given potential
energy, as well as the evolution of cosmological perturbations, influenced by
the presence of a mixing term between both helicities. In this scenario, the
temporal component of the helicity-1 mode is an auxiliary field and can be
integrated out in terms of the time derivative of the helicity-0 mode, so that
the background dynamics effectively reduces to that in single-field inflation
modulated by a parameter $\beta$ associated to the coupling between helicity-0
and helicity-1 modes. We discuss the evolution of a longitudinal scalar
perturbation $\psi$ and an inflaton fluctuation $\delta \phi$, and explicitly
show that a particular combination of these two, which corresponds to an
isocurvature mode, is subject to exponential suppression by the vector mass
comparable to the Hubble expansion rate during inflation. Furthermore, we find
that the effective single-field description corrected by $\beta$ also holds for
the power spectrum of curvature perturbations generated during inflation. We
compute the standard inflationary observables such as the scalar spectral index
$n_s$ and the tensor-to-scalar ratio $r$ and confront several inflaton
potentials with the recent observational data provided by Planck 2018. Our
results show that the coupling between helicity-0 and helicity-1 modes can lead
to a smaller value of the tensor-to-scalar ratio especially for small-field
inflationary models, so our scenario exhibits even better compatibility with
the current observational data.
