Inflation with multiple vector fields and non-Gaussianities

Abstract

We consider a model of inflation consisting a triplet of U (1) vector fields with the parity violating interaction which is non-minimally coupled to inflaton. The vector field sector enjoys global O(3) symmetry which admits isotropic configuration and provides not only vector modes but also scalar and tensor modes. We decompose the scalar perturbations into the adiabatic, entropy and isocurvature perturbations and compute all power spectra and cross correlations of the scalar and the tensor sectors. The tensor modes associated with the vector fields contribute to the power spectrum of gravitational waves while the parity violating term generates chirality in gravitational power spectra and bispectra. We study nonlinear scalar and tensor perturbations and compute all bispectra and three-point crosscorrelations. In particular, it is shown that the non-Gaussianity of curvature perturbations and gravitational waves are enhanced by the vector field perturbations. We show that non-Gaussianities put strong constraints on the model parameters such as the parity violating coupling and the fractional energy of the vector fields.

Geometric structure of multi-form-field isotropic inflation and primordial fluctuations

“…Here ρ and p are the total energy density and pressure of the system and in our model we have ρ + p = φ2 + 2f 2 Ȧ2 /a 2 . Then we obtain [54,55] On the super-horizon scales, for h > 0.3, the contribution to the R comes from the adiabatic c 1 modes in (5.8) and (5.9) so we have…”

“…The mode U i corresponds to the fluctuation of the magnetic, which has vanishing background value so decouples with other modes. In other words, U is a pure isocurvature mode [54]. Hence only the δQ contributes to the curvature perturbations.…”

“…Again, the destabilization does not depend on the number of fields. Hence the new inflation phase still occurs for the isotropic background [54,55].…”

“…As we mentioned at the end of section 3, unlike the hyperbolic inflation, we do not need to restrict us to a very large h or l because there also exist attractors even when the energy of gauge field is not too large compared to the kinetic energy of scalar field. The situation that h is very small has been studied in some literature before [54][55][56][57], where h is regraded as a perturbation so one can use the standard in-in formalism. Therefore we only consider the dynamics of perturbation in the regime h, l > O(1) in this section.…”

“…where ∆ U is fluctuations of the magnetic field that is decoupled with perturbations of scalar fields and electric fields in the action. In fact, it is an isocurvature mode which does not contribute to the curvature perturbations [54]. Hence we can ignore it from now on.…”