# Anisotropic inflation with coupled $\boldsymbol{p}$-forms

## TL;DR

This paper investigates anisotropic inflation driven by coupled p-forms in 4D cosmology, deriving conditions for sustained anisotropy and discovering new solutions with interactions between forms, supported by analytical and numerical analysis.

## Contribution

It introduces a comprehensive framework for anisotropic inflation with coupled p-forms, revealing new inflationary solutions and conditions for anisotropy survival during slow-roll.

## Key findings

- Conditions for anisotropic shear persistence during inflation.
- Existence of new anisotropic solutions with coupled 1- and 2-forms.
- Analytical formulas validated by numerical simulations.

## Abstract

We study the cosmology in the presence of arbitrary couplings between $p$-forms in 4-dimensional space-time for a general action respecting gauge symmetry and parity invariance. The interaction between 0-form (scalar field $\phi$) and 3-form fields gives rise to an effective potential $V_{\rm eff}(\phi)$ for the former after integrating out the contribution of the latter. We explore the dynamics of inflation on an anisotropic cosmological background for a coupled system of 0-, 1-, and 2-forms. In the absence of interactions between 1- and 2-forms, we derive conditions under which the anisotropic shear endowed with nearly constant energy densities of 1- and 2-forms survives during slow-roll inflation for an arbitrary scalar potential $V_{\rm eff}(\phi)$. If 1- and 2-forms are coupled to each other, we show the existence of a new class of anisotropic inflationary solutions in which the energy density of 2-form is sustained by that of 1-form through their interactions. Our general analytic formulas for the anisotropic shear are also confirmed by the numerical analysis for a concrete inflaton potential.