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