  We consider a new inflationary model in which an antisymmetric tensor field
$A_{\nu\rho\sigma}$ and its four-form field strength
$F_{\mu\nu\rho\sigma}=4\partial_{[\mu} A_{\nu\rho\sigma]}$ are coupled to the
scalar sector of the standard model and to the Ricci scalar $\mathcal{R}$. The
four-form field induces modifications to the Higgs self-coupling constant, the
cosmological constant, and the non-minimal coupling constant, which results in
the modification to the inflaton potential. We also show that there is no need
for the Higgs-gravity coupling in the presence of four-form-gravity
interaction, but still can produce the right amount of density perturbation for
inflation.
