  Constraints on inflationary models typically assume only the standard models
of cosmology and particle physics. By extending the neutrino sector to include
a new interaction with a light scalar mediator ($m_{\phi}\sim$MeV), it is
possible to relax these constraints, in particular via opening up regions of
the parameter space of the spectral index $n_s$. These new interactions can be
probed at IceCube via interactions of astrophysical neutrinos with the Cosmic
Neutrino Background for nearly all of the relevant parameter space.
