  New interactions of neutrinos can stop them from free streaming in the early
Universe even after the weak decoupling epoch. This results in the enhancement
of the primordial gravitational wave amplitude on small scales compared to the
standard $\Lambda$CDM prediction. In this paper we calculate the effect of dark
matter neutrino interactions in CMB tensor $B$-modes spectrum. We show that the
effect of new neutrino interactions generates a scale or $\ell$ dependent
imprint in the CMB $B$-modes power spectrum at $\ell \gtrsim 100$. In the event
that primordial $B$-modes are detected by future experiments, a departure from
scale invariance, with a blue spectrum, may not necessarily mean failure of
simple inflationary models but instead may be a sign of non-standard
interactions of relativistic particles. New interactions of neutrinos also
induce a phase shift in the CMB B-mode power spectrum which cannot be mimicked
by simple modifications of the primordial tensor power spectrum. There is rich
information hidden in the CMB $B$-modes spectrum beyond just the tensor to
scalar ratio.
