Dark neutrino interactions make gravitational waves blue

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.Comment: 31 pages, 10 figures. Version published in Phys. Rev.