Imprint of entanglement entropy in the power spectrum of inflationary fluctuations

If the inflaton couples to other degrees of freedom (d.o.f.) that populate the postinflationary stage, such coupling modifies the dynamics of the inflaton during inflation. We consider light fermions Yukawa coupled to the inflaton as “unobserved” d.o.f. integrated out of the total density matrix. Tracing out these d.o.f. yields a mixed density matrix whose time evolution is described by an effective field theory. We show that the coupling leads to profuse fermion pair production for super-Hubble inflaton fluctuations which lead to the growth of entanglement entropy during inflation. The power spectrum of inflaton fluctuations features scale invariance violations P(k)=P0(k)exp{8ξk} with corrections to the index and its running directly correlated with the entanglement entropy: SvN=−∑k[ln(1−ξk)+ξkln(ξk)1−ξk]. For super-Hubble fluctuations we find ξk=−Y248π2{2NTln(k/kf)+ln2(k/kf)} with Y the Yukawa coupling, NT the total number of e-folds during inflation, and kf a “pivot” scale corresponding to the mode that crosses the Hubble radius at the end of inflation.