Primordial cosmic complexity and effects of reheating

We study the effects of reheating phase on the evolution of complexities for the primordial curvature perturbation using the squeezed formalism. We examine the evolution of the out-of-time correlator, the quantum discord, and circuit complexity, starting from the inflationary epoch to the radiation-dominated epoch with different reheating scenarios. We find that for a mode that reenters the horizon after reheating, the effect of a finite reheating epoch on the characteristic freeze-in amplitude of these primordial complexities can only be distinguished up to three different classes depending on whether the equation of state (EOS) parameter: (i) wre=1/3, (ii) wre<1/3, or (iii) wre>1/3. For reheating with different EOSs within these classes, the final amplitude will be the same - hence the detailed signature of reheating on the complexity measures, within a class, will be lost. Taking the central value of the scalar spectral index (ns=0.9649) from Planck and the equation of state during reheating wre=0.25 as benchmark values, we found that the behavior of the complexities for all modes smaller than 1.27×1016 Mpc-1 can be classified as above. However, for the small-scale modes reentering the horizon during reheating, the signature of EOSs on the evolution of these complexities will be embedded in each of the cases separately.