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# Primordial Cosmic Complexity and effects of Reheating

Dec 2022

We study the effects of reheating phase on the evolution of complexities forthe primordial curvature perturbation using the squeezed formalism. We examinethe evolution of the out-of-time correlator (OTOC) and the quantum discordstarting from the inflationary epoch till the radiation-dominated epoch withdifferent types of reheating scenarios. We find that, for a mode that re-entersthe horizon after reheating, a finite reheating epoch clearly distinguishes thecharacteristic OTOC and quantum discord freeze-in amplitude into threedifferent classes that only depend on whether the equation of state parameter:$(i)$ $w_\mathrm{re}=1/3$ $(ii)$ $w_\mathrm{re}<1/3$, or, (iii)$w_\mathrm{re}>1/3$ and not on separate reheating histories within the classes.Taking the central value of the scalar spectral index ($n_s=0.9649$) fromPlanck and the equation of state during reheating $w_\mathrm{re}=0.25$ asbenchmark values, we found that the behavior of the complexities for all modessmaller than $1.27\times10^{16}\mathrm{Mpc^{-1}}$ can be classified as above.Conversely, for modes re-entering the horizon during reheating, the signatureof EoS on the evolution of the complexities will be embedded in each of thecases separately.

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