The initial states of high frequency gravitons

Abstract

After distinguishing the role of classical and quantum inhomogeneities in cosmological backgrounds, we constrain the initial states of the relic gravitons as soon as the different wavelengths of the spectrum cross the comoving Hubble radius, without any reference to earlier timescales. According to this pragmatic perspective the quantum states with finite energy density at the crossing time consistently affect the two-point functions and the related power spectra. An initial state different from the vacuum turns out to be marginally permitted in the low frequency range (associated with the largest observable wavelengths that crossed the comoving Hubble radius) while the intermediate and high frequency domains of the spectrum are populated by the gravitons produced from the vacuum. The non classical correlations are expected to dominate between the kHz and the THz since in this region gravitons are produced quantum mechanically with a negligible contribution from the initial state.

Figures (2)

• Figure 1: In both plots the larger shaded areas illustrate the constraint $\overline{\rho}_{gw}^{(in)}(\tau_{\ast})/( 3 H_{\ast}^2 \overline{M}_{P}^2) < 10^{-3}$. The triangular shapes correspond instead to the requirement of Eq. (\ref{['TS1']}) for slightly different values of $k = {\mathcal{O}}(k_{p})$. As we shall see larger values of $k_{\ast}$ turn out to be more constrained.
• Figure 2: In both plots we illustrate the values of $r_{T}$ as a function of $\Delta N= N_{t} - N_{p}$. While in the left plot $\Delta N \leq 1$, in the right plot $\Delta N\geq 1$. In both cases we considered $\zeta\to 1$ corresponding to a preinflationary stage dominated by radiation. As before $\epsilon_{p}$ has been estimated directly from the number of $e$-folds [see the discussion prior to Eq. (\ref{['FFF1']})] and not from the consistency relations that are only restored when $k \gg T$.