Minimal decoherence from inflation

TL;DR

The paper develops an Open EFT framework to quantify how inflationary super-Hubble metric fluctuations decohere due to gravitational interactions with shorter-wavelength modes. By deriving a Nakajima-Zwanzig master equation and its Markovian Lindblad limit, it isolates a universal, UV-finite decoherence kernel $\mathfrak{F}_{\bm{k}}$ that, for scalar modes, drives rapid decoherence with a growth $\Xi_{\bm{k}} \propto (H^2/M_p^2) (aH/k)^3$. Tensor modes decohere even faster, with unsuppressed slow-roll factors, and the total decoherence rate for observable fluctuations combines scalar and tensor environmental contributions. The results imply that, for CMB-relevant scales, decoherence is effective once inflation occurs above roughly $5\times 10^{9}$ GeV, while also predicting minute corrections to the power spectrum. Overall, the work clarifies how gravitational open-system dynamics produce classical primordial fluctuations and provides a calculable route to seek quantum signatures in cosmology.

Abstract

We compute the rate with which super-Hubble cosmological fluctuations are decohered during inflation, by their gravitational interactions with unobserved shorter-wavelength scalar and tensor modes. We do so using Open Effective Field Theory methods, that remain under control at the late times of observational interest, contrary to perturbative calculations. Our result is minimal in the sense that it only incorporates the self-interactions predicted by General Relativity in single-clock models (additional interaction channels should only speed up decoherence). We find that decoherence is both suppressed by the first slow-roll parameter and by the energy density during inflation in Planckian units, but that it is enhanced by the volume comprised within the scale of interest, in Hubble units. This implies that, for the scales probed in the Cosmic Microwave Background, decoherence is effective as soon as inflation proceeds above $\sim 5\times 10^{9}$ GeV. Alternatively, if inflation proceeds at GUT scale decoherence is incomplete only for the scales crossing out the Hubble radius in the last ~ 13 e-folds, of inflation. We also compute how short-wavelength scalar modes decohere primordial tensor perturbations, finding a faster rate unsuppressed by slow-roll parameters. Identifying the parametric dependence of decoherence, and the rate at which it proceeds, helps suggest ways to look for quantum effects.

Figures (7)

• Figure 1: We sketch out the domain of the system and environment modes. The black line denotes the Hubble radius and the coloured lines stand for the mode wavelengths. The system is comprised of co-moving scales between $k_{{ \mathrm{IR}}}$ and $k_{{ \mathrm{UV}}}$, both of which are outside the Hubble radius at the end of inflation. The environment is made of all scales such that $k>k_{ \mathrm{UV}}$.
• Figure 2: $\mathrm{Re}[\mathscr{C}_{\bm{k}}(\eta,\eta') ]$ and $\mathrm{Im}[\mathscr{C}_{\bm{k}}(\eta,\eta') ]$ as a function of $k \eta'$ for $k \eta = -0.2$ and ${k_{{ \mathrm{UV}}}}/k =5$. Note the singularity at $\eta' \simeq \eta$.
• Figure 3: A plot of the sign of Re $\mathfrak{A}_{\bm{k}}$ as a function of $k\eta$ and $\kappa = {k_{{ \mathrm{UV}}}}/k$ (for the case $k \eta_{\mathrm{in}} \to -\infty$), with blue representing positive and red being negative. The boundary between the two signs follows roughly the curve ${k_{{ \mathrm{UV}}}} \eta \simeq {\hbox{$\sqrt{3\,}$}}$.
• Figure 4: Purity as a function of the scale (namely, number of $e$-folds before the end of inflation) and the energy scale of inflation. Also plotted are predictions for how these two quantities are related for the value of $k$ that is just re-entering the Hubble scale today, as a function of assumptions made about the post-inflationary reheat epoch, with the solid, dashed and dotted lines respectively representing instantaneous reheating at the end of inflation, $T_\mathrm{reh}=10^{12}\mathrm{GeV}$ and $T_\mathrm{reh}=10^{9}\mathrm{GeV}$ (with $g_*\simeq 1000$ and $w=0$ during reheating for the latter two).
• Figure 5: Defining the integration region in $(p,q)$-space for computing $\mathscr{C}_{\bm{k}}(\eta,\eta')$ in eq. (\ref{['Ck_aftermu2']}) i.e. after the $\mu$-integration is completed in eq. (\ref{['Ck_beforemu2']}). The green region corresponds to $p,q>k_{{ \mathrm{UV}}}$ and the blue region corresponds to $- 1 < (p^2 + k^2 - q^2)/(2 p k) < 1$ (assuming $k < k_{{ \mathrm{UV}}}$) --- the intersection of these regions (in red) is the resulting integration region $U$ for computing $\mathscr{C}_{\bm{k}}(\eta,\eta')$ in $(p,q)$-space in eq. (\ref{['Ck_aftermu2']}).