Global quenches and correlator dynamics in de Sitter space

TL;DR

The paper develops a Keldysh–Schwinger formalism to study global quantum quenches in curved spacetime by treating them as unitary perturbations of the initial density matrix, enabling explicit post-quench two-point functions in arbitrary geometries. A Gaussian (quadratic) quench is analyzed, with expressions for the post-quench Keldysh propagator showing consistency with flat-space massive relaxation $\sim (mt)^{-3/2}$ and revealing massless non-relaxation, as well as a de Sitter regime where late-time decay of quench-induced corrections is mass-dependent and can affect the power spectrum. In de Sitter, the equal-time Keldysh correlator exhibits a mass threshold $m_{cr}=\sqrt{2}$ separating distinct decay regimes, implying sensitivity of local observables to the field spectrum; the power spectrum $\mathcal{P}_s(k)$ acquires characteristic features such as an initial peak and damped oscillations. The framework is further extended to non-Gaussian initial states, where non-quadratic perturbations generate loop-like corrections to correlators that remain controllable in low dimensions and point to future work on loop effects and primordial non-Gaussianities in cosmology.

Abstract

We study non-equilibrium initial states of quantum fields in curved space-time and develop a framework for describing global quenches as unitary perturbations of the initial density matrix. Using the Keldysh-Schwinger functional integral, we derive expressions for post-quench correlators in arbitrary geometries and apply the method to both Minkowski and de Sitter backgrounds. In flat space, the approach reproduces the known relaxation behaviour for massive fields and reveals qualitatively distinct dynamics in the massless case. In de Sitter space, we find that the late-time decay of quench-induced corrections depends sensitively on the mass and may influence the behaviour of cosmological observables such as the power spectrum. The framework also extends straightforwardly to non-Gaussian initial states, providing a basis for future studies of loop effects and primordial non-Gaussianities.

Figures (4)

• Figure 1: The numerical plots of $\left|\log(I_2)\right|$ as a function of time $t-t_0$ for masses $m<\sqrt{2}$, $r=1$ (left) and $r=0.001$ (right). The dashed lines show the analytical estimate. We chose $-t_0=\log(102)\simeq 4.6.$
• Figure 2: The numerical plot of $\left|\log(I_2)\right|$ as a function of time $t-t_0$ for masses $m>\sqrt{2}$. Here we see that up to $t\lesssim -\log(r)$ the slope equals $2<3-2\nu$ (blue dashed line), independently of the mass, and then for $t>-\log(r)$ it matches the slope $3-2\nu$ (red dashed line for $\nu=0.1$).
• Figure 3: Power spectrum $\mathcal{P}_s$ and spectral index $n_s-1$ as the functions of the scale $k\eta_0$ for $\alpha=1$. We chose $\eta_0=1$ and $\eta=10^{-6}$ so that all depicted scales are super-horizon.
• Figure 4: Numerical values of the integrals $I_1(t,r)$ and $I_2(t,r)$ in the case $D=2$. The "horizon effect" at $|r|<2t$ is clearly visible.