The Coherence of Primordial Fluctuations Produced During Inflation

The behaviour of quantum metric perturbations produced during inflation is considered at the stage after the second Hubble radius crossing. It is shown that the classical correlation between amplitude and momentum of a perturbation mode, previously shown to emerge in the course of an effective quantum-to-classical transition, is maintained for a sufficiently long time, and we present the explicit form in which it takes place using the Wigner function. We further show with a simple diffraction experiment that quantum interference, non-expressible in terms of a classical stochastic description of the perturbations, is essentially suppressed. Rescattering of the perturbations leads to a comparatively slow decay of this correlation and to a complete stochastization of the system.Comment: LaTeX (7 pages

Sterile neutrino production via active-sterile oscillations: the quantum Zeno effect

We study several aspects of the kinetic approach to sterile neutrino production via active-sterile mixing. We obtain the neutrino propagator in the medium including self-energy corrections up to $\mathcal{O}(G^2_F)$, from which we extract the dispersion relations and damping rates of the propagating modes. The dispersion relations are the usual ones in terms of the index of refraction in the medium, and the damping rates are $\Gamma_1(k) = \Gamma_{aa}(k) \cos^2\theta_m(k); \Gamma_2(k) = \Gamma_{aa}(k) \sin^2\theta_m(k)$ where $\Gamma_{aa}(k)\propto G^2_F k T^4$ is the active neutrino scattering rate and $\theta_m(k)$ is the mixing angle in the medium. We provide a generalization of the transition probability in the \emph{medium from expectation values in the density matrix}: $P_{a\to s}(t) = \frac{\sin^22\theta_m}{4}[e^{-\Gamma_1t} + e^{-\Gamma_2 t}-2e^{-{1/2}(\Gamma_1+\Gamma_2)t} \cos\big(\Delta E t\big)]$ and study the conditions for its quantum Zeno suppression directly in real time. We find the general conditions for quantum Zeno suppression, which for $m_s\sim \textrm{keV}$ sterile neutrinos with $\sin2\theta \lesssim 10^{-3}$ \emph{may only be} fulfilled near an MSW resonance. We discuss the implications for sterile neutrino production and argue that in the early Universe the wide separation of relaxation scales far away from MSW resonances suggests the breakdown of the current kinetic approach.Comment: version to appear in JHE