Cosmological perturbations from stochastic gravity

In inflationary cosmological models driven by an inflaton field the origin of the primordial inhomogeneities which are responsible for large scale structure formation are the quantum fluctuations of the inflaton field. These are usually computed using the standard theory of cosmological perturbations, where both the gravitational and the inflaton fields are linearly perturbed and quantized. The correlation functions for the primordial metric fluctuations and their power spectrum are then computed. Here we introduce an alternative procedure for computing the metric correlations based on the Einstein-Langevin equation which emerges in the framework of stochastic semiclassical gravity. We show that the correlation functions for the metric perturbations that follow from the Einstein-Langevin formalism coincide with those obtained with the usual quantization procedures when the scalar field perturbations are linearized. This method is explicitly applied to a simple model of chaotic inflation consisting of a Robertson-Walker background, which undergoes a quasi-de-Sitter expansion, minimally coupled to a free massive quantum scalar field. The technique based on the Einstein-Langevin equation can, however, deal naturally with the perturbations of the scalar field even beyond the linear approximation, as is actually required in inflationary models which are not driven by an inflaton field such as Starobinsky's trace-anomaly driven inflation or when calculating corrections due to non-linear quantum effects in the usual inflaton driven models.Comment: 29 pages, REVTeX; minor changes, additional appendix with an alternative proof of the equivalence between stochastic and quantum correlation functions as well as an exact argument showing that the correlation function of curvature perturbations remains constant in time for superhorizon modes, which clarifies a recent claim in arXiv:0710.5342v

Comment on "Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics"

This is a comment on [Phys. Rev. Lett. 91, 243004 (2003)] by Marlan O. Scully, Vitaly V. Kocharovsky, Alexey Belyanin, Edward Fry and Federico Capasso (quant-ph/0305178).Comment: 1 page, REVTeX

Stochastic description for open quantum systems

A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a Gaussian state. Using the influence functional formalism a formal Langevin equation can be introduced to describe the system's fully quantum properties even beyond the semiclassical regime. It is shown that the reduced Wigner function for the system is exactly the formal distribution function resulting from averaging both over the initial conditions and the stochastic source of the formal Langevin equation. The master equation for the reduced density matrix is then obtained in the same way a Fokker-Planck equation can always be derived from a Langevin equation characterizing a stochastic process. We also show that a subclass of quantum correlation functions for the system can be deduced within the stochastic description provided by the Langevin equation. It is emphasized that when the system is not Markovian more information can be extracted from the Langevin equation than from the master equation.Comment: 16 pages, RevTeX, 1 figure (uses epsf.sty). Shortened version. Partially rewritten to emphasize those aspects which are new. Some references adde

Overcoming loss of contrast in atom interferometry due to gravity gradients

Long-time atom interferometry is instrumental to various high-precision measurements of fundamental physical properties, including tests of the equivalence principle. Due to rotations and gravity gradients, the classical trajectories characterizing the motion of the wave packets for the two branches of the interferometer do not close in phase space, an effect which increases significantly with the interferometer time. The relative displacement between the interfering wave packets in such open interferometers leads to a fringe pattern in the density profile at each exit port and a loss of contrast in the oscillations of the integrated particle number as a function of the phase shift. Paying particular attention to gravity gradients, we present a simple mitigation strategy involving small changes in the timing of the laser pulses which is very easy to implement. A useful representation-free description of the state evolution in an atom interferometer is introduced and employed to analyze the loss of contrast and mitigation strategy in the general case. (As a by-product, a remarkably compact derivation of the phase-shift in a general light-pulse atom interferometer is provided.) Furthermore, exact results are obtained for (pure and mixed) Gaussian states which allow a simple interpretation in terms of the alignment of Wigner functions in phase-space. Analytical results are also obtained for expanding Bose-Einstein condensates within the time-dependent Thomas-Fermi approximation. Finally, a combined strategy for rotations and nonaligned gravity gradients is considered as well.Comment: 14+7 pages including appendices, 9 figures; v2 minor changes, matches published versio