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

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

Quantum Noise and Fluctuations in Gravitation and Cosmology

We give a short update of our research program on nonequilibrium statistical field theory applied to quantum processes in the early universe and black holes, as well as the development of stochastic gravity theory as an extension of semiclassical gravity and an intermediary in the 'bottom-up' approach to quantum gravity.Comment: 16 pages Latex; small changes in a couple of footnote

Unlocking higher harmonics in atomic force microscopy with gentle interactions

This is an Open Access article under the terms of the Creative Commons Attribution License.In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.This project was funded by Ministerio de Economía y Competitividad (MAT2012-38319).Peer Reviewe