Stochastic Inflation:The Quantum Phase Space Approach

Physical Review D, 1996

The stochastic approach to inflation relies on one key assumption, the emergence of a long-wave classical field that drives the inflation and is subject to a shortwave classical noise. In this work we consider explicitly the potential that acts on the inflaton field, and analyze classicality conditions that must be satisfied to have an effective classical stochastic approach. When these hold, the dynamics is given by a two-dimensional classical Fokker-Planck equation. We develop some examples, already widely considered in different approaches, and find a very suggestive result, which is the damping of the quantum fluctuations by the effect of the inflaton interaction potential. ͓S0556-2821͑96͒01624-4͔

2000

Stochastic semiclassical gravity is a theory for the interaction of gravity with quantum matter fields which goes beyond the semiclassical limit. The theory predicts stochastic fluctuations of the classical gravitational field induced by the quantum fluctuations of the stress energy tensor of the matter fields. Here we use an axiomatic approach to introduce the Einstein-Langevin equations as the consistent set of dynamical equations for a first order perturbative correction to semiclassical gravity and review their main features. We then describe the application of the theory in a simple chaotic inflationary model, where the fluctuations of the inflaton field induce stochastic fluctuations in the gravitational field. The correlation functions for these gravitational fluctuations lead to an almost Harrison-Zel'dovich scale invariant spectrum at large scales, in agreement with the standard theories for structure formation. A summary of recent results and other applications of the theory is also given.

Nuclear Physics B, 1994

We study stochastic inflation in the presence of a dynamical gravitational constant. We describe the Arnowitt-Deser-Misner formalism for Jordan-Brans-Dicke theory of gravity with an inflaton field. The inflaton and dilaton scalar fields can be separated into coarse-grained background fields and quantum fluctuations. We compute the amplitude of the perturbations generated by those quantum fluctuations in JBD theory with an arbitrary potential for the inflaton field. The effect of the quantum fluctuations on the background fields is equivalent to a Brownian motion of the scalar fields, which can be described with the use of a Fokker-Planck diffusion equation. The probability to find a given value of the fields in the comoving frame can be written as a Gaussian distribution centered on their classical trajectory, with decreasing dispersion along both field directions. We also calculate the condition for the Universe to enter a self-regenerating inflationary phase. The probability distribution in the physical frame, which takes into account the expansion of the proper volume of the inflationary domains, will be concentrated at the Planck boundary and will move along it towards large values of the fields.

2011

This is why the statement sometimes found in literature that, for H = const, a flat (Harrison-Zeldovich) ns = 1 spectrum is generated is also meaningless. Actually, it is a V (φ) ∝ φ −2 inflaton potential that leads to ns = 1 (and r = 0) in the slowroll approximation, see for the exact solution for V (φ) without using this approximation.

The European Physical Journal C

We study the quantum backreaction from inflationary fluctuations of a very light, non-minimally coupled spectator scalar and show that it is a viable candidate for dark energy. The problem is solved by suitably adapting the formalism of stochastic inflation. This allows us to selfconsistently account for the backreaction on the background expansion rate of the Universe where its effects are large. This framework is equivalent to that of semiclassical gravity in which matter vacuum fluctuations are included at the one loop level, but purely quantum gravitational fluctuations are neglected. Our results show that dark energy in our model can be characterized by a distinct effective equation of state parameter (as a function of redshift) which allows for testing of the model at the level of the background.

Observational evidence for the accelerated expansion of the Universe raises a fundamental challenge to standard cosmological models. It is generally presumed that acceleration of cosmic expansion emerges from an unknown physical component called dark energy whose contributions in negative pressure and energy density are substantial. One of the unsettled questions posed by the dark energy hypothesis relates to the magnitude of the cosmological constant: the observed vacuum energy density is exceedingly small as compared to predictions of quantum field physics. In this work we develop a derivation of the cosmological constant based on classical diffusion theory. Dynamics of the dark energy is modeled using the Langevin equation of a damped harmonic field in steady contact with a chaotic reservoir of vacuum fluctuations. The field evolves in the Friedmann-Robertson-Walker metric and dissipation arises as a result of expansion. The asymptotic limit of this process corresponds to setting the selfinteraction gravity scale as the largest temperature of the reservoir. Predictions on vacuum energy density and cosmological constant are shown to be consistent with current experimental bounds.

Physical Review D, 2001

2010

This is why the statement sometimes found in literature that, for H = const, a flat (Harrison-Zeldovich) ns = 1 spectrum is generated is also meaningless. Actually, it is a V (φ) ∝ φ −2 inflaton potential that leads to ns = 1 (and r = 0) in the slowroll approximation, see for the exact solution for V (φ) without using this approximation.

The European Physical Journal C, 2019

In this work, our prime focus is to study the one to one correspondence between the conduction phenomena in electrical wires with impurity and the scattering events responsible for particle production during stochastic inflation and reheating implemented under a closed quantum mechanical system in early universe cosmology. In this connection, we also present a derivation of quantum corrected version of the Fokker-Planck equation without dissipation and its fourth order corrected analytical solution for the probability distribution profile responsible for studying the dynamical features of the particle creation events in the stochastic inflation and reheating stage of the universe. It is explicitly shown from our computation that quantum corrected Fokker-Planck equation describe the particle creation phenomena better for Dirac delta type of scatterer. In this connection, we additionally discuss Itô, Stratonovich prescription and the explicit role of finite temperature effective potential for solving the probability distribution profile. Furthermore, we extend our discussion of particle production phenomena to describe the quantum description of randomness involved in the dynamics. We also present computation to derive the expression for the measure of the stochastic non-linearity (randomness or chaos) arising in the stochastic inflation and reheating epoch of the universe, often described by Lyapunov Exponent. Apart from that, we quantify the quantum chaos arising in a closed system by a more strong measure, commonly known as Spectral Form Factor using the principles of random matrix theory (RMT). Additionally, we discuss the role of out of time order correlation function (OTOC) to describe quantum chaos in the present non-equilibrium field theoretic setup and its cona e-mails: