Related papers: Functional Approach to Stochastic Inflation
The separate-universe approach gives an intuitive way to understand the evolution of cosmological perturbations in the long-wavelength limit. It uses solutions of the spatially-homogeneous equations of motion to model the evolution of the…
The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
We consider particle transport under the influence of time-varying driving forces, where fluctuation relations connect the statistics of pairs of time reversed evolutions of physical observables. In many "mesoscopic" transport processes,…
In this paper we investigate the induced inflation with two flat regions: one Starobinsky-like plateau in big field regime and one shorter plateau around the saddle point of the Einstein frame potential. This multi-phase inflationary…
We extend the Randall-Sundrum(RS) model by adding a fundamental scalar field in the bulk, then study the multi-field assisted inflationary solution on brane. We will show that this model satisfies not only the observation, but also provides…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
We present a systematic prescription for calculating cosmological correlation functions for models with derivative interactions through the wavefunction of the universe and compare this result with the "in-in" formalism -- canonical…
Functional It\^o calculus was introduced in order to expand a functional $F(t, X\_{\cdot+t}, X\_t)$ depending on time $t$, past and present values of the process $X$. Another possibility to expand $F(t, X\_{\cdot+t}, X\_t)$ consists in…
Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated…
New exact inflationary solutions are presented in the scalar field theory, minimally coupled to gravity, with a potential term. No use is made of the slow rollover approximation. The scale factors are completely nonsingular and the…
The usual description of inflationary fluctuations uses the framework of quantum field theory (QFT) in curved spacetime, in which quantum fluctuations are superimposed on a classical background spacetime. Even for large fluctuations, such…
We reinterpret Starobinsky's stochastic inflation as an open quantum system, where short-wavelength modes act as the environment for long-wavelength modes. Using the Schwinger-Keldysh formalism, we systematically trace out the environment…
In this paper we investigate the inflationary dynamics of an $f(R)$ gravity in the presence of a canonical scalar field. We specifically choose the cosmological evolution to be a quasi-de Sitter evolution and also the $f(R)$ gravity is…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is…
We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables…
The curvaton paradigm can realise a part of or all the observed curvature perturbation. Based on the stochastic formalism of inflation and closed-form exact distributions therein, the distribution of the curvature perturbation is presented…
The Eliashberg theory of superconductivity is based on a dynamical electron-phonon interaction as opposed to a static interaction present in BCS theory. The standard derivation of Eliashberg theory is based on an equation of motion…
In this paper the computational aspects of probability calculations for dynamical partial sum expressions are discussed. Such dynamical partial sum expressions have many important applications, and examples are provided in the fields of…