Related papers: Derivative Interactions during Inflation: A System…
Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional…
In the standard approach to deriving inflationary predictions, we evolve a vacuum state in time according to the rules of a given model. Since the only observables are the future values of correlators and not their time evolution, this…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point…
We develop a quantum-cosmological framework in which the inflationary potential emerges from the structure of the wave function of the universe rather than being postulated. Starting from the Wheeler-DeWitt equation for a flat…
In inflation with nonminimal derivative coupling there is not a conformal transformation to the Einstein frame where calculations are straightforward, and thus in order to extract inflationary observables one needs to perform a detailed and…
We present a new efficient method for computing the non-linearity parameters of the higher order correlation functions of local type curvature perturbations in inflation models having a $\cal N$-component scalar field, focusing on the…
A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving…
We show that the wavefunction of the universe in theories of conformally coupled scalars in power-law Friedmann-Robertson-Walker (FRW) cosmologies satisfies a graphical coaction, by means of which we can understand its complete analytic…
We present a method based on the Path Integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose…
A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. The formalism is applied to inflationary Universe models and yields a consistent and unified description of the generation and…
We calculate line shapes of correlation functions by use of complete diagonalization data of finite chains and analytical implications from conformal field theory, density of states, and Bethe ansatz. The numerical data have different…
We investigate spatially flat isotropic cosmological models which contain a scalar field with an exponential potential and a perfect fluid with a linear equation of state. We include an interaction term, through which the energy of the…
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…
We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the…
Both the Wavefunction of the Universe and the Schwinger-Keldysh in-in formalism are central tools for analyzing primordial cosmological observables, such as equal-time correlation functions. While their conceptual equivalence is well…
Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…
The method of a conformal transformation is applied to a general class of single field inflation models with non-minimal coupling to gravity and non-standard kinetic terms, in order to reduce the cosmological perturbative calculation to the…
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived…
We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is…