Related papers: Functional Approach to Stochastic Inflation
Within the framework of stochastic inflationary cosmology we derive steady-state distributions P_c(V) of domains in comoving coordinates, under the assumption of slow-rolling and for two specific choices of the coarse-grained inflaton…
Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich…
We analyse the dynamics of spinodal decomposition in inflationary cosmology using the closed time path formalism of out of equilibrium quantum field theory combined with the non-perturbative Hartree approximation. In addition to a general…
In this work, focused on the production of exact inflationary solutions using dimensional analysis, it is shown how to explain inflation from a pragmatic and basic point of view, in a step-by-step process, starting from the one-dimensional…
We analyze the flow into inflation for generic "single-clock" systems, by combining an effective field theory approach with a dynamical-systems analysis. In this approach, we construct an expansion for the potential-like term in the…
We consider stochastic inflation in an interacting scalar field in spatially homogeneous accelerating space-times with a constant principal slow roll parameter $\epsilon$. We show that, if the scalar potential is scale invariant (which is…
The stochastic solution with Gaussian stationary increments is establihsed for the symmetric space-time fractional diffusion equation when $0 < \beta < \alpha \le 2$, where $0 < \beta \le 1$ and $0 < \alpha \le 2$ are the fractional…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…
We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…
We investigate the inflationary universe in a theory where two scalar fields non-minimally coupling to the scalar curvature and an extra $R^2$ term exist and the conformal invariance is broken. In particular, the slow-roll inflation is…
We construct a pathwise calculus for functionals of integer-valued measures and use it to derive an martingale representation formula with respect to a large class of integer-valued random measures. Using these results, we extend the…
Cosmic inflation may exhibit stochastic periods during which quantum fluctuations dominate over the semi-classical evolution. Extracting observables in these regimes is a notoriously difficult program as quantum randomness makes them fully…
We study the ultra slow roll model in the context of stochastic inflation. Using stochastic $\delta N$ formalism, we calculate the mean number of $e$-folds, the power spectrum, the bispectrum and the stochastic corrections into these…
Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary $e$-folds, which give rise to all…
We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the…
An appealing feature of inflationary cosmology is the presence of a phase-space attractor, "slow roll", which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from…
We study inflation in a random multifield potential, using techniques developed by Marsh et al. The potential is a function of a large number of fields, and we choose parameters so that inflation only occurs in regions where the potential…
We solve time-reversed stochastic inflation in the semi-infinite flat potential with a constant drift term and derive an exact expression for the probability distribution of the curvature fluctuations. It exhibits exponential decaying tails…
Various scenarios of the initial inflation of the universe are distinguished by the choice of a scalar field {\em potential} $U(\phi)$ which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Our new method, which…
In inflationary scenarios with more than one scalar field, inflation may proceed even if each of the individual fields has a potential too steep for that field to sustain inflation on its own. We show that scalar fields with exponential…