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$δn$ formalism: A new formulation for the probability density of the curvature perturbation Open
$δN$ formalism is a useful method to calculate the curvature perturbation. Contrary to what it is typically done in the literature, we re-formulate the $δN$ formalism by using the $e$-folding number $n$ counted forward in time. For a fixed…
Small noise expansion of stochastic inflation Open
By introducing the small noise expansion techniques, we show that the fully non-linear (non-Markovian) stochastic inflationary system, may be re-cast in terms of an infinite set of Wiener processes (stochastic equations with white noises).…
Small noise expansion of stochastic inflation Open
By introducing the small noise expansion techniques, we show that the fully nonlinear (non-Markovian) stochastic inflationary system, may be re-cast in terms of an infinite set of Wiener processes (stochastic equations with white noises). …
An update on adiabatic modes in cosmology and $δ$N formalism Open
In this paper, we generalize the Weinberg's procedure to determine the comoving curvature perturbation $\cal R$ to non-attractor inflationary regimes. We show that both modes of $\cal R$ are related to a symmetry of the perturbative equati…
Review on Stochastic Approach to Inflation Open
We present a review on the state-of-the-art of the mathematical framework known as stochastic inflation, paying special attention to its derivation, and giving references for the readers interested in results coming from the application of…
Stochastic inflation at all order in slow-roll parameters: Foundations Open
In this paper we develop the formalism for the stochastic approach to\ninflation at all order in slow-roll parameters. This is done by including the\nmomentum and Hamiltonian constraints into the stochastic equations. We then\nspecialise t…