arXiv subjects

Diego Cruces

Publications and source records attributed to Diego Cruces.

8 recordsLinked to original sources

arXiv2026

A consistent formulation of stochastic inflation I: Non-Markovian effects and issues beyond linear perturbations

We investigate the origin of non-Markovianity in stochastic inflation and its implications for nonlinear perturbation theory. In the Schwinger--Keldysh formulation, the noise terms sourcing the infrared (IR) Langevin equations are determined by ultraviolet (UV) modes evolving on top of the stochastic IR background. Since the UV-mode evolution generally depends on the past history of the IR sector, the resulting stochastic dynamics is intrinsically non-Markovian. Working perturbatively, we derive the UV-mode solutions up to second order and decompose the corresponding noise contributions into two parts. The first is a ``deterministic'' contribution, generated by the functional Taylor expansion of the first-order UV solution around the background trajectory. The second is a genuinely ``stochastic'' contribution, originating from terms in the UV-mode equations that are quadratic in the noise variables and are usually neglected in the standard formulation of stochastic inflation. Under this conventional truncation, the deterministic contribution reduces to a Markovian correction in attractor backgrounds, whereas it could become history dependent in non-attractor phases and gives rise to non-Markovian terms involving integrals over first-order IR perturbations. We finally show that the stochastic contribution is of the same perturbative order as the deterministic one, which indicate that the conventional truncation is generically inconsistent and quadratic-noise terms may be required for a consistent treatment of nonlinear perturbations in stochastic inflation. Our analysis clarifies the perturbative structure of non-Markovianity and provides the basis for a systematic treatment of quadratic-noise effects beyond the standard formulation.

astro-ph.CO↗

arXiv2026

Natura Non Facit Saltum: An Analytical Model of Smooth Slow-Roll to Ultra-Slow-Roll Transition

In this letter, we propose a single-field inflation model that realizes a slow-roll-to-ultra-slow-roll transition while keeping the second slow-roll parameter smoothly varying throughout. The model is built through a minimal modification by introducing a simple time dependence in the effective mass term of the Mukhanov-Sasaki equation. We obtain fully analytical solutions for both the background evolution and the curvature perturbations, which makes the parameter dependence of the curvature power spectrum easy to track. To the best of our knowledge, this is the first analytical model that describes a smooth transition of this kind. We also compare its signatures with those of the corresponding sharp-transition counterpart.

astro-ph.CO↗

arXiv2025

$\delta n$ formalism: A new formulation for the probability density of the curvature perturbation

$\delta N$ formalism is a useful method to calculate the curvature perturbation. Contrary to what it is typically done in the literature, we re-formulate the $\delta N$ formalism by using the $e$-folding number $n$ counted forward in time. For a fixed initial time $\bar{n}_0$, the probability density function (PDF) of the field perturbation $\delta\phi_0$ and its velocity $\delta\pi_0$ are specified by the solutions of the perturbation equation on subhorizon scales. As $\delta\pi_0$ is fully correlated with $\delta\phi_0$ after horizon exit, we find a novel $\delta n$ formalism to calculate the curvature perturbation as well as its PDF. It can naturally incorporate those trajectories for which inflation never ends, which are lost when counting $N$ backward in time.

astro-ph.CO↗

arXiv2024

Small noise expansion of stochastic inflation

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). As a byproduct, we show that the Starobinsky test field approximation might only provide information about the linear regime of cosmological perturbations and scalar-feld non-Gaussianities might only appear at leading order in slow-roll parameters.

astro-ph.CO↗

arXiv2023

An update on adiabatic modes in cosmology and $δ$N formalism

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 equations in the Newtonian gauge. As a byproduct, we clarify that adiabaticity does not generally imply constancy of $\cal R$, not even in the $k\rightarrow 0$ limit. We then show that there exist non-equivalent definitions of $δN$ that would reproduce $\mathcal{R}$ or the uniform density curvature perturbation $ζ$ at linear order. We have then shown that the perturbative $δN$ definition in terms of difference between the number of e-foldings of different gauges, can be extended non-perturbatively at leading order in gradient expansion. Nevertheless, the computer friendly definition in terms of the difference of e-foldings obtained from the evolution of a local FRW Universe, respectively with perturbed and un-perturbed initial conditions, might only give information about the linear order curvature perturbations, contrary to what stated in the literature.

astro-ph.CO↗

arXiv2022

Review on stochastic approach to inflation

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 on results coming from the application of the stochastic framework to different inflationary scenarios, especially to those of interest for primordial black hole formation. During the derivation of the stochastic formalism, we will emphasise two aspects in particular: the difference between the separate universe approach and the true long wavelength limit of scalar inhomogeneities and the generically non-Markovian nature of the noises that appear in the stochastic equations.

gr-qc↗

arXiv2022

Stochastic inflation at all order in slow-roll parameters: foundations

In this paper we develop the formalism for the stochastic approach to inflation at all order in slow-roll parameters. This is done by including the momentum and Hamiltonian constraints into the stochastic equations. We then specialise to the widely used Starobinski approximation where interactions between IR and UV modes are neglected. We show that, whenever this approximation holds, no significant deviations are observed when comparing the two-point correlation functions (power spectrum) calculated with stochastic methods, to the ones calculated with the QFT approach to linear theory. As a byproduct, we argue that: a) the approaches based on the Starobinski approximation, generically, do not capture any loop effects of the quantum scalar-gravity system; b) correlations functions can only be calculated in the linear theory regimes, thus, no non-perturbative statistics can be extracted within this approximation, as commonly claimed.

gr-qc↗

arXiv2019

Failure of the stochastic approach to inflation beyond slow-roll

After giving a pedagogical review we clarify that the stochastic approach to inflation is generically reliable only at zeroth order in the (geometrical) slow-roll parameter $ε_1$ if and only if $ε_2^2\ll 6/ε_1$, with the notable exception of slow-roll. This is due to the failure of the stochastic $ΔN$ formalism in its standard formulation. However, by keeping the formalism in its regime of validity, we showed that, in ultra-slow-roll, the stochastic approach to inflation reproduces the power spectrum calculated from the linear theory approach.

gr-qc↗