arXiv subjects

S. Mohammad Ahmadi

Publications and source records attributed to S. Mohammad Ahmadi.

3 recordsLinked to original sources

arXiv2026

$δN$ formalism with gradient interactions

The standard $δN$ formalism is a cornerstone technique for calculating curvature perturbations on super-Hubble scales. However, its validity relies heavily on the separate universe assumption, in which spatial gradients are neglected. This approximation is known to break down in scenarios that are critical for primordial black hole formation, such as transitions to an ultra-slow-roll phase, where gradient interactions induce a significant non-conservation of the comoving curvature perturbation. In this paper, we introduce a framework for incorporating gradient corrections into the $δN$ formalism by adding an effective source term to the background Klein-Gordon equation. While preserving the nonlinear separate-universe dynamics at zeroth order, this approach consistently incorporates the leading gradient-sensitive effects and thereby improves the treatment of the nonlinear evolution of curvature perturbations up to the end of inflation, given initial conditions specified at horizon exit. By computing the equilateral non-Gaussianity parameter $f_{\mathrm{NL}}^{\mathrm{eq}}$, we demonstrate that our method captures some essential physical features missed by the standard $δN$ approach, offering a simple pathway to determine the nonlinear evolution expected from cosmological perturbation theory.

gr-qc↗

arXiv2026

Continuous Sensitivity Analysis for $δN$ Formalism

The $δN$ formalism provides a powerful non-perturbative framework for following the evolution of primordial curvature perturbations on super-horizon scales. However, its standard implementation relies on the separate universe assumption, which neglects significant spatial gradient interactions. Recent work has addressed this limitation by incorporating gradient interactions directly into the background dynamics through an effective source term in the Klein--Gordon equation, thereby extending the applicability of the $δN$ framework beyond the separate universe approximation. Despite this conceptual progress, practical calculations within the $δN$ formalism remain technically challenging, as cosmological observables require evaluating the sensitivity of the total number of $e$-folds to initial conditions, a task that becomes even more involved once gradient contributions are included. In this work, we develop a systematic method to simplify these calculations by applying Continuous Sensitivity Analysis to the gradient-corrected $δN$ framework. In this approach, the required phase-space derivatives are obtained by solving a set of coupled first-order differential equations for the field Jacobian and Hessian, which significantly streamlines both analytical and numerical evaluations of the $δN$ formalism. As an explicit demonstration, we apply the method to the Starobinsky model, which features a sharp transition into an ultra-slow-roll phase. Within this setup, we derive analytical expressions for the $k$-dependent power spectrum including full gradient corrections, and obtain an analytical estimate of the equilateral non-Gaussianity parameter $f_{\rm NL}^{\rm eq}$ that accurately captures the main non-Gaussian features.

gr-qc↗

arXiv2024

Analytical Insights into Constant-Roll Condition: Extending the Paradigm to Non-Canonical Models

In this work, we explore the prospect of generalizing the constant-roll condition in canonical inflationary model to non-canonical models. To find a natural generalization, we focus on three manifestations of this condition and construct constant-roll models corresponding to each manifestation. These models are not equivalent but reduce to the familiar constant-roll model in canonical limit. To showcase the applicability of our generalized mechanism, we examine a specific class of non-canonical models, which can be viewed as extensions of k/G inflation. In these models sound speed is constant. We conduct a comparative study, and with an analytical examination of the model, specify instances when our constant-roll conditions yield dissimilar outcomes and when they exhibit analogies. We also apply our findings to scrutinize another kinetically driven inflationary model with varying sound speed. We demonstrate that each of our constant-roll conditions leads to a unique set of solutions. Afterward, we construct a four-stage constant-roll kinetically driven inflation that complies with CMB constraints, it sustains for a sufficiently long period of time, and finally gracefully exits. In this model the spectrum of curvature perturbations is enhanced in a brief phase of non-slow-roll inflationary evolution. Employing numerical methods, we analyse this scenario to elucidate how altering the constant-roll condition impacts the power spectrum and the model's dynamics.

gr-qc↗