arXiv subjects

Nahid Ahmadi

Publications and source records attributed to Nahid Ahmadi.

9 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↗

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↗

arXiv2023

On the constant roll complex scalar field inflationary models

In this paper we wish to point out the possibility of using a complex scalar field in a constant roll inflationary model, as needed for observational viability. We extend the idea of real field inflaton with constant rate of roll to a complex field, showing the feasibility of solving Einstein Klein-Gordon equations constrained by an \emph{appropriate} form of constant roll definition. As compared to the well known (two-parametric class of) real field models, there is one more degree of flexibility in constant roll inflationary solutions which is represented by an arbitrary function of time, $γ(t)$. We work with an arbitrary but constant function $γ$ (where $γ=0$ refers to the corresponding real field model) and find new inflationary class of potentials. In this class of models, the behavior of real and complex field models are similar in some aspects, for example the solutions with large constant roll parameter are not stable and should be considered as early time transients. These field solutions relax at late time on a dual attractor trajectory. However, complex fields phase space trajectories reach this stable regime after real fields. We performed the stability analysis on $γ$ function space solutions and found that dynamically stable trajectories in phase space are stable under $γ$ variations. We extended this study by considering multifield models of constant roll inflation with non-canonical kinetic terms. By enlarging the size of field space, we showed that a multifield constant roll model is dynamically a single field effective theory. If field space is parametrized by $N$ non-canonical fields, there will be $N$ free parameters in the potential that can be attributed to the interaction between the fields.

gr-qc↗

arXiv2022

Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase

Transitions between different inflationary slow-roll scenarios are known to provide short non-slow-roll periods with non-trivial consequences. We consider the effect of quantum diffusion on the inflationary dynamics in a transition process. Using the stochastic δN formalism, we follow the detailed evolution of noises through a sharp transition modeled by the Starobinsky potential, although some of our results apply to any sharp transition. We find how the stochastic noise induced by the transition affects the coarse-grained fields. We then consider the special case that the potential is flat after the transition. It is found that the particular noise we obtain cannot drive the inflaton past the classically unreachable field values. By deriving the characteristic function, we also study the tail behavior for the distribution of curvature perturbations ζ, which we find to decay faster than e^(-3ζ).

gr-qc↗

arXiv2018

\bf $δM$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation

We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the $δM $ formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in {\it almost} the same way that the so-called $δN$ formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twin formula, $δN$, this new method can substantially reduce the amount of calculations related to the evolution of tensor modes. However, it is not as general as $δN$, it is a "perturbative" formula and solves the shear only to linear order. In other words, it is restricted to weak shear limit.

gr-qc↗

arXiv2018

\bf $δM$ Formalism and Anisotropic Chaotic Inflation Power Spectrum

A new analytical approach to linear perturbations in anisotropic inflation has been introduced in [A. Talebian-Ashkezari, N. Ahmadi and A.A. Abolhasanib, JCAP 03(2018)001] under the name of $δM$ formalism. In this paper we apply the mentioned approach to a model of anisotropic inflation driven by a scalar field, coupled to the kinetic term of a vector field with a $U(1)$ symmetry. The $δM$ formalism provides an efficient way of computing tensor- tensor, tensor- scalar as well as scalar- scalar 2-point correlations that are needed for the analysis of the observational features of an anisotropic model on the CMB. A comparison between $δM$ results and the tedious calculations using in-in formalism shows the aptitude of the $δM$ formalism in calculating accurate two point correlation functions between physical modes of the system.

gr-qc↗

arXiv2015

Deflection of light by the field of a binary system

We examine the motion of a photon in the gravitational field of a binary system. The equations of motion are geodesic equations in a Schwarzchild background with a tidal force. We specialize the equations to that of an edge-on binary and use the method of osculating elements to integrate them. This work helps to identify a binary system through the gravitational light deflection of one member in the gravitational field of the other member. It is found that the effects of the companion body on a photon passing the edge of the star can be potentially detected by astrometric satellites with $μ$as precision, if the ratio of the Schwarzchid radius to the star radius, $\frac{Gm}{c^2 R}\geq 10^{-5}$. Two different cumulative effects on the photon path are identified.

gr-qc↗

arXiv2013

Can non-local or higher derivative theories provide alternatives to inflation?

The standard mechanism for producing the observed scale-invariant power spectrum from adiabatic vacuum fluctuations relies on first order derivative of fields in the action for curvature perturbations. It has been proven \cite{Geshnizjani:2011dk} that, under this ansatz, any theory of early universe that matches cosmological observations should include a phase of accelerated expansion (i.e. inflation) or it has to break at least one of the following tenets of classical general relativity: Null Energy Conditions (NEC), subluminal signal propagation, or sub-Planckian energy densities. We extend this proof to a large class of theories with higher (spatial) derivative or non-local terms in the action. Interestingly, only theories in the neighborhood of Lifshitz points with $ω_k \propto k^0$ and $k^3$ remain viable.

hep-th↗

arXiv2012

Second order gauge invariant measure of a tidally deformed black hole

In this paper, a Lagrangian perturbation theory for the second order treatment of small disturbances of the event horizon in Schwarzchild black holes is introduced. The issue of gauge invariance in the context of general relativistic theory is also discussed. The developments of this paper is a logical continuation of the calculations presented in \cite{Vega+Poisson}, in which the first order coordinate dependance of the intrinsic and exterinsic geometry of the horizon is examined and the first order gauge invariance of the intrinsic geometry of the horizon is shown. In context of second order perturbation theory, It is shown that the rate of the expansion of the congruence of the horizon generators is invariant under a second order reparametrization; so it can be considered as a measure of tidal perturbation. A general expression for this observable, which accomodates tidal perturbations, is also presented.

gr-qc↗