S. Mohammad Ahmadi

Welcome! I am a recent graduate of the University of Tehran, applying for PhD programs in Physics. My research interests include inflation (theory and observations), primordial black holes and gravitational waves, string cosmology, and quantum gravity. For further information on my research interests, please refer to the Thesis Summary or Publications pages. If you have any questions, please do not hesitate to contact me.

Education

Jan 2023
University of Tehran

M.Sc. in Gravitation and Astrophysics (GPA: 3.5/4)

July 2018
Ferdowsi University of Mashhad

B.Sc. in Physics

Research Experience

Jan 2023 – Present
University of Tehran

Inflation Model Building

  • Developed a generalized model of constant-roll inflation.
  • Investigated the potential formation of primordial black holes in different inflationary scenarios.
  • Created a unified framework for analyzing featured inflationary potentials.
  • StudyingdeviationsfromGaussianstatisticsusingbothperturbativeandnon-perturbativemethods.
  • Checking the validity of Maldacena’s consistency relation.
  • My research resulted in a first-author paper.

Work Experience

2015 - 2019
Founder

Onbik (E-Commerce Organisation)

I initiated my online business with a focus on importing, selling, and educating intellectual toys. Upon gaining admission to the University of Tehran, I resigned from my job to dedicate myself to my studies.

Volunteering Activities

2021

Technical Assistant at “The Physics Society of Iran Annual Meeting 2021”

  • Provided support to speakers and attendees.
  • Contributed to the organization of meeting rooms and provided leadership support.

2021

Numerical evaluation of correlation functions in QSFI

  • Utilized Wolfram Mathematica to perform a comprehensive analysis of the power spectrum and nonGaussianity parameter in quasi-single field inflation.

2014

Managing a website for science news

  • Led the design and development of a website dedicated to science news.
  • Successfully mobilized and led a team of students in content creation, featuring scientific news, and providing relevant course materials.

2013

Generating practical Rubik’s Cube algorithms with Python

  • As a speedcuber (someone who competitively solves combination puzzles), I was looking for optimum algorithms to solve the Rubik’s Cube. I developed a Python program to generate and analyze all potential solutions for a specific cube configuration.

Selected Conferences

2024

Iranian Conference on High Energy Physics, IPM

2022
Bu-Ali Sina University

Conference on Gravity and Cosmology 1400

2021
University of Tehran

The Physics Society of Iran Annual Meeting 2021

2020
University of Tehran

Conference on Gravity and Cosmology 1398

Awards

2012

Awarded Tuition Waiver, Ferdowsi University of Mashhad

Hard Skills

Wolfram Mathematica

50%

Maple

50%

Latex

80%

Python

40%

Microsoft Office

80%

WordPress

80%

Adobe Photoshop

50%

Soft Skills

Time management

80%

Communication

90%

Adaptability

75%

Problem-solving

95%

Teamwork

95%

Creativity

85%

Leadership

85%

Interpersonal skills

90%

Work ethic

95%

Attention to detail

80%

Hobbies

Drawing

70%

Rubik’s Cube

90%

Video Games

40%

Tennis

50%

Badminton

65%

Standardized Tests

IELTS Academic test

IELTS Academic test

Overall Score: 7 (L=7, R=8, W=6, S=6.5)

GRE General Test

GRE General Test

Verbal: 152/170, Quant: 169/170

Publications

My Research

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

Abstract: 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.

JCAP 05(2024)005

arXiv:2312.05998 [gr-qc] 10 Dec 2024

Thesis

What I have been up to

Following the University of Tehran regulations, I wrote my master's thesis in Persian. Therefore, not everyone can read it. On this page, I have provided an English translation of my thesis's abstract, introduction, and table of contents. This is to give you a general view of what I studied during my master's program.
Note: My thesis is mainly a review of the following papers:

  • Maldacena, Juan. "Non-Gaussian features of primordial fluctuations in single field inflationary models." (arXiv:astro-ph/0210603v5)
  • Seery, David, and James E. Lidsey. "Primordial non-Gaussianities in single-field inflation." (arXiv:astro-ph/0503692v2)
  • Cheung, Clifford, et al. "The effective field theory of inflation." (arXiv:0709.0293)
  • Martin, Jerome, and L. Sriramkumar. "The scalar bi-spectrum in the Starobinsky model: The equilateral case." (arXiv:1109.5838v1)
  • Martin, Jerome, Hayato Motohashi, and Teruaki Suyama. "Ultra slow-roll inflation and the non-Gaussianity consistency relation." (arXiv:1211.0083v1)
  • Cai, Yi-Fu, et al. "Revisiting non-Gaussianity from non-attractor inflation models." (arXiv:1712.09998v2)
  • Chen, Xingang, and Yi Wang. "Quasi-single field inflation and non-Gaussianities." (arXiv:0911.3380v4)

Abstract

Inflation has become the leading paradigm of the early universe. However, the detailed dynamics of inflation are still a mystery. A major theme in cosmology is building inflationary models and comparing their predictions with experimental data. Primordial non-Gaussianity is widely known for its strength in discriminating different inflationary models or alternative scenarios. In this work, we introduce some practical methods for evaluating the non-Gaussianity. Then, we use these methods to study the non-Gaussianity in some cosmological inflationary models. We start by introducing the simplest inflation scenarios as a toy model. We continue by discussing models that allow us to get significant levels of non-gaussianity and violation of Maldacena's consistency relation; This relation proves that non-Gaussianities are small in any single field inflationary model, and hence, studies of non-Gaussianity will not resolve the degeneracy between models. We finish our thesis by presenting a two-field scenario as an example of models that produce large local non-Gaussianity while satisfying the consistency relation.

Introduction

The Big Bang theory successfully explains the "blackbody spectrum" of the cosmic microwave background radiation and the origin of the light elements. Nevertheless, it leaves three fundamental questions unanswered:

  • Why is the geometry of the universe nearly flat?
  • Why is the large-scale structure of the universe homogeneous and isotropic?
  • Why have magnetic monopoles never been observed?

The Inflation theory developed around 1980 to explain these puzzles with the standard big bang theory, in which the universe gradually expands throughout its history. Inflation has become the leading paradigm of the early universe due to its precise predictions. However, the detailed dynamic of inflation is still a mystery. Therefore, A major theme in cosmology is to build inflationary models and compare their predictions with experimental data.

Scientists use the concepts like primordial non-Gaussianity, primordial gravitational waves, and primorial features to probe the early universe. Professor Xingang Chen at Harvard University points out three questions that primordial features and non-Gaussianity might answer:

  • Was the primordial universe inflationary or non-inflationary?
  • What were the details of the inflation model and the inflationary dynamics?
  • What were the particle contents of the primordial universe?

In this thesis, we only focus on the second question above; We describe the inflation model building and methods to evaluate the non-Gaussianity in each model. With great advancements in our theoretical and observational techniques, our understanding of the inflationary paradigm has developed significantly. However, the nature of inflation is still hidden from us; we do not know which fields are responsible for the accelerated expansion, the Lagrangian of these fields is yet to be determined, and inflation theory must be distinguished from the alternatives.

The Lagrangian for the simplest inflation model contains one scalar field with a canonical kinetic term. This model successfully predicts the scale-invariance fluctuations and agrees well with the CMB temperature observations. The non-Gaussianity amplitude in this model is of order of the slow roll parameter, which satisfies Maldacena's consistency relation. Consistency relation proves that non-Gaussianities are small in any single field inflationary model; hence, studies of non-Gaussianity will not resolve the degeneracy between models.

Studies of the inflation models with standard kinetic terms are indeed instructive. However, it is not always the case; in models descending from supergravity or superstring, it is generally expected that corrections to the kinetic term will arise. To study such cases, we can consider an inflation model with a kinetic term in the general form. These models are called P(X) theories, which reproduce the results of standard models in a particular case. These classes of models, again, predict a small among of non-Gaussianity and satisfy the consistency relation. However, P(X) theories are not yet the most general action for single field models. In order to write the most general action for describing the cosmological perturbation that unifies all the single field models we need to use a more fundamental theory - the effective field theory. In the context of the EFT of inflation, we look at perturbations as goldstone modes produced as a result of spontaneous symmetry breaking.

Another powerful inflationary scenario is the Starobinsky model. The Starobinsky model consists of a linear inflaton potential with a sudden change in the slope. The change in the slope causes a brief period of departure from slow-roll, which in turn could produce a large among of non-Gaussianity. These features in the spectrum are known to lead to a better fit to the data.

The importance of consistency relation relies on the fact that deviations from it might be detected in future experiments, allowing us to rule out all single field inflationary models. However, not all the single field models follow the consistency relation. Ultra slow-roll (USR) inflation has long been used to challenge the non-Gaussianity consistency relation. The canonical USR model is constructed by assuming that the inflaton's potential is almost constant. This model leads to an order one slow-roll parameter, which will result in large non-Gaussianity and violation of consistency relation. The experimental data prove neither USR nor the consistency relation. Therefore, we can not rule out either of them. However, by studying the reasons for violation of consistency relation in USR we can improve our understanding of this relation.

To study the ultra slow-roll inflation, one should consider that this scenario is incomplete by itself and should be followed by a phase of slow-roll attractor (URS is only stable for a few efolds and having a second phase is necessary to have 60 efold of accelerating expansion). Therefore, USR consists of at least three phases: the USR phase, the transition phase, and the slow-roll phase. The transition phase here can be defined in different ways, and each kind will have a different impact on the non-Gaussianity parameter. Studying different types of transitions can reveal rich information about the USR and consistency relation.

As we said before, consistency relation states that every single field inflation model leads to a small among of non-Gaussianity. Therefore, it seems logical that one search for the large non-Gaussianity in multi-field models. Quasi-Single Field is a two-field inflationary scenario in which large non-Gaussianity is produced while the consistency relation stays satisfied. In this scenario, we consider a non-flat path for the inflation field. The flat inflation path is tilted by the effect of a heavy isocurvature field (carvaton have a mass at least of order the Hubble parameter H). If the inflaton decouples from the isocurvatons or the isocurvaton mass are all much larger than O(H), quasi-single field inflation makes the same prediction as the single field inflation. It can be shown that these massive isocurvatons can have important effects on density perturbations.

Table of Contents

Following is the table of contents of my master's thesis. Please note that this list includes titles of chapters, sections, and sub-sections, while titles of sub-sub-sections and appendixes are removed.

Chapter 1: Primordial Non-Gaussianity

  1. Why Non-Gaussianity
  2. Statistics
    • Power Spectrum and Correlation Function
    • Gaussian Random Fields
    • Wick's Theorem
    • The simplest form of Non-Gaussianity
    • Sources of Non-Gaussianity
  3. Shape and Amplitude of Non-Gaussianity
  4. In-In Formalism and Correlation Function
    • In-In Formalism
    • Mode Functions and Vacuum
    • Contractions
    • Three forms
  5. Slow-roll single-field inflation
    • ADM Formalism
    • Minimally coupled Scalar Field
    • The Quadratic Action
    • The Cubic Action
    • The three point function
  6. Consistency Condition
  7. δN formalism

Chapter 2: General Single Field Models

  1. Non-standard kinetic terms: P(x) theories
    • The background model
    • The Quadratic Action
    • The Cubic Action
  2. The effective field theory of inflation
    • Spontaneous symmetry breaking
    • Unitary Gauge
    • Most general action in unitary gauge
    • Recovering gauge invariance and decoupling limit

Chapter 3: Non-Gaussianity in the Starobinsky Model

  1. Background evolution
  2. The scalar power spectrum
  3. The dominant contribution to the bi-spectrum
    • The three point function
    • Evaluating the dominant contribution
  4. The sub-dominant contributions to the bi-spectrum
    • The contribution due to the second term
    • The contribution due to the first and the third terms
    • The contribution due to the fifth and the sixth terms
    • The contribution due to the field redefinition
  5. Amplitude of Non-Gaussianity
    • Can Non-Gaussianity parameter be large in the Starobinsky model?
    • The hierarchy of contributions to the bi-spectrum

Chapter 4: Ultra Slow-Roll Inflation and Consistency Relation

  1. Ultra Slow-Roll Inflation
  2. Power Spectrum and Non-Gaussianity
  3. Transition to slow-roll phase

Chapter 5: Quasi-Single Field Inflation and Non-Gaussianities

  1. Quasi-single field inflation
  2. Lagrangian and mode functions
  3. Two gauges
  4. Power spectrum and spectral index
  5. Bispectra

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Mashhad - Iran

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