A Mathematical Analysis of Cosmic Inflation

Kaya, Aylan (2024) A Mathematical Analysis of Cosmic Inflation. Bachelor's Thesis, Physics.

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Abstract

This paper provides a comprehensive mathematical analysis of cosmic inflation, demonstrating its effectiveness in addressing several fundamental puzzles in cosmology and its robustness against current observational constraints. The thesis begins with an overview of the Big Bang model and the Cosmic Microwave Background (CMB), supported by the mathematical framework of the Friedmann-Robertson-Walker (FRW) metric and Friedmann equations. The paper then delves into the primary shortcomings of the Big Bang model, such as the horizon, flatness, and monopole problems, and presents initial conditions leading to their resolution through inflation. The theory of inflation is introduced, focusing on the single-field slow-roll model based on the inflation field and its parameters to explore the model's limitations. Cosmological perturbations are then introduced which are followed by quantum fluctuations of both massless and massive generic scalar fields. With the derivation of the power spectrum and spectral index, we illustrate how inflation provides a robust framework for explaining the observed large-scale structure and temperature anisotropies in the CMB. The paper concludes by affirming the success of the inflationary paradigm in solving the major issues of the Big Bang model and suggesting avenues for further research to refine and test the predictions of inflationary models.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Dimastrogiovanni, E. and Mazumdar, A.
Degree programme:	Physics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	16 Jul 2024 11:46
Last Modified:	16 Jul 2024 11:46
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/33442

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