Conformal and disformal transformations of the primordial cosmological perturbations

Date

8-2023

Degree

Bachelor of Science in Applied Physics

College

College of Arts and Sciences (CAS)

Adviser/Committee Chair

Allan L. Alinea

Restrictions

Restricted: Not available to the general public. Access is available only after consultation with author/thesis adviser and only to those bound by the confidentiality agreement.

Request Access

To request access of this material, please email the administrator at uscs-mainlib.uplb@up.edu.ph

Abstract

The theory of cosmic inflation provides a mechanism to explain the quantum inhomogeneities that were amplified, becoming the seeds that gave birth to large-scale structures in the Universe. We call these inhomogeneities the primordial cosmological perturbations. While most papers involve disformal transformations with first-order scalar field covariant derivatives, extending the transformation to having higher-order covariant derivatives would give us more insights about the mathematical and symmetry nature of perturbations. Hence, this study extends the usual disformal transformation to include a second-order scalar-derivative; that is gμν → A(Ф, X)gμν + Β(Ф, X) ∇μФ∇νФ + Z (Ф) ∇μ∇νФ, where gμν is the metric, and A, B are conformal and disformal factors, respectively, that are functionals of the scalar field Ф and the kinetic term X = -½gμν ∇μФ∇νФ. The quantity Z is a small scalar functional that limits the magnitude of the added term. With this general-ization, the transformation encompasses the effects of the conformal and the usual disformal transformations. Specifically, the main objective of the study is to calculate the transformation of the gauge-invariant scalar and tensor primordial cosmological perturbations, ς and γij, respectively. After the transformation, at the linear or-der, the results showed the disformal invariance of γij, extending its symmetry to transformations having a second-order scalar-derivative. On the other hand, the scalar perturbation receives & correction and transforms as ζ → ζ - HZ2A where H is the Hubble parameter. The magnitude of the correction term is comparable to the perturbation ζ , and in the limit that Z → 0, the scalar perturbation is disformally invariant; it exhibits symmetry similar to the case for the usual disformal transformations.

Language

English

LC Subject

Cosmology -- Mathematical models, Perturbation (Mathematics), Inflationary universe

Location

UPLB Main Library Special Collections Section (USCS)

Call Number

LG 993.5 2023 P51 A68

Document Type

Thesis

This document is currently not available here.

Share

COinS