Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Cosmological Models with Symmetric Teleparallel Gravity and its Extension

S. A. Narawade

TL;DR

The thesis investigates late-time cosmic acceleration within symmetric teleparallel gravity by focusing on f(Q) models as alternatives to ΛCDM. It develops and constrains several f(Q) forms including log-square-root, exponential and power-law/logarithmic reconstructions, employing phase-space analysis and extensive observational data via MCMC on H(z), SNe Ia Pantheon+SH0ES and BAO/CMB. The work demonstrates that f(Q) gravity can produce stable late-time de Sitter behavior and Phantom or Quintessence regimes depending on the model, with Om z diagnostics and cosmographic parameters broadly compatible with current data while offering potential resolutions to H0 and σ8 tensions. It also explores both coincident and non coincident gauge formulations, reconstructing viable f(Q) functions and validating them against data, thereby highlighting f(Q) gravity as a competitive framework for describing cosmic acceleration and the dark sector. The findings suggest that non metricity based modifications can replicate key ΛCDM features while providing new insights into the dynamics of dark energy and the structure of spacetime, with implications for future gravitational tests and cosmological surveys.

Abstract

This thesis investigates late-time cosmic acceleration using modified gravity theories with a focus on $f(Q)$ gravity, as an alternative to the $Λ$CDM model. The standard cosmological model attributes the acceleration to a cosmological constant, but it faces issues like the unexplained nature of dark matter and dark energy and discrepancies with certain observations. Modified gravity including $f(Q)$ gravity, offers a potential solution by incorporating dynamic dark energy or changes to gravitational interactions, avoiding the need for a constant cosmological term. Also, thesis evaluates the viability of $f(Q)$ gravity by analyzing observational data from Type Ia Supernovae, Hubble parameter measurements and other cosmological datasets. Using statistical tools like Markov Chain Monte Carlo (MCMC) analysis, this work constrains the parameters of $f(Q)$ gravity and compares it to the $Λ$CDM model.....

Cosmological Models with Symmetric Teleparallel Gravity and its Extension

TL;DR

The thesis investigates late-time cosmic acceleration within symmetric teleparallel gravity by focusing on f(Q) models as alternatives to ΛCDM. It develops and constrains several f(Q) forms including log-square-root, exponential and power-law/logarithmic reconstructions, employing phase-space analysis and extensive observational data via MCMC on H(z), SNe Ia Pantheon+SH0ES and BAO/CMB. The work demonstrates that f(Q) gravity can produce stable late-time de Sitter behavior and Phantom or Quintessence regimes depending on the model, with Om z diagnostics and cosmographic parameters broadly compatible with current data while offering potential resolutions to H0 and σ8 tensions. It also explores both coincident and non coincident gauge formulations, reconstructing viable f(Q) functions and validating them against data, thereby highlighting f(Q) gravity as a competitive framework for describing cosmic acceleration and the dark sector. The findings suggest that non metricity based modifications can replicate key ΛCDM features while providing new insights into the dynamics of dark energy and the structure of spacetime, with implications for future gravitational tests and cosmological surveys.

Abstract

This thesis investigates late-time cosmic acceleration using modified gravity theories with a focus on gravity, as an alternative to the CDM model. The standard cosmological model attributes the acceleration to a cosmological constant, but it faces issues like the unexplained nature of dark matter and dark energy and discrepancies with certain observations. Modified gravity including gravity, offers a potential solution by incorporating dynamic dark energy or changes to gravitational interactions, avoiding the need for a constant cosmological term. Also, thesis evaluates the viability of gravity by analyzing observational data from Type Ia Supernovae, Hubble parameter measurements and other cosmological datasets. Using statistical tools like Markov Chain Monte Carlo (MCMC) analysis, this work constrains the parameters of gravity and compares it to the CDM model.....

Paper Structure

This paper contains 80 sections, 148 equations, 26 figures, 14 tables.

Table of Contents

  1. Introduction
  2. Geometric Setup
  3. Foundation of Cosmological Dynamics
  4. The FLRW metric
  5. Redshift in cosmology
  6. Energy conservation in cosmology
  7. The stress-energy-momentum tensor
  8. Energy conditions
  9. Cosmographic parameters
  10. Overview of the $\Lambda$CDM model
  11. Successes and shortcomings of standard cosmological model
  12. Exploring Alternative Cosmological Theories
  13. Dark energy models
  14. Modified gravity models
  15. Symmetric Teleparallelism
  16. ...and 65 more sections

Figures (26)

  • Figure 1: Depending on the properties of connection, the subclasses of metric-affine geometry. [Credit: Phys. Rev. D. 97, 124025 (2018)]
  • Figure 2: Evolution of cosmographic parameters as a function of redshift.
  • Figure 3: Evolution of log-square-root model as a function of redshift.
  • Figure 4: The behavior of the dynamical parameter for log-square-root model in redshift.
  • Figure 5: Evolution of exponential model as a function of redshift.
  • ...and 21 more figures

Theorems & Definitions (8)

  • Definition 1.1: Metric tensor
  • Definition 1.2: Christoffel symbol
  • Definition 1.3: Covariant derivative
  • Definition 1.4: Parallel transport
  • Definition 1.5: Geodesic
  • Definition 1.6: Non-metricity Tensor
  • Definition 1.7: Superpotential tensor
  • Definition 1.8: Non-metricity scalar