Study of General Relativity and $f(R)$ Modified Gravity with Cosmological Constant for Einstein and Jordan Frames

Abstract

This thesis investigates a toy model for inflation in a class of modified theories of gravity in the metric formalism. Instead of the standard procedure -- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from a simple ϕ^2 potential in the Einstein frame and investigate the corresponding $f(R)$ in the former picture. Such approach yields plenty of new pieces of information, namely a self-terminating inflationary solution with a linear Lagrangian, a robust criterion for stability of such theories, a dynamical effective potential for the Ricci scalar $R$, the addition of an ad-hoc Cosmological Constant in the Einstein frame leads to a Thermodynamical interpretation of this physical system, which allows further insight on its (meta)stability and evolution.

arXiv commentPhd thesis (2020)

References in corpus (22)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• f(R) Theories Of Gravity
• The Confrontation between General Relativity and Experiment
• Disappearing cosmological constant in f(R) gravity
• Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
• A new approach to the evolution of cosmological perturbations on large scales
• A general proof of the conservation of the curvature perturbation
• The cosmological constant and the black hole equation of state
• On Physical Equivalence between Nonlinear Gravity Theories
• TASI Lectures on Inflation
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Boundary Terms, Variational Principles and Higher Derivative Modified Gravity
• Model independent constraints on dark energy evolution from low-redshift observations
• Thermodynamic Properties of the van der Waals Fluid
• The Weak Lensing Signal and the Clustering of BOSS Galaxies II: Astrophysical and Cosmological Constraints
• $f(R)$ constant-roll inflation
• Stochastic inflation in phase space: Is slow roll a stochastic attractor?
• Modified gravity with $f(R)=\sqrt{R^2-R_0^2}$
• The Origin of the Large-Scale Structure in the Universe: Theoretical and Statistical Aspects
• Dark Energy and Modified Gravities