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# Aspects of modified gravity

## Abstract

To date, General Relativity provides the best description of the gravitational interaction. It can accurately describe the motion of the planets within the solar system. However, on large scales general relativity is unable to explain the accelerating expansion of the Universe. Furthermore, so far, no complete self-consistent quantum theory of gravity based on General Relativity has been constructed. This has motivated physicists to explore alternative theories of gravity. In this thesis, I explore three different problems confronting gravitational physics. First, I explore a gauge theory of gravity. In these models one has to choose a gauge group and localize its global symmetries. In this thesis I consider a Yang-Mills gauge gravity of the conformal group SO(4,2). This work was done in collaboration with J. Gegenberg and S. Seahra. In the thesis, I show the derivation of the equations of motion and investigate the cosmological solutions in the case that the matter content of the Universe is a mixture of dust and radiation. Our model predicts a big bounce in the early Universe followed by a period of nearly exponential slow roll inflation that can last long enough to explain the large scale homogeneity of the cosmic microwave background. Furthermore, our model incorporates a de Sitter-like accelerating phase in the late Universe that agrees with observations. Second, I explore a toy model of gravity. This work is in collaboration with V. Husain and J. Ziprick. General relativity in four-dimensional spacetime is a complicated theory to quantize. Therefore, it is useful to study simpler models. Einstein gravity in three dimensions has been a subject of much study, especially for the purpose of quantization. However, there are no local propagating degrees of freedom in three dimensions. It is fruitful to study three-dimensional gravitational theories with local field degrees of freedom. I consider here a method for obtaining local degrees of freedom: three dimensional general relativity coupled to a pressureless “dust”. The dust time gauge is imposed with the upshot that the gravitational part of the Hamiltonian constraint becomes the physical Hamiltonian. This yields an extra degree of freedom in the metric field. In the thesis, I examine the action in canonical form and derive the evolution equations for the spatial metric and its conjugate momentum. Linearizing the equations about the flat background and imposing the transverse (or traceless) gauges indicates that the extra degree of freedom in the metric is a scalar mode and is ultra local. Finally, I examine parametric resonance in cosmology, in collaboration with S. Seahra. According to dynamical dark energy models or theories of quantum gravity, it can be possible that kinetic terms appearing in matter actions get modified at high or low energies. The modification of the matter kinetic term can directly influence the parametric resonance and therefore the preheating phase near the end of inflation. Preheating is a process required to reheat the universe and create elementary particles. To incorporate exotic kinetic terms into this scenario, one can modify the action of the inflaton, the reheaton, or both. In the last part of this thesis, I study the effects of nonstandard kinetic terms from several different models on resonant preheating.