Late time Cosmology in Modified Theories of Gravity Dual Bouncing and Collapsing Universes

Abstract

newline Abstract newlineThe search for a theory of dark energy beyond the standard model of cosmology falls newlineinto two categories: one can introduce an exotic fluid source to model dark energy, such newlineas the quintessence field, or one can extend general relativity by considering a modified newlinetheory of gravity to explain the late-time acceleration, such as the scalar-tensor theo- newlineries or f (R ) theories of gravity. A spacetime-dependent re-scaling of the metric, or con- newlineformal transformation, allows for the modified theories to be recast as Einstein s grav- newlineity with a scalar field, referred to as the Jordan and Einstein frame representations. Al- newlinethough the conformal frames are equivalent, the cosmological evolutions in the frames newlinecan be drastically different. Using the conformal correspondence, this thesis explores newlinealternative descriptions of dark energy-driven late-time cosmology through bouncing newlineand collapsing universes. We study f (R ) models which provide an effective descrip- newlinetion of quintessence models of dark energy in the Einstein frame. For a class of viable newlinequintessence models, the Jordan frame universe grows to a maximum size, after which newlineit collapses and eventually approaches a singularity, while the Einstein frame universe newlinekeeps on expanding. We show that the standard and#923;CDM cosmology and all quintessence newlinemodels of dark energy can alternatively be seen as bouncing or collapsing universes newlinedriven by scalar-tensor theories. These dual descriptions of the late-time universe are newlinestable against linear perturbations. We further study the expansion-collapse duality in newlinea quantum gravity framework. As the collapsing universe becomes sufficiently small, newlineit expectedly develops significant quantum fluctuations; more surprisingly, its dual ex- newlinepanding universe also develops similar quantum features, regardless of its size. Our re- newlinesults suggest that the rise in quantum characteristics is a frame-independent effect. The newlineexpansion-collapse duality between conformal frames has potential implications for the newlinestudy of perturbat