Investigating the parameter space of viable models for f(R) gravity
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The accelerated expansion of spacetime intuitively points to the existence of new, unknown energy fields pervading the universe, but it is has also spurred the growth of the research field of modified gravity theories. Of these, f(R) theories of gravity is the first and simplest modification to General Relativity, and have been studied extensively for their astrophysical and cosmological predictions. Power law f(R) modifications have been shown to exhibit desirable characteristics, producing the late time accelerated expansion as well as satisfying local tests of gravity. However, there is wide degeneracy among models in this class, and they are known to suffer from cosmological instabilities, which could lead to curvature singularities at finite times. This thesis addresses questions directly relating to model degeneracy and sudden singularities. Cosmologies and cosmological perturbations, resulting from a general broken power law modification to GR are generated, studied and evolved. Simulations are performed using 1+3 space time decomposition of the field equations and a dynamical systems approach to f(R) cosmology. The parameter space of this model, which includes the HuSawicki , Starobinsky  and Miranda  f(R) forms as subclasses, is investigated. It is found that there are regions in the parameter space which are completely singular and bound by continuous curves. We also investigate regions of the parameter space in which the attractive nature of gravity is preserved, and find that these regions intersect. The results of a Markov Chain Monte Carlo analysis significantly narrowed the viable region of the exponent parameter space of the general power law f(R) model. Current cosmological distance data; SNIa (Union 2), BAO (6dFGS, BOSS, SDSS, WiggleZ) as well as the LRG power spectrum (SDSS DR9), were used to obtain these constraints. The best fits are compared with the ΛCDM model, and leads to the conclusion that this class is still a candidate for the gravitational interaction.
Kandhai, S. 2019. Investigating the parameter space of viable models for f(R) gravity.