Abstract
Inflation is a much discussed topic within the field of cosmology; it represents a time in the history of the Universe where a very rapid, exponential expansion was taking place. This expansion is needed in order for the currently used Big Bang model to fit with what we observe today; however the nature of this inflation is still not well understood.
Among the theories of how inflation starts, evolves and ends, f(R) gravity is the one we will focus on in this thesis. The most attractive trait of f(R) gravity is that it can explain the accelerated expansion without the need of introducing exotic, new particles and/or energies into the Universe, such as dark energy and dark matter.
During the research in this thesis of f(R) gravities we came across what seems to be an as of yet unappreciated problem that arises when we perform a so-called conformal transformation between the Jordan and Einstein frames. If we are not careful, the conformal transformation can tangle our coordinates, so that we might produce errors in codes that have not accounted for this entanglement. This understanding allowed us to produce a paper titled "Gauge Issues in Extended Gravity and f(R) Cosmology'', published in the Journal of Cosmology and Astroparticle Physics Issue 04, 2012. From this spawned a new direction of the research, to modify an existing Boltzmann code in order to fully safeguard against these problems.
After reviewing the biggest Boltzmann codes, the choice fell to either CLASS or CAMB, where we chose CAMB due to the fact that Fortran is a much more familiar language than C, even though it could be argued that CLASS is the more readily modifiable while remaining stable program. The process of modifying CAMB is almost complete at this point; however, it is not yet in a state suitable for presentation.
The thesis also performs an analysis of the so-called "non-Gaussianity'' parameter fNL, CMB power spectrum and CMB bispectrum for a specific f(R) model, in order to probe its viability, and to demonstrate the techniques we will apply to more general models.