The Bounce, the bang, and the bounds: Models of Modified Gravity

The current paradigm of cosmology lacks a fundamental and definitive description of the accelerated expansion in the early and late Universe. Moreover, the issue of the initial singularity is often overlooked in cosmology. Motivated by these phenomena, we investigate modified gravity models in three epochs. We forecast how gravitational wave experiments will constrain dark energy models by producing mock data and predicting an improved accuracy for the model parameters. In the following chapter, we implement scale invariance into the theory of inflation, extending the work of Starobinsky's model, resulting in non-trivial features for the primordial power spectrum. Furthermore, we consider cosmology before inflation, replacing the initial singularity with a bounce. Creating a model based on Starobinsky's model, we successfully create a classical bounce, which results in enhanced stability and a natural transition into slow-roll inflation. With studies conducted in these three epochs, we conclude that modified gravity in future research will lead to a greater insight into the fundamental phenomenology of gravity and cosmology.