Some Observable Effects of Modified Gravity in Cosmology and Astrophysics

In Chapter 1 I present the current picture of the universe and brieï¬y review the cosmological constant problem and some of the theories proposed to solve it. The following Chapters essentially contain the published papers with some modiï¬cations and additions: in Chapter 2 I study the radiation-dominated epoch in $R^2$ gravity, gravitational particle production and its implications for the early and contemporary universe; in Chapter 3 I investigate the formation of curvature singularities in contracting astronomical systems; in Chapter 4, I discuss some mechanisms to prevent such singularities and calculate the related cosmic-ray production; ï¬nally, in Chapter 5, I deal with spherically symmetric solutions and explore the possibility of gravitational repulsion