## Giving Love to modified gravity; an examination of neutron star properties in scalar-tensor gravity

##### Summary

Abstract:
A major goal of astrophysics involves the study of neutron stars to determine their nuclear matter equation of state. The first detection of gravitational waves from a binary pair neutron star merger, GW170817, in 2017 opened a new channel for the way in which the equations of state may be constrained or eliminated. This is namely through the extraction of the binary system's *tidal Love number*, which encodes how the neutron stars statically respond to tidal fields. It is possible, however, that deviations from general relativity in strong gravity regimes could lead to differences in measurements that are consistent with uncertainties in the equation of state. To accurately untangle these differences means that efficient modelling of neutron stars in modified theories of gravity is essential.
In this thesis, we review some recent work in calculating neutron star properties - namely the mass, radius and tidal Love number - in scalar-tensor gravity before attempting to extend this work for a larger class of theories - *generalized scalar-tensor theories*. We will do this through the use of an effective action, which in the so-called *Einstein frame* allows for a decoupling of the scalar field from the gravitational part of the action. We find that the formalism for extracting the Love number is not straightforward to extend, due in part to the generic nature of the theory. We finally focus on a numerical case study which involves solving for the equilibrium configuration of the neutron star, such that we can examine how generalized scalar-tensor theories impact the mass and radius. The case study has a successful preliminary calculation, but results in a degeneracy of the mass-radius curves that also correspond to so-called f(R) gravity. We conclude that further analysis is needed to determine the authenticity of this degeneracy. Nevertheless we have still paved the way for future neutron star calculations in generalized scalar-tensor theories, such that they can be better included in the constraining of the neutron star equation of state.