In recent years, theories of gravity incorporating a scalar field coupled to gravity---'scalar-tensor' theories---have been subject to increased attention. In these theories, the scalar field mediates gravitational-strength 'fifth forces'.

For such scalar fields to retain cosmological relevance while also evading stringent constraints from high-precision post-Newtonian tests of gravity, 'screening mechanisms' are invoked, in which the fifth force is suppressed in regions of high density or deep gravitational potential. One example of a screening mechanism is the 'chameleon' mechanism, in which the scalar has a density-dependent mass, such that the mass becomes very large in regions of high density, and the fifth force is exponentially suppressed as a consequence. While the primary effect of screening mechanisms is to mask the effects of modified gravity in the Solar System, they can nevertheless give rise to interesting astrophysical signatures elsewhere, searches for which can serve as tests of screened modified gravity. These signatures are the subject of this thesis.

The Introduction of this thesis in Chapter 1 presents some historical background and scientific context, particularly in the fields of cosmology, the astrophysics of galaxies, and screened modified gravity theories. Subsequently, Chapters 2, 3, and 4 present original research regarding two galaxy-scale signatures of screened modified gravity: 'upturns' in galaxy rotation curves and asymmetries in stellar streams.

If a galaxy is partially screened, it will have a 'screening radius', within which the fifth force is suppressed. Outside the screening radius, the fifth force on a test particle will be proportional to the mass enclosed in the shell between the test particle and the screening radius. Thus, the fifth force will contribute to the galaxy's rotation curve, but only outside the screening radius. At the screening radius itself, there will be an upturn in the curve. In Chapter 2, based on an article published in the Monthly Notices of the Royal Astronomical Society (Naik et al., 2018), I give the first prediction of this effect, specifically in the context of Hu-Sawicki f(R) gravity, a widely-studied example of a chameleon theory. By post-processing simulated galaxies of the Auriga Project using the f(R) gravity code MG-Gadget, I produce mock rotation curves for a range of galaxy masses and values of the key theory parameter fR0, forecasting competitive constraints on fR0. In Chapter 3, also based on an article published in the Monthly Notices (Naik et al., 2019), I turn to observational data. Analysing the high-quality rotation curves of the SPARC sample, I find that in certain f(R) parameter regimes there is a strong signal, but it is better explained with standard gravity plus a 'cored' dark matter halo profile than with modified gravity plus a theoretically-predicted 'cuspy' halo. I am thus able to place competitive constraints on f(R) gravity, with the caveat that if cored haloes can not ultimately be motivated under the standard ΛCDM cosmological paradigm, then screened modified gravity could feasibly ease the tension between observed cores and predicted cusps.

In Chapter 4, I consider the observable imprints of screening on stellar streams around the Milky Way. For reasonable parameter regimes in chameleon theories, main sequence stars will be screened, and thus neither source nor couple to the fifth force. Thus, a situation can arise in which a dark matter dominated dwarf galaxy is unscreened, but the stars within it are screened. If such a galaxy were to be tidally disrupted by the Milky Way, its stars would be preferentially stripped into the trailing stellar stream rather than the leading stream. The streams would therefore be asymmetric about their progenitor. Using a restricted N-body method, I explore this effect for a variety of satellite orbits and modified gravity regimes. Taking f(R) gravity as a fiducial theory, I forecast some of the strongest constraints to date from future data releases of the Gaia satellite. This chapter is based on an article submitted to Physical Review D (Naik et al., 2020).

Finally, Chapter 5 gives some concluding remarks and a discussion of future prospects in this field.