A note on classical and quantum unimodular gravity

We discuss unimodular gravity at a classical level, and in terms of its extension into the UV through an appropriate path integral representation. Classically, unimodular gravity is simply a gauge fixed version of General Relativity (GR), and as such it yields identical dynamics and physical predictions. We clarify this and explain why there is no sense in which it can "bring a new perspective" to the cosmological constant problem. The quantum equivalence between unimodular gravity and GR is more of a subtle question, but we present an argument that suggests one can always maintain the equivalence up to arbitrarily high momenta. As a corollary to this, we argue that whenever inequivalence is seen at the quantum level, that just means we have defined two different quantum theories that happen to share a classical limit.Comment: 5 pages; v2: Some clarifying comments added. Version to appear in European Physical Journal

Modified gravity and cosmology

Having as a starting point the problem of dark energy described before, this thesis studies modifications of General Relativity (GR), as possible gravitational scenarios for the early and late time Universe, motivated by both classical as well as quantum considerations. In particular, it focuses on modifications of GR of the type f(R) as well as the f(R;G) ones, where R and G is the Ricci scalar and Gauss-Bonnet term respectively. On the same time, a modification of GR based on the Renormalisation Group approach to quantum gravity is considered, as well as its link to f(R) gravity. The main goal of the investigations carried out in this thesis, is to understand the structure, as well as the phenomenological implications of non-linear modifications of GR for cosmology, at both the background as well as the linear perturbation level. In particular, chapter 2 presents a brief introduction to the dynamics of GR in the presence of a "dark component" at the background, as well as at the linear perturbation level, while chapter 3 is an introduction to the fundamental properties of non-linear modifications of GR, reviewing important results of the relevant literature. Chapter 4 elaborates with a fundamental property of non{linear gravity models, namely the study of different representations of vacuum actions proportional to f(R) as well as f(G), in view of Legendre transformations, for the case of spacetime manifolds with a boundary. As it is explicitly shown there, although the dynamical equivalence is always true in the bulk, it is not guaranteed on the boundary of the spacetime manifold. On the other hand, chapter 5 focuses on understanding the role of the effective anisotropic stress present in f(R;G) gravity models, attempting to construct particular models of the latter type, with a vanishingly small anisotropic stress, so as to agree with current observations. As it turns out, suppression of the effective anisotropic stress in this class of models is very difficult, highlighting the role of the effective anisotropic stress as a smoking gun for testing modified gravity models with current and future observations. Chapter 6 serves as an introduction to the idea of the Renormalisation Group (RG) and its applications in cosmology, while chapter 7 starts from an RG improved Einstein{Hilbert action and studies its connection with f(R) gravity, as well as its implications for the primordial and the late time acceleration of the Universe. It is shown that the effective f(R) model has some remarkable properties and interesting implications for both early and late time cosmology

A Sun-like star orbiting a boson star

The high-precision astrometric mission GAIA recently reported the remarkable discovery of a Sun-like star closely orbiting a dark object, with a semi-major axis and period of $1.4\, \rm{AU}$ and $187.8$ days respectively. While the plausible expectation for the central dark object is a black hole, the evolutionary mechanism leading to the formation of such a two-body system is highly challenging. Here, we challenge the scenario of a central black hole and show that the observed orbital dynamics can be explained under fairly general assumptions if the central dark object is a stable clump of bosonic particles of spin-0, or spin-1, known as a boson star. We further explain how future astrometric measurements of similar systems will provide an exciting opportunity to probe the fundamental nature of compact objects and test compact alternatives to black holes.Comment: 11 pages, 4 figures. Comments are very welcom