Related papers: Mathematical problems in higher order gravity and …
This work investigates alternative theories of gravity, the solutions to their field equations and the constraints that can be imposed upon them from observation and experiment. Specifically, we consider the cosmologies and spherically…
I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general…
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…
A very short, non-technical review of the main problems which are presently open in the context of the gravitational theory and of its cosmological applications, and which are currently under investigation and deep discussion. We will talk…
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the…
In this thesis, we study the implications of Quantum Gravity models for the dynamics of spacetime and the ensuing departures from classical General Relativity. The main focus is on cosmological applications, particularly the impact of…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the…
We consider the Lovelock theory of gravity that assumes a nonlinearity of the field equations in the second-order derivatives of the metric. We prove the opportunity of obtaining cosmological solutions without isotropization in the presence…
A review is given of recent work on topology changing solutions to the first order form of general relativity. These solutions have metrics which are smooth everywhere, invertible almost everywhere, and have bounded curvature. The…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
In Chapter 1 I present the current picture of the universe and briefly review the cosmological constant problem and some of the theories proposed to solve it. The following Chapters essentially contain the published papers with some…
In the present paper we give conclusive arguments pointing at physical equivalence among conformally related metrics. Based on the argument that any consistent effective theory of spacetime must be invariant under the one-parameter group of…
Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is…
The difficult issues related to the interpretation of quantum mechanics and, in particular, the "measurement problem" are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary…
The problem of formation of generic structures in the Universe is addressed, whereby first the kinematics of inertial continua for coherent initial data is considered. The generalization to self--gravitating continua is outlined focused on…
Possible models of modified gravity are being extensively studied now, with most phenomenological motivations coming from puzzles and tensions in cosmology due to a natural desire to better fit the known and newly coming data. At the same…
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
In the bibliography a certain confusion arises in what regards to the classification of the gravitational theories into scalar-tensor theories and general relativity with a scalar field either minimally or non-minimally coupled to matter.…