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Intuitively, the totality of physical reality -- the Cosmos -- has a beginning only if (i) all parts of the Cosmos agree on the direction of time (the Direction Condition) and (ii) there is a boundary to the past of all non-initial…
We present a foliation-focused critical review of the boundary conditions and dynamics of 4D gravitational theories. A general coordinate transformation introduces a new foliation and changes the hypersurface on which a natural boundary…
We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge theoretic conditions, the cohomology ring of the complement of the hypersurface functorially…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary problems. It turns out that these encompass and extend aspects of already known…
We analyze the Hamilton-Jacobi action of gravity and matter in the limit where gravity is treated at the background field approximation. The motivation is to clarify when and how the solutions of the Wheeler-DeWitt equation lead to the…
We study the possible generalized boundary conditions and the corresponding solutions for the quantum mechanical oscillator model on K\"{a}hler conifold. We perform it by self-adjoint extension of the the initial domain of the effective…
Modelling structure formation across the full dynamical range of the Universe remains a major challenge in cosmology. This difficulty originates from a fundamental limitation of geodesics in general relativity: a one-parameter family of…
The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of…
In this note, we describe how the study of backgrounds for general quantum systems can be formulated in terms of the representation theory of abstract $C^*$ algebras. We illustrate our general framework through two example systems:…
In the context of the absolute parallelism formulation of General Relativity, and because of the fact that the scalar curvature can be written in purely torsional terms, it was known for a long time that a surface term based solely on the…
In this talk we entertain the possibility that the synthesis of general covariance and quantum mechanics requires an extension of the basic kinematical setup of quantum mechanics. According to the holographic principle, regions of spacetime…
Loop quantum cosmology of the closed isotropic model is studied with a special emphasis on a comparison with traditional results obtained in the Wheeler-DeWitt approach. This includes the relation of the dynamical initial conditions with…
We show how the (globally supersymmetric) model of Mirabelli and Peskin can be formulated in the boundary (``downstairs'' or ``interval'') picture. The necessary Gibbons-Hawking-like terms appear naturally when using (codimension one)…
In canonical quantum gravity, when space is a compact manifold with boundary there is a Hamiltonian given by an integral over the boundary. Here we compute the action of this `boundary Hamiltonian' on observables corresponding to open…
The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal $A^{\mu}$ and nonminimal $X^{\mu}$) and scalar ($V_{s}$) interactions embedded in the background of a cosmic string is explored in the context of…
We consider cosmological constraints arising from the background expansion history on the ef- fective field theory of cosmic acceleration, a theoretical framework that allows for a unified way to classify both models of dark energy and…
In canonical quantum gravity, the presence of spatial boundaries naturally leads to a boundary quantum states, representing quantum boundary conditions for the bulk fields. As a consequence, quantum states of the bulk geometry needs to be…
We consider generalizations of Gale's colored KKM lemma and Shapley's KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions.
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…