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Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
We covariantize the decoupling limit of massive gravity proposed in arXiv:1011.1232 and study the cosmology of this theory as a proxy, which embodies key features of the fully non-linear covariant theory. We first confirm that it exhibits a…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $\Lambda\to\infty$ limit of general relativity. This allows an…
We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The present model may be seen as an improvement of the theory proposed in Ref. [Lazo et al, Phys. Rev. D…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local…
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…
In this paper, we study a projectable Ho\v{r}ava-Lifshitz cosmology without the detailed balance condition minimally coupled to a non-linear self-coupling scalar field. In the minisuperspace framework, the super Hamiltonian of the presented…
In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical…
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic…
We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which…
Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and…
Gravitation is described in the context of a dilatonic theory that is conformally related to general relativity. All dimensionless ratios of fundamental dimensional quantities, e.g. particle masses and the Planck mass, as well as the…
We study the breakdown of conformal symmetry in a conformally invariant gravitational model. The symmetry breaking is introduced by defining a preferred conformal frame in terms of the large scale characteristics of the universe. In this…
The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical…
The unified generalized non-local quantum kinetic and hydrodynamic theory is applied for mathematical modeling of objects in the giant scale diapason from the galaxy and Universe scale to atom structures. The principle of universal…
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…