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Future measurements of primordial non-Gaussianity can reveal cosmologically produced particles with masses of order the inflationary Hubble scale and their interactions with the inflaton, giving us crucial insights into the structure of…
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy-momentum is now regarded as \emph{quasi-local} (associated with a closed…
We discuss the initial value problem for the Einstein equations in Hitchin's generalised geometry for the case of closed divergence (which correspond to the equations of motion in the bosonic part of the NS-NS sector in type II…
This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity…
We study the thermodynamics of Einstein gravity with vanishing cosmological constant subjected to conformal boundary conditions. Our focus is on comparing the series of subextensive terms to predictions from thermal effective field theory,…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
A new set of field equations for a space-time dependent Newton's constant $G(x)$ and cosmological constant $\Lambda(x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent,…
We provide a cosmological implementation of the evolutionary quantum gravity, describing an isotropic Universe, in the presence of a negative cosmological constant and a massive (preinflationary) scalar field. We demonstrate that the…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
We show how the non-linearity of general relativity generates a characteristic non-Gaussian signal in cosmological large-scale structure that we calculate at all perturbative orders in a large scale limit. Newtonian gravity and general…
It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…
We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert…
In recent years it has been shown for hard sphere gas that, by retaining the correlation information, dynamical fluctuation and large deviation of empirical measure around Boltzmann equation could be proved, in addition to the classical…
We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing function,'' $\alpha$---the quantity that relates the lapse…
The paper extends basic Einstein--Hilbert action by adding a newly proposed invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the…