Related papers: Constraints are not enough
It is known that the action of Euclidean Einstein gravity is not bounded from below and that the metric of flat space does not correspond to a minimum of the action. Nevertheless, perturbation theory about flat space works well. The deep…
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main…
A modified theory of gravity with the function $F(R) = R\exp(\alpha R)$ instead of Ricci scalar $R$ in the Einstein$-$Hilbert action is considered and analyzed. The action of the model is converted into Einstein$-$Hilbert action at small…
The path integral of 4D Einstein-Hilbert gravity for the de Sitter-like Universe with fluctuations is investigated, and the transition amplitude from one boundary configuration to another is computed. The gravitational system is described…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
We analyse the impact of various boundary conditions on the (minisuperspace) Lorentzian gravitational path integral. In particular we assess the implications for the Hartle-Hawking no-boundary wavefunction. It was shown recently that when…
We show that for an eikonal limit of gravity in a space-time of any dimension with a non-vanishing cosmological constant, the Einstein -- Hilbert action reduces to a boundary action. This boundary action describes the interaction of…
We initiate a systematic study of Einstein-Gauss-Bonnet gravity in the presence of boundaries subject to conformal boundary conditions, in which the conformal class of the boundary metric is kept fixed. In Einstein gravity, the trace of the…
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the…
According to common lore, massive elementary higher spin particles lead to inconsistencies when coupled to gravity. However, this scenario was not completely ruled out by previous arguments. In this paper, we show that in a theory where the…
The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Dirichlet conditions on the boundary induced metric;…
There is strong evidence coming from Lorentzian dynamical triangulations that the unboundedness of the gravitational action is no obstacle to the construction of a well-defined non-perturbative path integral. In a continuum approach, a…
A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of…
The gravitational path-integral of Gauss-Bonnet gravity is investigated and the transition from one spacelike boundary configuration to another is analyzed. Of particular interest is the case of Neumann and Robin boundary conditions which…
We discuss the set of constraints for Einstein-aether theories, comparing the flat background case with what is expected when the gravitational fields are dynamic. We note potential pathologies occurring in the weak gravitational field…
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…
We discuss the factorization and continuity properties of fields in the Euclidean gravitational path integral with higher dimension operators constructed from powers of the Riemann tensor. We construct the boundary terms corresponding to…
We develop variation formulas on almost-product (e.g. foliated) pseudo-Riemannian manifolds, and we consider variations of metric preserving orthogonality of the distributions. These formulae are applied to Einstein-Hilbert type actions:…
The very early universe is understood in terms of quantum field theories on curved spacetime, where the classical background spacetime is typically an FLRW cosmology and the quantum fields which propagate on it include gravitational waves…
We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons…