Invariant states and quantized gravitational perturbations

Abstract

We study the problem of quantizing the gravitational fluctuations about a symmetric vacuum background spacetime with compact caucdy surfaces. In the context of lowest-order perturbation theory we show that the allowed physical states must all be invariant under the symmetry transformations of the background spacetime. This constraint does not unduly restrict the range of allowed states and is consistent with temporal evolution (in the presence of a timelike symmetry) or spacial localization (for a spacelike symmetry) provided the evolution or localization is interpreted intrinsically rather than with reference to the background spacetime.

A global picture of quantum de Sitter space

“…As a result, one expects the interesting dynamics to be relational [28,29,30,31,32,33,34,35,36,37], and in particular to describe, e.g., the relative positions of various features of the quantum state. In the quantum dS context, this feature was pointed out in the original work [6], where the dS-invariance of states was first described.…”

“…The picture then changes at first non-trivial order in gravitational interactions. Here, so called linearization stability constraints [4,5,6,7,8,9,10] arise, which state that only zeroth order states satisfying B = 0 lead to consistent first order perturbations. The statement is akin to the fact that the total electric charge on a compact space must vanish.…”

“…At first order in 1/m p , one finds 'linearization stability constraints' [4,5,6,7,8,9,10] [12]. As suggested in [12], one may nevertheless proceed by considering formally dS-invariant sums of states in H 0 , so long as one introduces a 'renormalized' inner product on the space of such sums.…”

Stratification of the orbit space in gauge theories: the role of nongeneric strata

“…For quantized gravitational fluctuations around a symmetric background spacetime, it has been found [27] that the effect of quadratic constraints is to suppresses transitions to configurations of lower symmetry. This led some authors [28] [6] to conjecture that the amplitude of the Schrödinger functional would display particular enhancements (or suppressions) near the singularities.…”

Wormholes in Spacetimes With Cosmological Horizons

“…We can solve this equation by separation of variables. By imposing standard boundary conditions for the quantum harmonic oscillators, and restricting all considerations to rotationally invariant states of the scalar field [7,9] (i.e., states that depend on the inhomogeneous configuration variables only through the rotationally invariant combinations χ 2 n = σn χ 2 nσn ), we arrive at wave functions of the form…”