Effective constraints of loop quantum gravity

Abstract

Within a perturbative cosmological regime of loop quantum gravity corrections to effective constraints are computed. This takes into account all inhomogeneous degrees of freedom relevant for scalar metric modes around flat space and results in explicit expressions for modified coefficients and of higher order terms. It also illustrates the role of different scales determining the relative magnitude of corrections. Our results demonstrate that loop quantum gravity has the correct classical limit, at least in its sector of cosmological perturbations around flat space, in the sense of perturbative effective theory.

Loop quantum gravity corrections to gravitational wave dispersion

“…As in the case of gravitational waves, we see that v EM > 1 is larger than the classical value, since bothᾱ EM andβ EM are always greater than one in perturbative regimes [10]. Secondly, the group velocity is no longer constant but varies with time as the universe expands.…”

“…In the last few years, applications of the method used in loop quantum gravity (LQG) [1,2,3], a candidate quantum theory of gravity, to early universe cosmology have led to significant progress. In particular, the quantization of homogeneous cosmological models known as loop quantum cosmology (LQC) [4] has led to a resolution of the big bang singularity [5,6,7,8,9], and techniques have become available to include inhomogeneous perturbations [10,11].…”

Lattice refining loop quantum cosmology, anisotropic models, and stability

“…Perturbative corrections, derived by Taylor expanding the difference terms and keeping higher order corrections to the classical expression, are thus larger. (This can have cosmological implications [37,38,39].) Non-perturbative effects as observed for the inverse scale factor operator in isotropic loop quantum cosmology which has an upper bound at finite volume [40], start to arise for p ∼ N 2/3 when the local volume is used but only at the much smaller p ∼ N −1/3 for the total volume.…”

Observational issues in loop quantum cosmology

“…This has been done for exactly isotropic models [42] and for regular lattice states with inhomogeneities [43], with explicit parametrizations of the quantization ambiguities affecting the values of the parameters [44] [45]. For now on, most studies on inverse volume corrections have been done considering the semiclassical limit where quantum corrections are small and are generically defined as…”