Ultraviolet Divergences and Scale-Dependent Gravitational Couplings

Abstract

I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely unrelated non-perturbative approaches, and how it relates to the vacuum state of quantum gravity, and specifically to the running of G. One distinctive feature of the new fixed point is the emergence of a second genuinely non-perturbative scale, analogous to the scaling violation parameter in non-abelian gauge theories. I argue that it is natural to identify such a scale with the small observed cosmological constant, which in quantum gravity can arise as a nonperturbative vacuum condensate. I then show how the lattice cutoff theory of gravity can in principle provide quantitative predictions on the running of G, which can then be used to construct manifestly covariant effective field equations, and from there estimate the size of non-local quantum corrections to the standard GR framework.

Quantum Gravity and Cosmological Density Perturbations

“…with G(a) given in Equation 9andρ(a) in Equation (10). In this last expression, the exponent is γ ν = 3/2ν 9/2 for a matter dominated background universe, although more general choices, such as γ ν = 3(1 + w)/2ν, are possible and should be explored (see the discussion later).…”

“…The specific nature of the scenario we will be investigating here is motivated by the treatment of field-theoretic models of quantum gravity, based on the Einstein action with a bare cosmological term. Its long-distance scaling properties are derived from the existence of a non-trivial ultraviolet fixed point of the renormalization group in Newton's constant, G [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”