Vacuum Condensate Picture of Quantum Gravity

Abstract

In quantum gravity perturbation theory in Newton's constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge-Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of G and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale ξ in many ways analogous to the scaling violation parameter ΛM S of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments.

Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

“…Many more details on the nonperturbative approach to quantum gravity used in this paper can be found in a number of earlier works [16,17], and many references therein. The current section will therefore only serve to summarize the key points and main results which will become relevant for the subsequent discussion.…”

“…Here, we shall take this as a motivation to utilize the plethora of wellestablished nonperturbative methods to deal with other quantum field theories where perturbation theory fails, and attempt to derive sensible physical predictions that can hopefully be tested against observations. More detailed accounts on the various issues associated with the theory of quantum gravity can be found for example in [16,17], and references therein.…”

“…For the present discussion, we will mention that the nonperturbative treatment of quantum gravity via Wilson's 2 + ǫ double expansion (in G and the dimension) and the Regge-Wheeler lattice path integral formulation [23] both reveal the existence of a new quantum phase, involving a nontrivial gravitational vacuum condensate [16]. Along with this comes a nonperturbative characteristic correlation length scale, ξ, and a new set of non-trivial scaling exponents, as is common for well-studied perturbatively non-renormalizable theories ν [24][25][26][27][28][29][30][31].…”

“…Together, these two parameters characterize quantum corrections to physical observables such as the long-distance behavior of invariant correlation functions, as well as the renormalization group (RG) running of Newton's constant G, which in coordinate space leads to a covariant G( ) with = g µν ∇ µ ∇ ν [17]. In particular, in can be shown [16,32] that for r < ξ, the correlation functions of the Ricci scalar curvatures over large geodesic separation r ≡ |x − y| scales as…”

“…As a result, it is thus conceivable that these nonperturbative methods may find use in deriving physical consequences of perturbatively nonrenormalizable theories such as gravity. Previous efforts [16,17] have shown that many such effects may manifest themselves and become important on very large cosmological scales. In particular, we found that much of the matter power spectrum can be derived and reproduced from Einstein gravity and standard ΛCDM cosmology alone, utilizing nonperturbative quantum field methods, without the need of additional scalar fields as advocated by inflation.…”