Two-loop quantum gravity corrections to the cosmological constant in Landau gauge

Abstract

The anomalous dimensions of the Planck mass and the cosmological constant are calculated in a renormalizable quantum conformal gravity with a single dimensionless coupling, which is formulated using dimensional regularization on the basis of Hathrell's works for conformal anomalies. The dynamics of the traceless tensor field is handled by the Weyl action, while that of the conformal-factor field is described by the induced Wess-Zumino actions, including the Riegert action as the kinetic term. Loop calculations are carried out in Landau gauge in order to reduce the number of Feynman diagrams as well as to avoid some uncertainty. Especially, we calculate two-loop quantum gravity corrections to the cosmological constant. It suggests that there is a dynamical solution to the cosmological constant problem.

Physical cosmological constant in asymptotically background-free quantum gravity

“…The first two terms have been calculated explicitly as χ 1 = 1/2 and χ 2 = 3/4 [37,12]. 2 We have then shown that these are universal values independent of the gauge group and the contents of matter fields as far as they are conformally coupled.…”

“…5 No coupling constant thus implies that there is no field-renormalization factor. This is one of the most significant proper- 4 This nonrenormalization theorem has been demonstrated explicitly in loop calculations of higher order [10,11,12].…”

“…In order to settle such ambiguities, we have recently analyzed Hathrell's RG equations for quantum field theories with conformal couplings in curved space [34,35,36]. We then found that the ambiguities disappear and the D dependence of the gravitational action can be determined at all orders [37,12]. The renormalizable quantum gravity has been defined by using this action, because it should reduce to the curved theory in the classical limit of gravity such as the large number limit of matter fields.…”

“…First, we briefly summarize recent developments of the renormalizable quantum field theory of conformal gravity with adding the Einstein-Hilbert action and the cosmological constant term [11,12]. The theory has been formulated using dimensional regularization.…”

“…In those days, however, one could not avoid the problem that the negative-metric mode emerges as a gauge-invariant mode as far as one dealt with all gravitational fields perturbatively. 1 To further resolve the ghost problem, we constructed renormalizable quantum conformal gravity several years ago [10,11,12] by applying a nonperturbative method learned from the development of two-dimensional quantum gravity [13,14,15,16,17,18]. The conformal factor of the metric field is treated exactly without introducing a coupling constant for it [19,20,21,22,23,24,25], and as a result the theory has Becchi-Rouet-StoraTyutin (BRST) conformal symmetry in the UV limit, which represents the background-free property of quantum gravity as a gauge equivalency under conformal transformations [26,27].…”