Nonperturbative renomalization group for Einstein gravity with matter

we investigate the exact renormalization group (RG) in Einstein gravity coupled to N-component scalar field, working in the effective average action formalism and background field method. The truncated evolution equation is obtained for the Newtonian and cosmological constants. We have shown that screening or antiscreening behaviour of the gravitational coupling depends cricially on the choice of scalar-gravitational ξ and the number of scalar fields. There has recently been much activity in the study of nonperturvative RG dynamics in field theory models ( for recent references, see [1] ). One of the versions of nonpertubative RG based on the effective average action has been developed in ref.[2] for Einstein gravity ( the gauge dependence problem in this formalism has been studied in ref. [3] ) and in [4] for gauged supergravity. The nonperturbative RG equation for cosmological and Newtonian coupling constants have been obtained in ref.[2] for the Einstein gravity and in ref [5] for R gravity. The comparison between quantum correction to Newtonian coupling from nonperturvative RG [2] and from effective field theory technique [6] has been done. It is quite interesting to study nonperturbative RG ( or evolution equation ) for the gravity coupled to N-component scalar field in orden to evaliate the influence of the scalar coupling and the number of scalar in the nonperturbative behaviour of the Newtonian and cosmological constants. We follow the formalism of ref. [2] developed for gravitational theories. The basic elements of it are the background field method ( see [7] for a review ) and the truncated nonperturbative evolution equation for the effective average action [2]. We will start from the theory with the following action. S = ∫ dx √−g [ 1 16πḠ ( −R+ 2λ ) + 1 2 ∂μφ ∂φi + 1 2 ξRφφi ] , (1) e-mail: [email protected]