E. Elizalde et al., GUTS IN CURVED SPACETIME - RUNNING GRAVITATIONAL CONSTANTS, NEWTONIANPOTENTIAL, AND THE QUANTUM-CORRECTED GRAVITATIONAL EQUATIONS, Physical review. D. Particles and fields, 52(4), 1995, pp. 2202-2213
The running coupling constants (in particular, the gravitational one)
are studied in asymptotically free GUT's and in finite GUT's in curved
spacetime, with explicit examples. The running gravitational coupling
is used to calculate the leading quantum GUT corrections to the Newto
nian potential, which turn out to be of logarithmic form in asymptotic
ally free GUT's. A comparison with the effective theory for the confor
mal factor, where leading quantum corrections to the Newtonian potenti
al are again logarithmic, is made. A totally asymptotically free O(N)
GUT with quantum higher derivative gravity is then constructed, using
the technique of introducing renormalization group (RG) potentials in
the space of couplings. RG equations for the cosmological and gravitat
ional couplings in this theory are derived, and solved numerically, sh
owing the influence of higher-derivative quantum gravity on the Newton
ian potential. The RG-improved effective gravitational Lagrangian for
asymptotically free massive GUT's is calculated in the strong (almost
constant) curvature regime, and the nonsingular de Sitter solution to
the quantum-corrected gravitational equations is subsequently discusse
d. Finally, possible extensions of the results here obtained are brief
ly outlined.