GUTs in Curved Spacetime: Running Gravitational Constants, Newtonian Potential and the Quantum Corrected Gravitational Equations

TL;DR

This paper investigates how quantum effects in grand unified theories (GUTs) influence gravitational constants, the Newtonian potential, and gravitational equations in curved spacetime, revealing logarithmic corrections and non-singular solutions.

Contribution

It introduces a framework for calculating quantum corrections to gravity in GUTs, including the construction of an asymptotically free GUT with higher-derivative gravity and deriving RG equations.

Findings

Quantum GUT corrections to Newtonian potential are logarithmic.

Constructed a totally asymptotically free GUT with higher-derivative gravity.

Derived and numerically solved RG equations for gravitational couplings.

Abstract

The running coupling constants (in particular, the gravitational one) are studied in asymptotically free GUTs and in finite GUTs in curved spacetime, with explicit examples. The running gravitational coupling is used to calculate the leading quantum GUT corrections to the Newtonian potential, which turn out to be of logarithmic form in asymptotically free GUTs. A comparison with the effective theory for the conformal factor ---where leading quantum corrections to the Newtonian potential 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 gravitational couplings in this theory are derived, and solved numerically, showing the influence of higher-derivative quantum gravity on the Newtonian potential. The RG-improved effective gravitational Lagrangian for asymptotically free massive GUTs is calculated in the strong (almost constant) curvature regime, and the non-singular De Sitter solution to the quantum corrected gravitational equations is subsequently discussed. Finally, possible extensions of the results here obtained are briefly outlined.