At what energy does gravity unite with grand unified theories in the early universe?

Abstract

Unification of gravity with GUTs is usually expected at the Planck energy E pl≈10/sup19 GeV. However, the vastly different values of the two couplings at E Pl ( α GUT« 1, α grav≈ 1) would make such unity (at E Pl) implausible unless there is a drastic change in the behavior of either gravity or GUTs around E Pl. We picture gravity and GUTs to be unified at energies >EPl with a single dimensionless coupling constant ( α U « 1) and described by a scale-invariant action quadratic in the Weyl curvature (with Yang-Mills fields). Breaking of scale invariance at E Pl then separates the interactions into gravity, now described by a Hilbert action with a dimensional G and GUTs woth a dimensionless α GUT and YM action. Problems with Klein-Kaluza unification of gravity with GUTs are also discussed in this context.