摘要：We review the status of the fourth-order (quartic in the spacetime curvature) terms induced by superstrings/M-theory (compactified on a warped
torus) in the leading order with respect to the Regge slope parameter, and
study their (nonperturbative) impact on the evolution of the Hubble scale
in the context of the four-dimensional FRW cosmology. After taking into
account the quantum ambiguities in the definition of the off-shell superstring
effective action, we propose the generalized Friedmann equations, find the
existence of their (de Sitter) exact inflationary solutions without a spacetime
singularity, and constrain the ambiguities by demanding stability and
the scale factor duality invariance of our solutions. The most naive (Bel-Robinson tensor squared) quartic terms are ruled out, thus giving the evidence
for the necessity of extra quartic (Ricci tensor-dependent) terms in
the off-shell gravitational effective action for superstrings. Our methods are
generalizable to the higher orders in the spacetime curvature.
