Validity of the effective field theory for sharply varying warp-factor parameters

Determine whether the effective field theory description remains valid for heterotic SO(32) de Sitter Glauber–Sudarshan states with a rapidly varying parameter \(\beta(t)\), particularly when \(|\dot{\beta}(t)|\gg 1\), by establishing whether the associated exponent \(\mathrm{B}(t)\) satisfies the required effective-field-theory bound.

Background

In the heterotic SO(32) analysis, the time-dependent warp-factor exponent $\beta(t)$ modifies the derivative of the effective string coupling. The effective field theory criterion depends on the sign and magnitude of a derived function $\mathrm{B}(t)$, which in turn depends on the precise value of $|\dot{\beta}(t)|$.

For sufficiently smooth choices of $\beta(t)$, the thesis later exhibits an ansatz satisfying the effective-field-theory constraint throughout the TCC interval. However, the sharply varying regime is explicitly left indeterminate in the cited passage.