Abstract
Assuming that the early universe had (i) a description using perturbative string theory and its field theory limit, (ii) an epoch of slow-roll inflation within a four-dimensional effective field theory and a hierarchy of scales [Formula: see text] that keeps the latter under control, we derive an upper bound on the amplitude of primordial gravitational waves. The bound is very sensitive to mild changes in numerical coefficients and the expansion parameters. For example, allowing couplings and mass-squared hierarchies [Formula: see text] implies [Formula: see text], but asking more safely for hierarchies [Formula: see text], the bound becomes [Formula: see text]. Moreover, large volumes — typically used in string models to keep backreaction and moduli stabilization under control — drive [Formula: see text] down. Consequently, any detection of inflationary gravitational waves would present an interesting but difficult challenge for string theory.
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