Prospects for Primordial Gravitational Waves in String Inflation
  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
$M_{inf} < m_{kk} < m_s \lesssim M_{pl}$ 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 $\lesssim 0.2$, implies $r \lesssim 0.05$, but asking more safely
for hierarchies $\lesssim 0.1$, the bound becomes $r \lesssim 10^{-6}$.
Moreover, large volumes -- typically used in string models to keep backreaction
and moduli stabilisation under control -- drive $r$ down. Consequently, any
detection of inflationary gravitational waves would present an interesting but
difficult challenge for string theory.
