Some inequalities bridging stringy parameters and cosmological
  observables
  By demanding the validity of an effective field theory description during
inflation, in this note we derive some peculiar inequalities among the three
interesting stringy and cosmological parameters, namely the tensor-to-scalar
ratio ($r$), the string coupling ($g_s$) and the compactification volume
(${\cal V}$). In deriving these inequalities, we explicitly demand that the
inflationary scale and the Hubble parameter during inflation are well below the
Kaluza-Klein (KK) mass scale, string scale, and the four dimensional Planck
mass. For the inflationary models developed within the framework of type IIB
orientifold comapctification, we investigate the regions of parameters space
spanned by the three parameters $(r, g_s, {\cal V})$ by satisfying our
inequalities, and we find that the same can reduce the size of available
parameter space quite significantly. Moreover, we comment on obtaining further
constraints on the parameters by comparing gravitino mass ($m_{3/2}$) with the
Hubble scale ($H$), which also provides a lower bound on tensor-to-scalar ratio
($r$), for the cases when $m_{3/2} <H$. We also illustrate the outcome of our
bounds in some specific class of string(-inspired) models.
