  A characteristic signature of String Gas Cosmology is primordial power
spectra for scalar and tensor modes which are almost scale-invariant but with a
red tilt for scalar modes but a blue tilt for tensor modes. This feature,
however, can also be realized in the so-called G-inflation model, in which
Horndeski operators are introduced which leads to a blue tensor tilt by softly
breaking the Null Energy Condition. In this article we search for potential
observational differences between these two cosmologies by performing detailed
perturbation analyses based on the Effective Field Theory approach. Our results
show that, although both two models produce blue tilted tensor perturbations,
they behave differently in three aspects. Firstly, String Gas Cosmology
predicts a specific consistency relation between the index of the scalar modes
ns and that of tensor ones nt, which is hard to be reproduced by G-inflation.
Secondly, String Gas Cosmology typically predicts non-Gaussianities which are
highly suppressed on observable scales, while G-inflation gives rise to
observationally large non-Gaussianities because the kinetic terms in the action
become important during inflation. However, after finely tuning the model
parameters of G-inflation it is possible to obtain a blue tensor spectrum and
negligible non-Gaussianities with a degeneracy between the two models. This
degeneracy can be broken by a third observable, namely the scale dependence of
the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt
in the case of String Gas Cosmology. Therefore, we conclude that String Gas
Cosmology is in principle observationally distinguishable from the single field
inflationary cosmology, even allowing for modifications such as G-inflation.
