Creating Spatial Flatness by Combining String Gas Cosmology and Power
  Law Inflation
  We show that it is possible to combine an early phase of String Gas Cosmology
which can explain the origin of the observed structures on cosmological scales
with a short later period of power law inflation which creates spatial
flatness. The resulting model is consistent with the ``swampland criteria'' and
the constraints coming from the {\it Trans-Planckian Censorship Conjecture}.
Such a construction is not possible using only canonical slow-roll inflation,
but it can emerge in the warm inflation scenario or in cold inflation with an
exponential potential. The resulting cosmology is non-singular. We discuss the
spectrum of cosmological perturbations resulting in our scenario. On large
scales (scales which remain larger than the Hubble radius after the initial
string gas phase) the spectrum is determined by the thermal string gas
fluctuations set up in the primordial phase, and it is almost scale-invariant
with a slight red tilt. On small scales, the perturbations produced during the
inflationary phase dominate. On these scales, the spectrum is once again nearly
scale-invariant. There is an intermediate range (scales which enter the Hubble
radius during the period of inflation) where the string gas fluctuations are
damped but continue to dominate over those produced during the period of
inflation. On these scales the spectrum has a sharp red spectral index of $n_s
- 1 \sim -2$.
