String Cosmology - Large-Field Inflation in String Theory
  This is a short review of string cosmology. We wish to connect string-scale
physics as closely as possible to observables accessible to current or
near-future experiments. Our possible best hope to do so is a description of
inflation in string theory. The energy scale of inflation can be as high as
that of Grand Unification (GUT). If this is the case, this is the closest we
can possibly get in energy scales to string-scale physics. Hence, GUT-scale
inflation may be our best candidate phenomenon to preserve traces of
string-scale dynamics. Our chance to look for such traces is the primordial
gravitational wave, or tensor mode signal produced during inflation. For
GUT-scale inflation this is strong enough to be potentially visible as a B-mode
polarization of the cosmic microwave background (CMB). Moreover, a GUT-scale
inflation model has a trans-Planckian excursion of the inflaton scalar field
during the observable amount of inflation. Such large-field models of inflation
have a clear need for symmetry protection against quantum corrections. This
makes them ideal candidates for a description in a candidate fundamental theory
like string theory. At the same time the need of large-field inflation models
for UV completion makes them particularly susceptible to preserve imprints of
their string-scale dynamics in the inflationary observables, the spectral index
$n_s$ and the fractional tensor mode power $r$. Hence, we will focus this
review on axion monodromy inflation as a mechanism of large-field inflation in
string theory.
