Dissipative Axial Inflation
  We analyze in detail the background cosmological evolution of a scalar field
coupled to a massless abelian gauge field through an axial term
$\frac{\phi}{f_\gamma} F \tilde{F}$, such as in the case of an axion. Gauge
fields in this case are known to experience tachyonic growth and therefore can
backreact on the background as an effective dissipation into radiation energy
density $\rho_R$, which which can lead to inflation without the need of a flat
potential. We analyze the system, for momenta $k$ smaller than the cutoff
$f_\gamma$, including numerically the backreaction. We consider the evolution
from a given static initial condition and explicitly show that, if $f_\gamma$
is smaller than the field excursion $\phi_0$ by about a factor of at least
${\cal O} (20)$, there is a friction effect which turns on before that the
field can fall down and which can then lead to a very long stage of inflation
with a generic potential. In addition we find superimposed oscillations, which
would get imprinted on any kind of perturbations, scalars and tensors. Such
oscillations have a period of 4-5 efolds and an amplitude which is typically
less than a few percent and decreases linearly with $f_\gamma$. We also stress
that the comoving curvature perturbation on uniform density should be sensitive
to slow-roll parameters related to $\rho_R$ rather than $\dot{\phi}^2/2$,
although we postpone a calculation of the power spectrum and of non-gaussianity
to future work and we simply define and compute suitable slow roll parameters.
Finally we stress that this scenario may be realized in the axion case, if the
coupling $1/f_\gamma$ to U(1) (photons) is much larger than the coupling
$1/f_G$ to non-abelian gauge fields (gluons), since the latter sets the range
of the potential and therefore the maximal allowed $\phi_0\sim f_G$.
