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 phi/f(gamma) FF, 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 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 the backreaction numerically. 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 O (20), there is a friction effect which turns on before 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 curvature perturbation on uniform density slices should be sensitive to slow-roll parameters related to rho(R) rather than phi(2)/2 and we discuss the existence of friction terms acting on the perturbations, although we postpone a calculation of the power spectrum and of non-gaussianity to future work and we simply de fine 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) similar to f(G)