1212.3290 (Richard Lieu et al.)

On the density perturbations of pre-inflationary thermal radiation    [PDF]

Richard Lieu, Tom Kibble

The claim of the inflation theory having explained large scale flatness and absence of monopoles and strings is examined from the viewpoint of the observed scales having originated from very small ones, on which the density fluctuations of the curvaton and relics are inevitably of order unity or larger. By analyzing (in two different gauges to ensure consistency) the density evolution of the smoothest possible pre-inflationary component -- radiation -- it is found that the O(1) thermal fluctuations on the thermal wavelength scale (or larger than O(1) for smaller scales, by a quantum calculation) can cause problems to the linear growth theory. Specifically, by the time of horizon exit of this scale the radiation density contrast $\de\rh_r/\rh_r$ has become, {\it by a classical thermodynamic argument} which may not be relevant, an insignificant contribution to the $3H\de\rh/\dot\rh$ term of the conserved parameter $\ze$. Still, this optimistic `way out' would work only if the inflationary vacuum is a cosmological constant: $1+w_v =0$. During the coherent oscillation stage of reheating, however, $1+w_v$ vanishes completely every time the inflaton scalar field reaches its highest point on either side of the potential well, points at which the relic radiation `reclaims' its influence of $3H\de\rh/\dot\rh$ via its $3H\de\rh_r/\dot\rh_r = -3\de\rh_r/(4\rh_r)$ with $\de\rh_r/\rh_r \sim 1$. Since the radiation thermal wavelength scale exited the horizon early, this calls to question the validity of perturbation to the evolution of relic densities. One could avoid the difficulty presented by this `best case scenario' by invoking a {\it dissipating} inflaton during even slow-roll, i.e. scenarios like warm inflation seem to be indispensable.

View original: http://arxiv.org/abs/1212.3290