Saxion Cosmology for Thermalized Gravitino Dark Matter
  In all supersymmetric theories, gravitinos, with mass suppressed by the
Planck scale, are an obvious candidate for dark matter; but if gravitinos ever
reached thermal equilibrium, such dark matter is apparently either too abundant
or too hot, and is excluded. However, in theories with an axion, a saxion
condensate is generated during an early era of cosmological history and its
late decay dilutes dark matter. We show that such dilution allows previously
thermalized gravitinos to account for the observed dark matter over very wide
ranges of gravitino mass, keV < $m_{3/2}$ < TeV, axion decay constant, $10^9$
GeV < $f_a$ < $10^{16}$ GeV, and saxion mass, 10 MeV < $m_s$ < 100 TeV.
Constraints on this parameter space are studied from BBN, supersymmetry
breaking, gravitino and axino production from freeze-in and saxion decay, and
from axion production from both misalignment and parametric resonance
mechanisms. Large allowed regions of $(m_{3/2}, f_a, m_s)$ remain, but differ
for DFSZ and KSVZ theories. Superpartner production at colliders may lead to
events with displaced vertices and kinks, and may contain saxions decaying to
$(WW,ZZ,hh), gg, \gamma \gamma$ or a pair of Standard Model fermions. Freeze-in
may lead to a sub-dominant warm component of gravitino dark matter, and saxion
decay to axions may lead to dark radiation.
