Self-resonance after inflation: oscillons, transients and radiation
  domination
  Homogeneous oscillations of the inflaton after inflation can be unstable to
small spatial perturbations even without coupling to other fields. We show that
for inflaton potentials $\propto |\phi|^{2n}$ near $|\phi|=0$ and flatter
beyond some $|\phi|=M$, the inflaton condensate oscillations can lead to
self-resonance, followed by its complete fragmentation. We find that for
non-quadratic minima ($n>1$), shortly after backreaction, the equation of state
parameter, $w\rightarrow1/3$. If $M\ll m_{pl}$, radiation domination is
established within less than an e-fold of expansion after the end of inflation.
In this case self-resonance is efficient and the condensate fragments into
transient, localised spherical objects which are unstable and decay, leaving
behind them a virialized field with mean kinetic and gradient energies much
greater than the potential energy. This end-state yields $w=1/3$. When $M\ll
m_{pl}$ we observe slow and steady, self-resonace that can last many {\it
e}-folds before backreaction eventually shuts it off, followed by fragmentation
and $w\rightarrow 1/3$. We provide analytical estimates for the duration to
$w\rightarrow 1/3$ after inflation, which can be used as an upper bound (under
certain assumptions) on the duration of the transition between the inflationary
and the radiation dominated states of expansion. This upper bound can reduce
uncertainties in CMB observables such as the spectral tilt $n_{\rm{s}}$, and
the tensor-to-scalar ratio $r$. For quadratic minima ($n=1$), $w\rightarrow0$
regardless of the value of $M$.
