Constraints on planet formation via gravitational instability across
  cosmic time
  We estimate the maximum temperature at which planets can form via
gravitational instability (GI) in the outskirts of early circumstellar disks.
We show that due to the temperature floor set by the cosmic microwave
background, there is a maximum distance from their host stars beyond which gas
giants cannot form via GI, which decreases with their present-day age.
Furthermore, we show that planet formation via GI is not possible at
metallicities < 10^-4 Z_Sun, due to the reduced cooling efficiency of
low-metallicity gas. This critical metallicity for planet formation via GI
implies a minimum distance from their host stars of ~ 6 AU within which planets
cannot form via GI; at higher metallicity, this minimum distance can be
significantly greater, out to several tens of AU. We show that these maximum
and minimum distances significantly constrain the number of observed planets to
date that are likely to have formed via GI at their present locations. That
said, the critical metallicity we find for GI is well below that for core
accretion to operate; thus, the first planets may have formed via GI, although
only within a narrow region of their host circumstellar disks.
