  According to a variant of the hoop conjecture, if we localize two particles
within the Schwarzschild radius corresponding to their center of mass energy,
then a black hole will form. Despite a large body of work on the formation of
primordial black holes, so far this conjecture has not been generalized to
expanding spacetimes. We derive a formula which gives the distance within which
two particles must be localized to give a black hole, and which crucially
depends on the expansion rate of the background space. In the limit of a very
slow expansion, we recover the flat spacetime case. In the opposite limit of
the large expansion rate when the inverse Hubble radius is smaller than the
Schwarzschild radius of a "would be" black hole, the new critical distance
between two particles that can make a black hole becomes equal to the particle
horizon, which is just a requirement that the particles are in a causal
contact. This behavior also nicely illustrates why the Big Bang singularity is
not a black hole. We then use our formula to calculate the number density,
energy density and production rate of black holes produced in collisions of
particles. We find that though black holes might be numerous at high
temperatures, they never dominate over the background radiation below the
Planck temperature.
