### Instructions and notes for Cosmology Calculator

Unless otherwise specified, all quantities are presented in natural Planck units.

The earliest time for which the Calculator may be used is the Planck time.

The lower bound on the particle horizon integral is the Planck time.

The "pseudo particle horizon" is calculated in the same manner as the particle horizon, but the lower bound on the associated integral is the end of inflation.

**Black hole population**:

The calculator is capable of introducing a population of identical black holes, which may represent, for instance, the observed population of supermassive black holes. (The default initial mass is of order near the mass of a typical supermassive black hole.) The formation of the black holes is modeled by a smooth, relatively rapid increase in the mass of each black hole just before the formation era, which is defined when the apparent horizon is somewhat larger than the user-specified initial horizon (being twice the mass). After that, the mass decreases according to the usual Hawking radiation prescription.