  The transfer function of the baryon power spectrum from redshift $z\approx
1100$ to today has recently been, for the first time, determined from data by
Pardo and Spergel. We observe a remarkable coincidence between this function
and the transport function of a cold ideal Fermi gas at different redshifts.
Guided by this, we unveil an infinite set of critical temperatures of the
relativistic ideal Fermi gas which depend on a very finely quantized
long-distance cutoff. The sound horizon scale of Baryon Acoustic Oscillations
(BAO) seems to set such a cutoff, which dials a critical temperature that is
subsequently reached during redshift. At the critical point the Fermi gas
becomes scale invariant and may condense to subsequently undergo gravitational
collapse, seeding small scale structure. We mention some profound implications
including the apparent quantization of Fermi momentum conjugate to the cutoff
and the corresponding "gapping" of temperature.
