Living on the Fermi Edge: On Baryon Transport and Fermi Condensation

TL;DR

This paper uncovers a surprising link between baryon transport in the universe and Fermi gas physics, revealing critical temperatures and potential condensation phenomena influencing cosmic structure formation.

Contribution

It introduces a novel analogy between baryon transfer functions and Fermi gas transport, identifying quantized critical temperatures related to cosmological cutoffs and structure seeding.

Findings

Transport function matches Fermi gas behavior at different redshifts

Identifies quantized critical temperatures dependent on a cutoff scale

Suggests Fermi condensation may seed small-scale cosmic structures

Abstract

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.