Recombination induced thermodynamic Gaussian cosmological baryonic
  fluctuations
  In some instances, e.g. near phase transitions, thermodynamic fluctuations
become macroscopically relevant, and relative amplitudes grow far above the
standard $N^{-1/2}$ scale, with $N$ the number of particles. Such large
fluctuations are characterised by a scale invariant Gaussian power spectrum. In
this letter I show that the abrupt drop in the baryonic sound speed across
recombination leads to conditions resulting in such large thermodynamic
Gaussian fluctuations in the ionisation fraction of the baryons. Under pressure
equilibrium, this will result in a mechanism for generating scale invariant
density and temperature fluctuations in the baryonic component, inherent to the
thermodynamics of the baryons themselves. Within a $\Lambda$CDM framework, this
extra random fluctuation source leads to a decoupling of the inflationary relic
small wave number spectrum and the amplitude of the Gaussian random
fluctuations at frequencies higher than the first acoustic peak, an effect
which could explain the mismatch between cosmic microwave background (CMB)
inferences and local kinetic determinations of the Hubble constant. Within
modified gravity theories in absence of dark matter, the mechanism proposed
serves as a source for random Gaussian density fluctuations in the acoustic
peak region.
