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.
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