Cosmic Molasses: How Viscosity Changes the Rules of Primordial Black Hole Birth ✛ ✎ ✦

In the search for the nature of dark matter, one of the most intriguing hypotheses traces back to the first moments after the Big Bang. Back then, quantum fluctuations of the inflation field gave rise to clumps of matter that could collapse into primordial black holes. Since the time of Stephen Hawking, the primordial plasma was usually treated as a perfect fluid — flowing and devoid of internal friction. But reality might have been different: instead of water — a thick molasses, where every motion meets resistance. It is precisely this 'viscosity' of the Universe and its role in black hole birth that has been assessed for the first time in a full numerical experiment.

A group of researchers applied the BSSN formalism of general relativity along with the equations of Eckart's viscous hydrodynamics to track the fate of overdense regions in the expanding Universe. The result is clear: the higher the viscosity, the harder it is for gravity to cause a clump to collapse. Mathematically, this is expressed in an effective equation of state for the background fluid: \( w_{\text{eff}} = w - \epsilon \sqrt{24\pi} \). The parameter ε is a measure of the medium's 'stickiness'. When it grows, pressure drops, the gas becomes softer, but simultaneously internal friction increases. Sound waves can no longer easily stabilize the perturbation, and a larger initial density contrast is required to trigger collapse. The shift in the critical amplitude µ_c follows a simple linear dependence: \(\mu_c - \mu_{c,0} = K \epsilon^\Gamma\), where Γ ≈ 1 and K is of order unity. This echoes classical Jeans instability: dissipation slows contraction, and gravity must overcome additional resistance — much like how James Jeans once showed the role of pressure in counteracting compression.

Beyond raising the threshold, viscosity also changes the mass of the resulting black holes. Near critical collapse, the mass obeys the scaling law \( M_{\text{PBH}} / M_H = k |\mu - \mu_c|^\gamma \). Viscosity increases the amplitude k (for example, from 8.30 to 10.22 for one perturbation profile), while weakly affecting the exponent γ. In other words, gravitational contraction in molasses produces more massive holes for the same relative deviations from the threshold. The mass function shifts toward larger values, directly impacting the interpretation of gravitational microlensing data and the stochastic gravitational wave background.

The obtained result is not just a refinement. It indicates that to make reliable predictions of the abundance of primordial black holes as candidates for dark matter, one must account for the non-ideality of the primordial plasma. Moreover, viscosity softens the background equation of state, which perhaps sheds light on the Hubble tension — the puzzling discrepancy in measurements of the Universe's expansion rate. In the future, modeling with more realistic second-order viscosity (Israel–Stewart theory) and including anisotropy will allow computation of the spins and ellipticities of newborn black holes, building a bridge between the microphysics of collapse and large-scale cosmology. Perhaps the 'stickiness' of the early Universe will turn out to be the key to unraveling the mystery of dark matter and the fate of cosmic expansion.