Primordial black holes with an accurate QCD equation of state (1801.06138v2)

Abstract: Making use of definitive new lattice computations of the Standard Model thermodynamics during the quantum chromodynamic (QCD) phase transition, we calculate the enhancement in the mass distribution of primordial black holes (PBHs) due to the softening of the equation of state. We find that the enhancement peaks at approximately $0.7M_\odot$, with the formation rate increasing by at least two orders of magnitude due to the softening of the equation of state at this time, with a range of approximately $0.3M_\odot<M<1.4M_\odot$ at full width half-maximum. PBH formation is increased by a smaller amount for PBHs with masses spanning a large range, $10^{-3}M_\odot<M_{\rm PBH}<10^{3}M_\odot$, which includes the masses of the BHs that LIGO detected. The most significant source of uncertainty in the number of PBHs formed is now due to unknowns in the formation process, rather than from the phase transition. A near scale-invariant density power spectrum tuned to generate a population with mass and merger rate consistent with that detected by LIGO should also produce a much larger energy density of PBHs with solar mass. The existence of BHs below the Chandresekhar mass limit would be a smoking gun for a primordial origin and they could arguably constitute a significant fraction of the cold dark matter density. They also pose a challenge to inflationary model building which seek to produce the LIGO BHs without overproducing lighter PBHs.

Primordial Black Holes with an Accurate QCD Equation of State

The paper explores the implications of the Quantum Chromodynamic (QCD) phase transition on the formation and mass distribution of primordial black holes (PBHs). Utilizing contemporary lattice computations, which provide an accurate description of the thermodynamics of the Standard Model during this transition, the authors seek to quantify the enhancement of PBH formation due to softening in the equation of state during the QCD phase transition.

Key Findings

The research reveals that the equation of state parameter $\omega = p/\rho$ decreases by approximately 30% during the QCD phase transition, leading to a significant enhancement in PBH formation. Specifically, the formation rate at the QCD transition increases by at least two orders of magnitude, with a peak mass distribution occurring around $0.7 M_\odot$. The full width at half maximum spans the mass range $0.3 M_\odot < M < 1.4 M_\odot$. This transition period results in increased PBH formation across a broader mass spectrum, ranging from $10^{-3} M_\odot$ to $10^3 M_\odot$, which includes masses for black holes that LIGO has detected.

Implications and Challenges

The significant increase in PBH formation near the QCD phase transition implies potential observational consequences, such as the existence of solar mass PBHs and the possibility that PBHs could account for a substantial fraction of cold dark matter. Additionally, detecting black holes with masses below the Chandrasekhar limit could serve as definitive evidence for their primordial origin.

This surge in PBH formation poses challenges for inflationary models that aim to generate PBHs without overproducing lighter PBHs. The paper contends that the softening of the equation of state prompts a reconsideration of PBH mass distributions in current models, emphasizing the need for a sharply peaked primordial power spectrum to avoid conflicts with observational constraints.

Speculation on Future Developments

The findings underscore the necessity for more refined numerical simulations to accurately predict PBH formation rates during phase transitions with time-varying equations of state. This could lead to a deeper understanding of the impact of various cosmological phase transitions on PBH formation. Moreover, integration of this QCD equation of state into broader models could refine predictions related to PBH as candidates for dark matter.

Conclusion

By using lattice QCD results, the authors provide a more comprehensive view on the influence of the QCD phase transition on PBH formation. Their work suggests a reinforcement of the PBH mass distribution at solar masses, making a compelling case for further exploration for observational manifestations and theoretical developments in the field of primordial cosmology. This paper reiterates the importance of accurately modeling the QCD phase transition to further elucidate the nature of the Universe's earliest epochs and its implications on contemporary astrophysical phenomena.