Beyond Standard Model equation of state and primordial black holes

TL;DR

The work investigates how beyond-Standard-Model sectors alter the early-Universe equation of state and, in turn, PBH formation. It develops and applies methods to compute the EoS for MSSM-like SUSY and composite Higgs models, demonstrating that large numbers of extra degrees of freedom can induce sizable drops in the EoS and exponentially enhance PBH abundances. Key results show SUSY scenarios can boost PBHs by up to ~3 orders of magnitude perturbatively, while certain composite-Higgs realizations can yield enhancements up to ~20 orders of magnitude in high-entropy, high-$T$ epochs. The findings imply that PBH populations and their gravitational-wave signatures could serve as probes of high-energy physics scales far beyond current collider reach, linking cosmology to UV completions of the SM.

Abstract

The Standard Model of particle physics successfully describes all known fundamental particles and their interactions; however, it leaves several unanswered questions. Theories beyond the Standard Model typically introduce new particles and symmetries to address these issues. In the early universe, when such particles become non-relativistic, or the symmetries are broken, there are associated reductions in the equation of state of the primordial plasma. These reductions lead to an exponential enhancement in the formation rate of primordial black holes. In this paper, we calculate the equation of state for several supersymmetric and composite Higgs models, which naturally predict a large number of additional degrees of freedom. Using these equations of state, we compute some example primordial black hole abundances, which we find can be enhanced by up to 20 orders of magnitude.

Figures (12)

• Figure 1: The pressure during the SM QCD PT, normalised to the Stefan-Boltzmann limit. At lower temperatures, we use the hadronic gas model. At high temperatures we employ finite-temperature QCD results, up to $\mathcal{O}(g_3^6\ln (1/g_3))$ in the strong coupling constant. During the non-perturbative phase we use lattice data from Borsanyi:2016ksw.
• Figure 2: The equation of state for our toy model, as a function of $T/m_*$, where $m_*$ is some input energy scale. We vary the number of scalars and fermions within the model, showing explicitly the sensitivity of the equation of state to the number of degrees of freedom becoming non-relativistic.
• Figure 3: We show the runnings of several sparticle masses as functions of renormalisation scale, for each of the SUSY breaking scenarios we consider: $Top\space Left:$ TeV-scale, $Top\space Right:$ PeV-scale, $Bottom\space Left:$ Intermediate-scale and $Bottom\space right:$ GUT-scale. We plot the running masses of the gauginos in solid, squarks in dashed and sleptons in dotdashed. As can be seen from the figure, in each of the scenarios we consider, there is not significant running.
• Figure 4: The equation of state for TeV-scale SUSY breaking. We split this into each sparticles contribution, with the largest contribution coming from the squarks.
• Figure 5: The equation of state for each of the SUSY breaking scenarios we considered. We found most of the sparticle mass spectra to be close to degenerate, leading to sharper drops.