Cosmological Impacts of Black Hole Mergers: No Relief in Sight for the Hubble Tension

TL;DR

The paper investigates whether converting matter to gravitational radiation through black hole mergers can alleviate the Hubble tension between local $H_0$ measurements and CMB inferences. By modeling energy transfer with a fixed conversion efficiency and a comoving merger/formation rate, and fitting late-time $H(z)$, it finds that plausible merger scenarios cannot relieve the tension: SMBH and stellar-mass mergers require unrealistically large rates, while SMBH formation from smaller BH mergers demands extreme overproduction of SMBHs; the ISW effect is too small to constrain such channels. These results imply that merger-induced radiation is not a viable solution, potentially pointing toward new physics beyond $\\\ ext{\Lambda CDM}$ to resolve the tension.

Abstract

The values of the Hubble constant inferred from local measurements and the cosmic microwave background (CMB) exhibit an approximately 5 sigma tension. Some have suggested this tension is alleviated if matter is converted to dark radiation via dark matter decay. As it is not clear that dark matter decays, we instead examine the effects of converting matter to gravitational radiation via black hole mergers. We consider mergers of supermassive black holes (SMBHs), mergers of stellar-mass black holes, and the formation of SMBHs from mergers of smaller black holes. We find that these processes cannot alleviate the tension, as an unrealistically large merger rate, or an overproduction of SMBHs is required. We also consider whether one can use the Integrated Sachs-Wolfe effect to constrain mechanisms that form SMBHs from mergers of smaller black holes. We find that this is also too small to be viable.

Figures (9)

• Figure 1: Here we plot the comoving SMBH formation rate in units of $\rm{Gpc}^{-3} yr^{-1}$, that results in a number density of $10^6$ SMBHs per $\rm{Gpc}^{3}$ at $z=0$.
• Figure 2: Here we show the evolution of the Hubble parameter with redshift, with and without SMBH mergers, with the best-fit comoving merger rate of around 2600 $\rm{Gpc}^{-3} \rm{yr}^{-1}$. This is unreasonably large, making this mechanism for alleviating the tension non-viable.
• Figure 3: Here we show the fractional change of the Hubble parameter with SMBH mergers as compared to the case without mergers. This is using the best-fit comoving merger rate of around 2600 $\rm{Gpc}^{-3} \rm{yr}^{-1}$. One can readily see that the case with mergers has a larger Hubble parameter at late times.
• Figure 4: Here we show the fractional change of the Hubble parameter (with a more realistic SMBH merger rate, here approximated as a constant $10^{-4}$$\rm{Gpc}^{-3} \rm{yr}^{-1}$) as compared to the case without mergers. To isolate the effects of the mergers from the effects of varying $h_i$, for this plot, we fix $h_{i} = 0.674$, yielding $\Omega_{m_{initial}} \approx \Omega_m(z=0) \approx 0.313$. We have plotted the fractional change in the Hubble parameter rather than $\rm{H(z)}$ because the effect is so small that it would be invisible on an $\rm{H(z)}$ plot.
• Figure 5: Here we show the evolution of the Hubble parameter with redshift, with and without SMBH formation from PBHs, with the best-fit comoving formation rate. This best-fit rate can alleviate the Hubble tension, but overproduces SMBHs by three to four orders of magnitude.