Can asteroid-mass PBHDM be compatible with catalyzed phase transition interpretation of PTA?

Abstract

Primordial black holes (PBHs) can catalyze first-order phase transitions (FOPTs) in their vicinity, potentially modifying the gravitational wave (GW) signals from PTs. In this study, we investigate the GWs from strong PTs catalyzed by PBHs. We consider high PBH number densities, corresponding to asteroid-mass PBH dark matter (DM) when the GWs from FOPTs peak in the nanohertz band. We calculate the PBH-catalyzed FOPT GWs from both bubble collision GWs and scaler-induced gravitational waves (SIGWs). We find that while low PBH number densities amplify the GW signals due to the formation of large bubbles, high PBH number densities suppress them, as the accelerated phase transition proceeds too rapidly. This suppression renders the signals unable to explain pulsar timing array (PTA) observations. By conducting data fitting with the NANOGrav 15-year dataset, we find that the PBH catalytic effect significantly alters the estimation of PT parameters. Notably, our analysis of the bubble collision GWs reveals that, the asteroid-mass PBHs ($10^{-16} - 10^{-12} M_\odot$) as the whole dark matter is incompatible with the PT interpretation of pulsar timing array signals. However, incorporating SIGWs can reduce this incompatibility for PBHs in the mass range $10^{-14} - 10^{-12} M_\odot$.

Figures (7)

• Figure 1: Left: The nucleation-time-distributions with various given normalized PBH number densities. We have chosen $G_0= 10^{-10}$ and $\beta/H = 1$. For visibility, we plot DiracDelta function by using approximate Guassian function expression. Right: Schematic diagram of PBH-catalyzed PTs. Universe transfered from unstable false vacuum to true vacuum.
• Figure 2: Left: Comparison between the numerical results and the analytical estimations from Eq. \ref{['eq:betaeff']} with $G_0 H^4/\beta^4 = 10^{-8}$. X-coordinate label is $\tilde{n}_{\rm pbh} = n_{\rm pbh} H^3/\beta^3$. We have chosen $F(t_p) = 0.7$. Right: Analytical estimations of $\beta_e/\beta$ in plane ($n_{\rm pbh}$, $\beta$). We have chosen $G_0 = 10^{-10}$.
• Figure 3: GW spectra in various normalized PBH number densities. Here $\tilde{n}=n_{\rm pbh}H^3/\beta^3$ and we have chosen $G_0H^4/\beta^4 =10^{-8}$.
• Figure 4: The comparisons between the bubble collision GWs (dashed line) and SIGWs (dotted line) with various PT inverse durations $\beta/H$. We have chosen $T_{\rm re} = 0.1\ {\rm GeV}$.
• Figure 5: The posterior probability distributions of bubble collision GWs in the analytical model with envelope approximation (yellow contours) and the bulk flow model (purple contours) fitting to the NANOGrav 15-year dataset NANOGrav:2023hdeNANOGrav:2023gorNANOGrav:2023hvmnano_grav_2023_dataset. We have chosen catalytic strength $G_0=10^{-10}$ and denoted $n_{\rm pbh}(0.1\ \mathrm{GeV})$ simply as $n_{\rm pbh}$. For the analytical model with envelope approximation, the $1\sigma,\, 2\sigma,\, \text{and } 3\sigma$ CL regions are depicted in progressively lighter shades of yellow, and for the bulk flow model, the same CL regions are enclosed by solid-, dashed- and dotted-lines. Left: The posterior probability distributions of PT parameters $\beta/H$ and $T_{\rm re}$ for given normalized PBH number densities $n_{\rm pbh}$. Right: The posterior probability distributions of PT parameters $\beta/H,\ T_{\rm re}$ and normalized PBH number densities $n_{\rm pbh}$. On top of each column, we report $1\sigma$ CL ranges.