Detection of gravitational waves from the QCD phase transition with pulsar timing arrays

TL;DR

This work investigates whether a strongly first-order cosmological QCD phase transition could produce a detectable stochastic gravitational-wave background in the nano-Hz band accessible to pulsar timing arrays. Using analytic fits for GW production from bubble collisions and MHD turbulence, and adopting an equipartition energy assumption with fixed $T_*\simeq 100~\mathrm{MeV}$ and $\beta=10\mathcal{H}_*$, the authors predict spectra in which MHD turbulence typically dominates and yields a peak at $f_p$ on the order of $10^{-7}$ Hz. The detectability of such a background depends on the ratio $\mathcal{H}_*/\beta$; for values around $0.1$–$1$ current and planned PTAs could observe the signal, while LISA is unlikely to detect it. A positive PTA detection would illuminate the nature of the QCD phase transition and the neutrino sector in the early Universe, potentially constraining the expansion rate at $T_*\sim 100$ MeV and related cosmological parameters.

Abstract

If the cosmological QCD phase transition is strongly first order and lasts sufficiently long, it generates a background of gravitational waves which may be detected via pulsar timing experiments. We estimate the amplitude and the spectral shape of such a background and we discuss its detectability prospects.

Figures (4)

• Figure 1: The GW spectra from bubble collisions (black, solid) and from MHD turbulence (red, dashed) are shown for different values of $\Omega_{S*}=0.1$ and $v=0.7$ (top panel) and $\Omega_{S*}=0.03$ and $v=0.57\simeq c_s$ (bottom panel). We set $\beta=10\,{\cal H}_*$ and $T_*=100$ MeV throughout.
• Figure 2: The GW signal from bubble collisions and MHD turbulence for $\Omega_{S*}=0.1$ and $v=0.7$. We choose $\beta=10\, {\cal H}_*$. The signal is dominated by the contribution from MHD turbulence. The bubble collision peak causes the hump on the left of the true peak of the spectrum.
• Figure 3: Comparison of the GW spectrum $h^2\Omega(f)$ with current NANOGrav pulsar timing array sensitivity and expected sensitivity of pulsar timing experiments in 2020 Demorest:2009ex. We have used $h=0.73$, $\Omega_{r0}=8.5\times 10^{-5}$, $\Omega_{S*}=0.1$ and $v=0.7$. We plot the GW spectra for the values ${{\cal H}_*}/{\beta}=1,~0.5,~0.2,~0.1$ (dashed lines from top to bottom). For ${{\cal H}_*}/{\beta} \sim 1$, the background of GWs can just be detected in present pulsar timing experiments, while for $0.1\lesssim {{\cal H}_*}/{\beta}$ it can be detected by the planned array IPTA2020 (very high values of ${{\cal H}_*}/{\beta}\sim 1$ are difficult to accommodate in the case of a thermally nucleated phase transition, c.f. discussion in the text). We also show the LISA sensitivity lisa1lisa2. Unfortunately, LISA will not be able to detect a signal from a first order QCD phase transition (the EW phase transition is more promising in this respect Kos92Kos93KKTapredaapreda2HuKo2HuKobubbleCRTGhogan832Kos02dolgovCRgogobTHelicalTHelical2CRGRnicolis).
• Figure 4: Same as Fig. \ref{['f:omega']} but comparing the characteristic strain $h_c$ as given by Eq. (\ref{['eq:hc']}).