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

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.

Figure 1

The GW spectra from bubble collisions (black, solid lines) and from MHD turbulence (red, dashed lines) 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 $\beta =10{\mathcal{H}}_{*}$ and $T_{*}=100\mathrm{MeV}$ throughout.

Figure 2

The GW signal from bubble collisions and MHD turbulence for ${\Omega }_{S*}=0.1$ and $v=0.7$. We choose $\beta =10{\mathcal{H}}_{*}$. 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 [5]. 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 ${\mathcal{H}}_{*}/\beta =1$, 0.5, 0.2, and 0.1 (dashed lines from top to bottom). For ${\mathcal{H}}_{*}/\beta \sim 1$, the background of GWs can just be detected in present pulsar timing experiments, while for $0.1\lesssim {\mathcal{H}}_{*}/\beta$ it can be detected by the planned array IPTA2020 (very high values of ${\mathcal{H}}_{*}/\beta \sim 1$ are difficult to accommodate in the case of a thermally nucleated phase transition, cf. discussion in the text). We also show the LISA sensitivity [52, 53]. Unfortunately, LISA will not be able to detect a signal from a first order QCD phase transition (the electroweak phase transition is more promising in this respect [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 44, 46]).

Figure 4

Same as Fig. 3 but comparing the characteristic strain $h_c$ as given by Eq. (7).