Signatures from pion condensation and lepton flavor asymmetries in the cosmological gravitational wave background

Abstract

Large lepton flavor asymmetries at the QCD epoch could generate a pion condensation phase in the early Universe. For large enough tau lepton flavor asymmetries, the speed of sound can exceed the conformal value, leaving a distinctive imprint on the low-frequency gravitational wave (GW) spectrum from causal sources. Beyond probing the formation of a pion condensation phase, the detection or non-detection of this signature would provide a novel constraint on lepton asymmetries in the early Universe. We estimate the GW signal and compare it with the standard case of vanishing lepton asymmetry. Finally, we discuss the implications for the stochastic GW background reported by Pulsar Timing Arrays, using the NANOGrav 15-year dataset.

Figures (5)

• Figure 1: A schematic cartoon showcasing how the cosmic trajectory could enter a region with a speed of sound surpassing the conformal value. The QCD phase diagram shown in the background is adapted from Ref.Brandt:2022hwy and is based on Lattice QCD simulations.
• Figure 2: EoS parameter $w$ for different equations of state. The orange and red lines correspond to nonzero lepton asymmetry (high-isospin) scenarios for different models, while the blue line refers to the Lattice QCD EoS of Refs. Borsanyi:2016kswSaikawa:2018rcsFranciolini:2023wjm. The high-isospin cases exhibit a peak above the conformal (pure radiation) value. The green band refers to a reference value for the peak of $w$ from Lattice QCD at high-isospin from Ref. Abbott:2023coj.
• Figure 3: GW tilt (top) and spectrum (bottom) for the different EoSs discussed in the text. Both EoSs representing high isospin QCD (and large lepton asymmetries) deviate from the standard prediction by Lattice QCD (vanishing lepton asymmetry).
• Figure 4: GW CT spectra from Lattice QCD (blue), HRGLatt (red) and Gaussian (orange) EoSs. We use the maximum posterior amplitudes (MAPs) of each model obtained from the NANOGRAV 15 dataset NANOGrav:2023gor (grey violins), see Appendix \ref{['appendix: posterior values']}. The MAPs were obtained using the https://andrea-mitridate.github.io/PTArcade/Mitridate:2023oarandrea_mitridate_2023lamb2023need wrapper.
• Figure 5: Posterior distributions for the logarithmic amplitude $\log_{10}A_{\mathrm{GW}}$ for the different models employed in this work.