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The NANOGrav, Parkes and European Pulsar Timing Array (PTA) experiments havecollected strong evidence for a stochastic gravitational wave background in thenHz-frequency band. In this work we perform a detailed statistical analysis ofthe signal in order to elucidate its physical origin. Specifically, we test thestandard explanation in terms of supermassive black hole mergers against theprominent alternative explanation in terms of a first-order phase transition.By means of a frequentist hypothesis test we find that the observedgravitational wave spectrum prefers a first-order phase transition at$2-3\sigma$ significance compared to black hole mergers (depending on theunderlying black hole model). This mild preference is linked to the relativelylarge amplitude of the observed gravitational wave signal (above the typicalexpectation of black hole models) and to its spectral shape (which slightlyfavors the phase-transition spectrum over the predominantly single power-lawspectrum predicted in black hole models). The best fit to the combined PTA dataset is obtained for a phase transition which dominantly produces thegravitational wave signal by bubble collisions (rather than by sound waves).The best-fit (energy-density) spectrum features, within the frequency band ofthe PTA experiments, a crossover from a steeply rising power law (causalitytail) to a softly rising power law; the peak frequency then falls slightlyabove the PTA-measured range. Such a spectrum can be obtained for a strongfirst-order phase transition in the thick-wall regime of vacuum tunneling whichreheats the Universe to a temperature of $T_*\sim \text{GeV}$. A dark sectorphase transition at the GeV-scale provides a comparably good fit.

Origin of the Stochastic Gravitational Wave Background: First-Order Phase Transition vs. Black Hole Mergers