Inflationary Phase Transitions in the Early Universe: A Bayesian Study with Space-Based Gravitational Waves Detectors

Abstract

Phase transitions during inflation can generate a stochastic gravitational-wave background that probes primordial physics. We study the detectability and parameter reconstruction of such a signal with a space-based gravitational-wave detector. Using a Taiji-like mission as a benchmark, we construct a realistic data-analysis framework that includes instrumental noise, astrophysical foregrounds and backgrounds, and the $A$, $E$, and $T$ time-delay interferometry channels. The target signal is described in a minimal, model-independent form and analyzed using both Fisher-matrix forecasts and Bayesian inference with nested sampling. We quantify detection significance and parameter-recovery thresholds, showing that while detection is achievable at moderate signal-to-noise ratios, stronger signals provide more reliable parameter reconstruction. These results offer a realistic assessment of the capability of future space-based missions to probe phase transitions during inflation through stochastic gravitational radiation.

Figures (2)

• Figure 1: Corner plot of the posterior distributions for the ten model parameters obtained from NS (red), compared with the corresponding FIM confidence ellipses (blue). Dark and light shaded regions indicate the $68\%$ and $95\%$ credible levels, respectively. Red crosshairs denote the posterior means inferred from NS, while blue crosshairs mark the injected fiducial values. The diagonal panels show the marginalized one-dimensional distributions, with dashed lines indicating the $1\sigma$ intervals (red for NS and blue for FIM). The inset displays the injected stochastic spectra, including the astrophysical foreground (gray), the astrophysical background (green), and the InPT signal (orange), together with the Taiji noise curve (purple). For this injection, the resulting SNRs are $\mathrm{SNR}_a=118$ and $\mathrm{SNR}_r=66$, and the NS analysis yields $\ln \mathrm{BF}=42.24$ when comparing models with and without an InPT component. Overall agreement between the NS and FIM results is observed, with small discrepancies arising from non-Gaussian posteriors and statistical fluctuations.
• Figure 2: Detectability and parameter recovery of the InPT signal. The left panel shows exclusion and detection contours in the $(\log_{10}(f_{\rm ref}/{\rm Hz}),\,\log_{10} B_{\rm ref})$ plane. The gray and blue curves correspond to absolute SNRs of 2 and 10, respectively, while the green curve marks the threshold for reliable parameter recovery at $\mathrm{SNR}=33$. Red ellipses denote representative $2\sigma$ confidence regions predicted by the FIM at $\log_{10}(f_{\rm ref}/{\rm Hz})=-3$ and $\log_{10} B_{\rm ref}=-14.5,-14,-13.5$. The middle panel shows the same contours expressed in terms of $\log_{10} A_{\rm ref}$, obtained from $B_{\rm ref}$ via Eq. \ref{['gbc']}. The right panel presents the relative uncertainty in $\log_{10} B_{\rm ref}$ as a function of its injected value for different astrophysical foreground and background amplitudes. The solid red curve corresponds to the fiducial model, red markers indicate NS results at selected injection points, and the dashed (dot-dashed) curves represent enhanced or suppressed astrophysical background (foreground) contributions.