Gauge-independent gravitational waves from a minimal dark $U(1)$ sector with viable dark matter candidates

TL;DR

This paper develops a gauge-independent method to predict gravitational wave signals from phase transitions in a minimal dark U(1) sector, linking these signals to dark matter candidates and providing reliable predictions for upcoming detectors.

Contribution

It introduces a gauge-invariant approach to compute gravitational wave spectra from dark sector phase transitions, improving prediction robustness and connecting to dark matter phenomenology.

Findings

Supercooled phase transitions produce stronger gravitational wave signals.

Predicted signals are within the sensitivity of current and future detectors.

The model links phase transition dynamics to viable dark matter candidates.

Abstract

Searches for stochastic gravitational wave backgrounds generated by first-order phase transitions offer a powerful probe of hidden sectors, but quantitative predictions in gauge theories are obstructed by the gauge dependence of the finite-temperature effective potential and the associated tunneling action. We study a minimal gauged $U(1)$ dark sector containing a dark Higgs and a dark photon, optionally supplemented by a vectorlike dark fermion, coupled to the Standard Model through the Higgs portal or kinetic mixing. Using the Nielsen identity together with a controlled derivative expansion and power counting, we construct a gauge-independent effective action in the high- and low-temperature limits, enabling model-intrinsic nucleation dynamics and robust gravitational wave predictions. We perform dedicated Monte Carlo scans in both limits and map viable microscopic parameters to detector-facing peak frequencies and amplitudes, spanning bands relevant to pulsar timing arrays and planned space-based interferometers. In our scans, supercooled phase transitions typically produce much stronger signals and are more likely to fall within the sensitivity range of current and future gravitational wave detectors, whereas parametrically high-temperature phase transitions generally yield weaker signals. We further connect the phase transition phenomenology to viable dark matter candidates within the same minimal field content, providing benchmark targets for dark photon dark matter and dark fermion dark matter, and highlighting their complementarity with gravitational wave observables. Overall, our results provide an end-to-end, gauge-independent pipeline from a minimal hidden sector Lagrangian to gravitational wave spectra and cosmologically viable dark matter benchmarks, yielding the most reliable and concrete predictions to date for a minimal gauged $U(1)$ dark sector.