Gravitational Waves from Spectator Scalar Fields

Abstract: We propose a novel mechanism for gravitational wave (GW) production sourced by spectator scalar fields during inflation. These fields, while not driving cosmic expansion, generate blue-tilted isocurvature fluctuations that naturally satisfy current CMB constraints at large scales while producing enhanced power spectra at smaller scales accessible to GW detectors. The resulting GW spectrum spans an exceptionally broad frequency range from $10^{-20}$ to $1$ Hz, with amplitudes ranging from $\Omega_{\text{GW}}h^2 \sim 10^{-20}$ to $10^{-12}$ depending on the reheating temperature and spectator field mass. For heavy spectator fields with effective masses near the inflationary Hubble scale $H_I$, the mechanism produces observable signals across multiple detector bands accessible to pulsar timing arrays, space-based interferometers, and ground-based detectors. Our analysis reveals multiple complementary constraints on spectator field parameters. GW-induced limits on the effective number of relativistic species ($\Delta N_{\text{eff}}$) require $m_\chi \gtrsim 0.61 H_I$, stronger than CMB isocurvature bounds alone ($m_\chi \gtrsim 0.54 H_I$). The non-observation of primordial B-modes by \textit{Planck} provides stronger constraints $m_\chi \gtrsim 0.66 H_I$, with projected LiteBIRD sensitivity potentially reaching $m_\chi \gtrsim 0.70 H_I$. This mechanism enables a unique multi-messenger probe of beyond the Standard Model physics during inflation, providing simultaneous constraints on inflationary dynamics, dark matter production, and reheating through current and next-generation GW experiments.