Primordial Stochastic Gravitational Waves from Massive Higher-Spin Bosons

Abstract

Can a stationary stone radiate gravitational waves (GWs)? While the answer is typically "no" in flat spacetime, we get a "yes" in inflationary spacetime. In this work, we study the stationary-stone-produced GWs in inflation with a concrete model, where the role of stones is played by massive higher-spin particles. We study particles of spin-2 and higher produced by helical chemical potentials, and show that the induced GWs feature a scale-invariant and helicity-biased power spectrum in the slow-roll limit. Including slow-roll corrections leads to interesting backreactions from the higher-spin boson production, resulting in an intriguing scale-dependence of GWs at small scales. Given the existing observational and theoretical constraints, we identify viable parameter regions capable of generating visibly large GWs for future observations.

Figures (6)

• Figure 1: Evolution of the chemical potential $\kappa_s$, the conformal weight $\mu_s$, the Hubble parameter $H$, and the difference $\kappa_s - \mu_s$, considering the backreaction of fields with different spins on the spacetime background. The figure illustrates results for spin values $s=1,2,3,4,10$, with the Hubble parameter at CMB scales given by $H_{\text{CMB}}\simeq 1.1\times10^{-5}M_{\rm pl}$, and the chemical potential and conformal weight evaluated as $\kappa_{\text{CMB}}=3$ and $\mu_{\text{CMB}}=2$, respectively. The shape factor of the potential is set to $\gamma=0.5$. The background field value at the end of inflation is $\phi_{\text{end}}=1.07~M_{\rm pl}$. The initial background field values at CMB scales depend on spin: $\phi^{s=1}_{N=60}\approx 6.17~M_{\rm pl}$, $\phi^{s=2}_{N=60}\approx 6.17~M_{\rm pl}$, $\phi^{s=3}_{N=60}\approx 6.20~M_{\rm pl}$, $\phi^{s=4}_{N=60}\approx 6.25~M_{\rm pl}$, and $\phi^{s=10}_{N=60}\approx 6.60~M_{\rm pl}$.
• Figure 2: Parameter space satisfying experimental and theoretical constraints in the $\kappa_s - \mu_s$ vs. $\mu_s$ plane. The spin parameter takes values $s = 1, 2, 10, 40$.
• Figure 3: The gravitational wave spectra generated by fields with different spin values. We consider spin values $s = 1,2,3,4,10$ with a fixed parameter $\gamma = 0.5$. The values of $\kappa_s$ and $\mu_s$ correspond to the six benchmark points listed in Tab. \ref{['tab:benchmarks']}. In the left column and the second plot of the right column, we fix $\kappa_s - \mu_s = 1$ while varying $\mu_s$ as $1, 2, 5, 7$. In the plots of the right column, we keep $\mu_s = 5$ fixed and progressively increase the difference $\kappa_s - \mu_s$ to $0.5, 1,$ and $1.5$. Additionally, we overlay the constraints from ongoing and proposed gravitational wave experiments.
• Figure 4: The gravitational wave spectra generated by the massive spin-$2$ field with $\gamma=0.5$. $\kappa$ and $\mu$ are set to be the 6 benchmark points in Tab. (\ref{['tab:benchmarks']}). We also present the constraints of ongoing and proposed gravitational wave experiments.
• Figure 5: The difference between chemical potential $\kappa$ and conformal weight $\mu$ of massive spin-$2$ field with potential parameter $\gamma=0.5$. $\kappa$ and $\mu$ are set to be the 6 benchmark points in Tab. (\ref{['tab:benchmarks']}).