Gravitational Waves from Gauge Quanta Produced during Inflation

Abstract

A fast-rolling axion can transfer its kinetic energy to a gauge field via the Chern-Simons coupling, leading to copious production of gauge quanta, which can act as a source of gravitational waves (GWs) with potentially observable amplitudes. In this work, we investigate GW production in a spectator axion model when strong backreaction is taken into account. We find that decreasing the decay constant of the axion enhances GW production. Since the initial value of the axion is larger than its quantum fluctuations, such a condition imposes a lower bound on the axion dacay constant, which sets an upper bound on the amplitude of the energy spectrum of GWs. As a result, the amplitude of the predicted GW energy spectrum is lower than $10^{-10}$ in the nHz to mHz frequency range.

Figures (4)

• Figure 1: Maximum value of the spectrum $k|A^{-}(k)|^{2}$ at the end of inflation as a function of $\alpha$ in the case of $f_{\rm a} = 0.08$.
• Figure 2: Maximum value of the GW spectrum $\Omega_{\mathrm{gw},0}h^{2}$ as a function of $f_{\rm a}$. For each value of $f_{\mathrm{a}}$, we scan the parameter space of $\alpha$ to determine the maximum spectrum. Since $\chi$ initially follows an attractor solution, the result is not sensitive to the initial value of $\chi$.
• Figure 3: Constraint on the parameter $f_{\rm a}$ for GW spectrum peaking at nHz region. The corresponding e-folding number is computed as $N_{*} = N_{\mathrm{p}} - 15.37$. The blue curve shows the variation of $\Delta \chi_{\mathrm{ini}}$ with respect to the parameter $f_{\rm a}$, plotted based on the LHS of Eq. \ref{['eq: f_constrain']}. The orange curve represents the uncertainty in the initial value of the axion due to the vacuum fluctuations, $\delta \chi_{\mathrm{ini}}$, plotted according to the RHS of Eq. \ref{['eq: f_constrain']}. The shadow area which lies above the orange curve is physically allowed region. The black dashed line corresponds to $f_{\rm a} = 0.0817$ at which $\delta \chi_{\mathrm{ini}} = \Delta \chi_{\mathrm{ini}}$.
• Figure 4: Constraint on the parameter $f_{\rm a}$ for GW spectrum peaking at mHz region. The corresponding e-folding number is computed as $N_{*} = N_{\mathrm{p}} - 29.19$. The blue curve shows the variation of $\Delta \chi_{\mathrm{ini}}$ with respect to the parameter $f_{\rm a}$, plotted based on the LHS of Eq. \ref{['eq: f_constrain']}. The orange curve represents the uncertainty in the initial value of the axion due to the vacuum fluctuations, $\delta \chi_{\mathrm{ini}}$, plotted according to the RHS of Eq. \ref{['eq: f_constrain']}. The shadow area which lies above the orange curve is physically allowed region. The black dashed line corresponds to $f_{\rm a} = 0.111$ at which $\delta \chi_{\mathrm{ini}} = \Delta \chi_{\mathrm{ini}}$.