Resonant production of heavy particles during inflation and its gravitational wave signature

Author(s)

Chen, Qi, Yin, Yuan

Abstract

We show that a quadratic $U(1)$-breaking term, together with an effective chemical potential induced by a dimension five derivative coupling between the inflaton and the $U(1)$ current, can drive efficient particle production during inflation even when the $U(1)$ field is heavier than the Hubble scale. Notably, the chemical potential enables efficient production even when the $U(1)$-breaking mass is smaller than the effective diagonal mass. We compute the gravitational wave signal generated by this mechanism during inflation, derive the primordial tensor spectrum, and map it to the present day energy density $Ω_{\mathrm GW}(f)$. Assuming the $U(1)$ field constitutes the dominant component of dark matter, this mapping fixes the characteristic frequency, which we compare with projected sensitivity curves of ongoing and proposed gravitational wave observatories. Finally, we argue that the same dynamics are accompanied by a cosmological collider signal, providing an independent cross validation of the framework.

Figures

The evolution of the real and imaginary part of the mode function with different momentum.
Caption The evolution of the real and imaginary part of the mode function with different momentum.
The evolution of the real and imaginary part of the mode function with different momentum.
Caption The evolution of the real and imaginary part of the mode function with different momentum.
\emph{Left panel}: The evolution of the comoving phase space number density of various mode with momentum range from $p/H \in (1,7)$, where blue/red denote mode with large/small momentum. \emph{Right panel}: The comoving phase space distribution at given comoving time $H\tau = -1$ and $H\tau = -0.5$. The rapid oscillation of $n_p$ is evident in this plot.
Caption \emph{Left panel}: The evolution of the comoving phase space number density of various mode with momentum range from $p/H \in (1,7)$, where blue/red denote mode with large/small momentum. \emph{Right panel}: The comoving phase space distribution at given comoving time $H\tau = -1$ and $H\tau = -0.5$. The rapid oscillation of $n_p$ is evident in this plot.
\emph{Left panel}: The evolution of the comoving phase space number density of various mode with momentum range from $p/H \in (1,7)$, where blue/red denote mode with large/small momentum. \emph{Right panel}: The comoving phase space distribution at given comoving time $H\tau = -1$ and $H\tau = -0.5$. The rapid oscillation of $n_p$ is evident in this plot.
Caption \emph{Left panel}: The evolution of the comoving phase space number density of various mode with momentum range from $p/H \in (1,7)$, where blue/red denote mode with large/small momentum. \emph{Right panel}: The comoving phase space distribution at given comoving time $H\tau = -1$ and $H\tau = -0.5$. The rapid oscillation of $n_p$ is evident in this plot.
Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
Caption Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
Caption Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
Caption Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
Caption Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
The shape of the gravitational wave energy density spectrum $\Omega_{\rm GW}h^2$ as a function of frequency $f$ scaled by the frequency $f_*$ of the reference mode.
Caption The shape of the gravitational wave energy density spectrum $\Omega_{\rm GW}h^2$ as a function of frequency $f$ scaled by the frequency $f_*$ of the reference mode.
Gravitational wave energy density spectrum $\Omega_{\rm GW}h^2$ as a function of frequency $f$ for the benchmark points listed in Table~\ref{table:Benchmark}. For reference, we overlay representative projected sensitivity curves of selected ongoing and planned gravitational wave observatories.
Caption Gravitational wave energy density spectrum $\Omega_{\rm GW}h^2$ as a function of frequency $f$ for the benchmark points listed in Table~\ref{table:Benchmark}. For reference, we overlay representative projected sensitivity curves of selected ongoing and planned gravitational wave observatories.
The Feynman diagrams that contributes to the bispectrum.
Caption The Feynman diagrams that contributes to the bispectrum.
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