Creation of spin-3/2 dark matter via cosmological gravitational particle production

TL;DR

The paper investigates the production of spin-3/2 dark matter (raritrons) via cosmological gravitational particle production during and after inflation. It treats a minimal free Rarita-Schwinger field minimally coupled to gravity and analyzes three mass-regime classes (high-mass, low-mass, evolving-mass) using Bogoliubov and Boltzmann formalisms. The authors find that high-mass raritrons can account for the observed dark matter density without catastrophic production, while low-mass raritrons undergo divergent spectra that require UV regulation; evolving-mass models can avoid vanishing sound speed but may still yield enhanced production depending on late-time mass. Overall, CGPP can be a viable dark matter production mechanism for spin-3/2 particles, with relic densities and spectra strongly sensitive to m_3/2/H_e, reheating temperature, and potential UV completions.

Abstract

We study the cosmological gravitational particle production (CGPP) of spin-3/2 particles during and after cosmic inflation, and map the parameter space that can realize the observed dark matter density in stable spin-3/2 particles. Originally formulated by Rarita and Schwinger, the relativistic theory of a massive spin-3/2 field later found a home in supergravity as the superpartner of the graviton, and in nuclear physics as baryonic resonances and nuclear isotopes. We study a minimal model realization, namely a free massive spin-3/2 field minimally coupled to gravity, and adopt the name raritron for this field. We demonstrate that CGPP of raritrons crucially depends on the hierarchy between the raritron mass $m_{3/2}$ and the Hubble parameter at the end of inflation $H_e$, with high-mass and low-mass cases distinguished by the evolution of the sound speed $c_s$ of the longitudinal (helicity-1/2) mode, which is approximately unity at all times for heavy (relative to Hubble) raritrons and can become small or vanish for lighter raritrons, leading to a dramatic enhancement of production of high momentum particles in the latter case. Assuming the raritrons are stable, this leads to a wide parameter space to produce the observed dark matter density. Finally, we consider a time-dependent raritron mass, which can be chosen to remove the vanishing sound speed of the longitudinal mode, but which nonetheless enhances the production relative to the constant high-mass case, and in particular does not necessarily tame the high momentum tail of the spectrum. We perform our calculations using the Bogoliubov formalism and compare, when applicable, to the Boltzmann formalism.

Figures (7)

• Figure 1: Evolution of the complex sound speed $c_s(\eta)$. Left: High-mass raritron with $m_{3/2}/H_e = 1.0$. Middle: Low-mass raritron with $m_{3/2}/H_e = 0.10$. Right: Evolving-mass raritron with initial condition $m_{3/2}/H_e = 6 \times 10^3$. Note that for the evolving-mass raritron both the initial and final values are $\mathrm{Re}(c_s)=1,\ \mathrm{Im}(c_s)=0.$
• Figure 2: Spectra of CGPP for high-mass raritron models. We plot the comoving number density spectra $a^3 n_p = a^3 \dd n / \dd \ln p$ as a function of the comoving momentum $p$ for several values of the raritron mass $m_{3/2}$. Left: Helicity-$3\mkern-2.2mu/2$ polarization mode. Right: Helicity-$1\mkern-2.2mu/2$ polarization mode. The dashed lines show the analytical Boltzmann calculation for 2-to-2 scattering (\ref{['eq:a3np_Boltzmann']}). Pauli blocking prohibits the spectrum from rising above the blue diagonal where the Bogoliubov coefficient is maximal, $|\beta_p| = 1$.
• Figure 3: Relic abundance and parameter space of high-mass raritron models. Left: We plot the predicted relic abundances of helicity-1/2 and helicity-3/2 raritrons, $\Omega_{1\mkern-2.2mu/2} h^2$ and $\Omega_{3\mkern-2.2mu/2} h^2$, as a function of the raritron mass $m_{3/2}$ while assuming Quadratic Inflation for which the Hubble parameter at the end of inflation is $H_e \approx 8.5 \times 10^{12} \ \mathrm{GeV}$. We take $T_{\text{\sc rh}} = 10^5 \ \mathrm{GeV}$ and more generally $\Omega h^2 \propto T_{\text{\sc rh}}$. The dotted curves show the relic abundances predicted by the 2-to-2 Boltzmann calculation for $m_{3/2} < m_\phi \approx 2 H_e$. Right: We vary the raritron mass $m_{3/2}$ and the reheating temperature $T_{\text{\sc rh}}$. Assuming that raritrons are cosmologically long lived, we show the regions of parameter space where raritrons make up a subdominant fraction of the dark matter ($\Omega h^2 < 0.12$), regions where they saturate the dark matter abundance ($\Omega h^2 = 0.12$), and regions that are excluded by the overproduction of raritrons ($\Omega h^2 > 0.12$). We also indicate the maximum reheating temperature $T_{\text{\sc rh}}^\mathrm{max} \approx 2.5 \times 10^{15} \ \mathrm{GeV}$ consistent with energy conservation; see Sec. \ref{['sub:inflation']}. In the red hatched region, the late-reheating assumption $H_{\text{\sc rh}} < m_{3/2}$ fails.
• Figure 4: Spectra of CGPP for low-mass raritron models. Style and notation is the same as Fig. \ref{['fig:highmass_spectra']}.
• Figure 5: Relic abundance and parameter space of low-mass raritron models. Style and notation is the same as Fig. \ref{['fig:highmass_Oh2']}. For the helicity-$1\mkern-2.2mu/2$ polarization we illustrate two values for the UV cutoff on the comoving momentum $\Lambda = a_e H_e$ and $10 a_e H_e$.