Cosmological bounds on non-Abelian dark forces

Non-Abelian dark gauge forces that do not couple directly to ordinary matter may be realized in nature. The minimal form of such a dark force is a pure Yang-Mills theory. If the dark sector is reheated in the early Universe, it will be realized as a set of dark gluons at high temperatures and as a collection of dark glueballs at lower temperatures, with a cosmological phase transition from one form to the other. Despite being dark, the gauge fields of the new force can connect indirectly to the standard model through nonrenormalizable operators. These operators will transfer energy between the dark and visible sectors, and they allow some or all of the dark glueballs to decay. In this work we investigate the cosmological evolution and decays of dark glueballs in the presence of connector operators to the standard model. Dark glueball decays can modify cosmological and astrophysical observables, and we use these considerations to put very strong limits on the existence of pure non-Abelian dark forces. On the other hand, if one or more of the dark glueballs are stable, we find that they can potentially make up the dark matter of the Universe.

Figure 1

Decay lifetimes $\tau =1/\mathrm{\Gamma }$ of the $0^{++}$ (left) and $1^{+-}$ (right) glueball states due to the dimension-8 operators as a function of $M$ and $m_0$ for ${\chi }_i={\chi }_Y=1$ and $G_x=SU(3)$. The masked regions at the upper left show where $m_0>M/10$ and our treatment in terms of effective operators breaks down, while the white dotted, solid, and dashed lines indicate reference lifetimes of $\tau =0.1\mathrm{s}$, $5\times 10^{17}\mathrm{s}$, $10^{26}\mathrm{s}$.

Figure 2

Decay lifetime $\tau =1/\mathrm{\Gamma }$ of the $0^{++}$ glueball due to the combined dimension-6 and dimension-8 operators as a function of $M$ and $m_0$ for ${\chi }_i={\chi }_Y=1$, $y_{\mathrm{eff}}=1$, and $G_x=SU(3)$. The masked region at the upper left shows where $m_0>M/10$ and our treatment in terms of effective operators breaks down, while the dotted, solid, and dashed white lines indicate lifetimes of $\tau =0.1\mathrm{s}$, $5\times {10}^{17}\mathrm{s}$, ${10}^{26}\mathrm{s}$.

Figure 3

Mass-weighted relic yields of the $0^{++}$ (left) and $1^{+-}$ (right) glueballs in the $m_0$–$R$ plane in the absence of connectors for $G_x=SU(3)$. The solid white lines in each panel indicate where the relic density saturates the observed dark matter abundance. The dark masked region at the lower right of both panels shows where $0^{++}$ freeze-out occurs for $x_x^{\mathrm{fo}}<5$ and our freeze-out calculation is not applicable due to the unknown dynamics of the confining phase transition.

Figure 4

Values of the minimal entropy ratio $R_{\min }$ in the $M$–$m_0$ plane for energy transfer via dimension-8 (left) and dimension-6 (right) operators for $G_x=SU(3)$. The black shaded region at the upper left indicates where our treatment in terms of effective operators breaks down. The diagonal black dotted, solid, and dashed lines show reference values of $R_{\min }=10^{-3}$, $10^{-6}$, $10^{-9}$. In the cyan region in the right panel, thermalization between the visible and dark sectors is maintained at least until confinement.

Figure 5

Cosmological constraints on dark glueballs in the $M$–$m_0$ plane for decay scenario 1 with dominant dimension-8 operators and broken $C_x$. The upper two panels have $R=R_{\min }$, $R_{\max }$, while the lower three panels have fixed $R=10^{-9}$, $10^{-6}$, $10^{-3}$. The grey shaded region in each panel indicates where our theoretical assumptions fail, while $R<R_{\min }$ to the left of the dashed line.

Figure 6

Cosmological constraints on dark glueballs in the $M$–$m_0$ plane for decay scenario 2 with dominant dimension-8 operators and conserved $C_x$. The upper two panels have $R=R_{\min }$,$R_{\max }$, and the lower three panels have fixed $R=10^{-9}$, $10^{-6}$, $10^{-3}$. The grey shaded region indicates where our theoretical assumptions fail, while to the left of the dashed line we find $R<R_{\min }$.

Figure 7

Cosmological constraints on dark glueballs in the $M$–$m_0$ plane for decay scenario 3 with dominant dimension-6 operators and broken $C_x$. The upper two panels have $R=R_{\min }$,$R_{\max }$, and the lower three panels have fixed $R=10^{-9}$, $10^{-6}$, $10^{-3}$. The black shaded region indicates where our theoretical assumptions fail, while to the left of the dashed line we find $R<R_{\min }$.

Figure 8

Cosmological constraints on dark glueballs in the $M$–$m_0$ plane for decay scenario 4 with dominant dimension-8 operators and conserved $C_x$. The upper two panels have $R=R_{\min }$, $R_{\max }$, and the lower three panels have fixed $R=10^{-9}$, $10^{-6}$, $10^{-3}$. The black shaded region indicates where our theoretical assumptions fail, while to the left of the dashed line we find $R<R_{\min }$.