String theory and the dark glueball problem

We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and $\mathrm{\Delta }{N}_{\mathrm{eff}}$ bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.

Figure 1

Glueball relic abundance as a function of ${\alpha }_{\mathrm{UV}}$ and ${\mathrm{\Lambda }}_{\mathrm{UV}}$ for $\xi =1$, $f=.1$, $g^{\prime }=1$. In each figure the relic abundance is oversaturated outside of the blue region. (Upper left panel) $G=SU(2)$ and radiation domination at decoupling. (Upper right panel) $G=E_8$ and radiation domination at decoupling. (Lower left panel) $G=SU(2)$ and matter domination at decoupling. (Lower right panel) $G=E_8$ and matter domination at decoupling.

Figure 2

(Left panel) Contours where the glueball relic abundance saturates the observed relic abundance for various groups as a function of ${\alpha }_{\mathrm{UV}}$ and ${\mathrm{\Lambda }}_{\mathrm{UV}}$ (in GeV), with oversaturation occurring in the region above each contour. The horizontal red line marks ${\alpha }_{\mathrm{UV}}={\alpha }_{\mathrm{GUT}}$. (Right panel) The glueball relic abundance matches the observed relic abundance along dark contours, with oversaturation above. To the right of the dashed contours the dark sector is not reheated above its confinement scale.

Figure 3

Glueball lifetimes as a function of $f_a$ and $\mathrm{\Lambda }$, with contours for ${\tau }_n={\tau }_{\mathrm{univ}}$ and ${\tau }_n={\tau }_{\mathrm{BBN}}=0.1s$ for $n=5$, 8 corresponding to decay via dimension-5 and -8 operators.

Figure 4

The red and orange regions are ruled out by a stable oversaturating glueball relic and an unstable glueball that spoils BBN; the yellow region is ruled out for $G\ne SU(2),SU(3)$ by dark radiation constraints; the green region is allowed since the glueball is unstable and decays to moduli or axions prior to BBN.