Quirks Live in Cool Universes

TL;DR

The paper analyzes a minimal quirk model—heavy SM-charged fermions bound by a new confining SU($N$) with scale $\\Lambda$—and shows that cosmological data from BBN, CMB, and gamma-ray observations impose a robust upper bound on the reheat temperature $T_ ext{RH}$ when quirky flux strings are observable at colliders. The irreversible dark-glueball relic abundance arises from UV freeze-in via dimension-8 portals, yielding a strong $T_ ext{RH}$ dependence that disfavors high reheating temperatures and many baryogenesis scenarios; this bound is particularly tight in the macroscopic/mesoscopic quirk regimes. The analysis separates freeze-in into three gluon-energy regimes (3.1–3.3) and then explores model extensions, including QCD-colored quirks, Yukawa couplings to the Higgs, and invisible glueball decays, finding that macroscopic signals keep the $T_ ext{RH}$ bound robust, while microscopic signals may be circumvented with additional structure. The results also reveal a narrow window where dark glueballs could constitute all of dark matter, requiring TeV-scale quirks and relatively large $\\Lambda$, a scenario largely inaccessible to near-term colliders. Overall, the study highlights a deep link between exotic collider signatures and early-universe cosmology, underscoring the importance of targeted quirks searches for informing the Universe’s thermal history and baryogenesis possibilities.

Abstract

We demonstrate that cosmological observations place strong bounds on the reheat temperature $T_\text{RH}$ of the Standard Model (SM) in minimal models of `quirks' -- heavy fermions transforming under the SM gauge group together with a new non-Abelian gauge interaction with a confinement scale far below the mass of the fermions. These models have unique collider signals associated with the confining flux strings, which cannot break due to the large mass of the quirks. Our work shows that in these models $T_\text{RH} \lesssim \mathcal{O}(100)$ GeV for the entire `quirky' parameter space where the effects of the flux string are important. These bounds are in tension with most models of baryogenesis, showing that the discovery of quirks at colliders can have far-reaching implications for cosmology. The bounds arise because the irreducible relic abundance of glueballs from UV freeze-in, combined with their long lifetimes, leads to constraints from the disruption of BBN, distortions of the CMB, excess $γ$-rays, an over-abundance of self-interacting dark matter, and contributions to $ΔN_{\rm eff}$. The glueball freeze-in abundance has a strong dependence on $T_\text{RH}$, making the bounds relatively insensitive to strong interaction uncertainties. The bounds are robust to the SM quantum numbers of the quirks and the presence of Yukawa couplings with the Higgs. In non-minimal extensions of the model where the glueballs can decay to an additional dark sector, the bounds remain for models where the flux string has a macroscopic length at colliders. We also show that for quirk masses above $\sim 10$ TeV, the dark glueballs can be the dominant component of dark matter. This work illustrates a striking connection between quirky collider signals and cosmological probes of new physics, strengthening the case for targeted quirk searches at colliders.

Figures (6)

• Figure 1: The diagram connecting the dark gluons to the SM in our UV theory (left) and the effective operator it matches onto once the heavy quarks are integrated out (right). This work focuses on a benchmark model where the quirks are charged only under the SU(2)$_L$ of the SM, so $V$ are electroweak gauge fields.
• Figure 2: The lifetime (black dashed) of the lightest glueball in seconds as a function of the dark confinement scale and the heavy quirk mass. The quirk pair lengths in meters are denoted by blue lines. These lines roughly demarcate various quirk regions discussed in the bullet points in the main text. Note that for most of the parameter range of interest, the glueballs will be long-lived or cosmologically stable.
• Figure 3: Schematic scaling of the energy density in the dark sector as a function of temperature. Our central estimate (black dashed) is given by assuming that the sector redshifts like radiation (orange lines) down to $T_\text{dark} \sim T_\text{c}$, and then redshifts like matter (purple lines). The uncertainties (purple band) are modeled by extrapolating the asymptotic equations of state through the regime $0.1 T_\text{c} \le T_\text{dark} \le 10T_\text{c}$. The upper limit is obtained by assuming that the equation of state becomes non-relativistic at $T_\text{dark} = 10T_\text{c}$ (the left red dot), while the lower limit is obtained by assuming that the theory becomes non-relativistic at $T_\text{dark} = 0.1T_\text{c}$ (the right red dot).
• Figure 4: The upper bound on the reheat temperature ($T_{\mathrm{RH}}$) of the universe as a function of the dark confinement scale $\Lambda$, for different values of the quirk masses $m_\mathbf{Q}$ (different panels). Different colored regions are ruled out by constraints on long-lived glueballs from BBN Kawasaki:2020qxm (purple), CMB Dimastrogiovanni:2015wvkSlatyer:2016qyl (green), $\gamma$-ray searches Essig:2013goa (orange), overclosure Planck:2018vygParticleDataGroup:2024cfk (yellow), DM self-interactions Randall:2008ppeHarvey:2015hhaTulin:2017ara (red), and $\Delta N_\mathrm{eff}$ at BBN Yeh:2022heq (turquoise). Above the black line, the two sectors reach equilibrium and the abundance of dark glueballs becomes independent of the reheat temperature. Discovering a quirk at colliders for any value of $m_\mathbf{Q}$ and $\Lambda$ where the colored region bounds extend below the black line, puts an upper bound on $T_{\mathrm{RH}}$. Different blue bars at the bottom demarcate different quirk size regions. The dashed brown lines mark milestone reheat temperatures of the dark sector, see the text for further details. The left (right) vertical dotted line marks where the glueball lifetime is equal to the age of the universe (is equal to one second). For lower values of $\Lambda$, $\Delta N_\mathrm{eff}$ bounds constrain the reheat temperature to around the black line, see the text for details. Quirks with larger values of $\Lambda$ are not constrained by cosmological observables considered here.
• Figure 5: The viable range of dark confinement scale $\Lambda$ and quirk masses $m_\mathbf{Q}$ in models of non-secluded dark glueball dark matter. We show the required $T_{\mathrm{RH}}$ (black) such that the glueballs have the right DM relic abundance today. Only the white part of the parameter space is viable thanks to the bounds on decaying DM lifetime from CMB (green) or from $\gamma$-ray (orange), as well as self-interaction constraints (red); future updates on these quantities can probe this parameter space.