Alleviating Cosmological Tensions with the Hadrosymmetric Twin Higgs

Technical Summary: Alleviating Cosmological Tensions with the Hadrosymmetric Twin Higgs

Problem Statement
The Standard Model (SM) of particle physics faces the "little hierarchy problem," necessitating Beyond Standard Model (BSM) theories to protect the Higgs mass. Twin Higgs (TH) models address this by introducing a twin sector with an approximate global symmetry, rendering the Higgs a pseudo-Nambu-Goldstone boson. However, the minimal Mirror Twin Higgs (MTH) model, which duplicates the full SM spectrum, introduces additional light relativistic states (twin photons and neutrinos). These states increase the effective number of relativistic species ($\Delta N_{\text{eff}}$), conflicting with stringent constraints from Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) observations. Furthermore, the MTH model's direct collider signatures are difficult to probe.

Simultaneously, modern cosmology faces two persistent tensions within the $\Lambda$CDM framework:

1. The Hubble Tension: A $\sim 4\sigma$ discrepancy between early-universe (CMB) and late-universe (distance-ladder) determinations of the Hubble constant ($H_0$).
2. The $\sigma_8$ Tension: A $\sim 2\text{--}3\sigma$ mismatch between the amplitude of matter clustering inferred from large-scale structure surveys and that predicted by the CMB.

While previous studies suggested the MTH model could alleviate these tensions, its violation of $\Delta N_{\text{eff}}$ bounds remains a critical issue. The Hadrosymmetric Twin Higgs (HTH) model offers a variant where the twin sector contains only hadronic states (all three generations of quarks) but no light leptons or gauge bosons (twin hypercharge is global, not gauged). This structure avoids $\Delta N_{\text{eff}}$ constraints but renders the model nearly invisible to colliders, necessitating cosmological tests.

Methodology
The authors investigate the cosmological phenomenology of the HTH model by implementing its dynamics into the Boltzmann solver CLASS (Cosmic Linear Anisotropy Solving System). The key physical mechanism modeled is the decay of twin neutral pions ($\pi'^0$), which are the lightest pseudo-Nambu-Goldstone bosons in the twin sector.

• Effective Modeling: The twin-sector states are treated as an effective Decaying Dark Matter (DDM) component. The $\pi'^0$ decays into Standard Model photons before BBN to avoid overclosure and ensure consistency with light element abundances.
• Modified Boltzmann Equations: The evolution equations for photon perturbations are modified to account for the energy transfer from the decaying DDM ($\rho_{\text{DDM}}$) to visible radiation ($\rho_{\bar{R}}$). The decay rate is denoted by $\gamma_{\text{DDM}}$.
• Statistical Analysis: A Monte Carlo Markov Chain (MCMC) analysis was performed using MONTEPYTHON-v3. The model was constrained against:
  • Planck 2018 CMB data (high-$\ell$ TT, TE, EE + low-$\ell$ TT, EE + lensing).
  • Local $H_0$ measurements (SH0ES: $73.04 \pm 1.04$ km s$^{-1}$ Mpc$^{-1}$).
• Parameter Space: Beyond the six standard $\Lambda$CDM parameters, the HTH model introduces two free parameters: the fractional density of decaying dark matter ($\Omega_{\text{DDM}}$) and the decay rate ($\gamma_{\text{DDM}}$). Flat priors were applied: $\Omega_{\text{DDM}} \in [0, 0.1]$ and $\gamma_{\text{DDM}} \times 10^{-8} \in [0, 2\times 10^3]$.

Key Contributions and Results
The study demonstrates that the HTH framework, originally motivated by particle physics naturalness, can simultaneously address cosmological anomalies without violating $\Delta N_{\text{eff}}$ bounds.

1. Alleviation of the Hubble Tension:

   • The HTH model reduces the statistical significance of the Hubble tension from $>4\sigma$ (in $\Lambda$CDM) to approximately $2.5\sigma$ when fitted to CMB data alone.
   • Mechanism: The decay of twin neutral pions injects energy into the photon bath prior to recombination. This modifies the early-time expansion history $H(z)$ and the sound speed $c_s(z)$. Specifically, the presence of the decaying component reduces the comoving sound horizon ($r_s$) at recombination from $147.09$ Mpc (in $\Lambda$CDM) to $145.22$ Mpc. A smaller $r_s$ allows for a higher inferred value of $H_0$ from CMB data.
   • The reduction in $r_s$ is primarily driven by the modification of the Hubble parameter ($H(z)$) due to the additional matter component that dilutes into radiation, rather than changes in the sound speed (which are negligible, $\sim 10^{-7}$).

2. Mitigation of the $\sigma_8$ Tension:

   • The model simultaneously alleviates the discrepancy in the matter clustering amplitude ($\sigma_8$).
   • When the local $H_0$ measurement is included in the analysis (the "HTH*" scenario), the tension in $\sigma_8$ is effectively removed, with the preferred value dropping to $\sigma_8 \approx 0.80 \pm 0.01$.

3. Cosmological Consistency:

   • The model introduces no extra ultra-relativistic degrees of freedom ($\Delta N_{\text{eff}} \simeq 0$), satisfying BBN and CMB constraints.
   • The injected photon energy density is extremely small ($\Delta \rho_\gamma / \rho_\gamma \sim 10^{-6}$), resulting in negligible spectral distortions ($\mu \sim 10^{-9}$), well below the FIRAS bound.
   • Model comparison via the Akaike Information Criterion (AIC) yields $\Delta \text{AIC} \approx 0.29$, indicating the HTH model is statistically comparable to $\Lambda$CDM despite having additional free parameters.

Significance and Claims
The paper claims that the Hadrosymmetric Twin Higgs model provides a "viable route" to mitigating current cosmological tensions. Its significance lies in bridging two distinct fields:

• Particle Physics: It offers a solution to the little hierarchy problem that is consistent with LHC null results and $\Delta N_{\text{eff}}$ bounds, unlike the MTH model.
• Precision Cosmology: It demonstrates that a theoretically motivated BSM scenario can naturally resolve the $H_0$ and $\sigma_8$ tensions through early-universe dynamics (specifically, the decay of twin pions) rather than late-time modifications to dark energy.

The authors conclude that the HTH framework strengthens the link between fundamental theory and precision cosmology, suggesting that the resolution of the little hierarchy problem may be intrinsically connected to present-day cosmological observations. The work highlights that even models with "elusive" collider signatures can be rigorously tested and constrained through cosmological data.