Effective Models of QCD and Their Implications for Dark Matter Phenomenology

This paper investigates the implications of effective Quantum Chromodynamics (QCD) models for dark matter phenomenology, with a particular focus on the role of QCD phase transitions, topological defects, and low-energy effective models in understanding dark matter's nature and behavior. We begin by analyzing the formation and thermodynamic properties of the quark-gluon plasma (QGP) in the early Universe, emphasizing the speed of sound \( c_s^2 \) and its effects on primordial density fluctuations, which are crucial for the formation of large-scale structures. The thermodynamic relation \( c_s^2 = \frac{\partial p}{\partial \epsilon} \) is used to model the impact of these fluctuations on the evolution of the Universe. Topological structures arising from scale symmetry breaking during the rapid cooling phase of the early Universe, are explored as potential candidates for dark matter. These structures are shown to bridge the gap between QCD and cosmology, providing insights into the dark matter sector and predicting the presence of axions or other relic particles that could contribute to dark matter's observed properties. The paper also presents an in-depth study of Skyrme solitons and their potential to act as dark matter analogues. We examine the clustering dynamics of Skyrme solitons within dark matter halos, revealing a significant dependence of the soliton's energy density and stability on soliton number \( N \) and dark matter density \( \rho_{\text{DM}} \). Numerical simulations show a strong increase in system energy as both \( N \) and \( \rho_{\text{DM}} \) are increased, highlighting the role of solitons in dark matter clustering and the formation of cosmological structures. The dynamical mass \( M(T) \) of scalar fields in the presence of gravitational couplings and chemical potentials is analyzed, showing clear dependencies on the scalar field mass \( m_0 \), temperature \( T \), and gravitational coupling \( G \). The findings indicate that variations in the chemical potential \( \mu \) lead to significant changes in mass distribution, corroborating predictions from quantum field theory (QFT) and cosmological models. Further, Chiral Perturbation Theory (ChPT) is extended to the dark sector, where SU(N) symmetries govern dark matter interactions. This extension reveals new annihilation channels for dark matter and links dark sector dynamics with cosmological observables, such as the cosmic microwave background (CMB) and dark matter relic abundance. The effect of ChPT on dark matter perturbations and large-scale structure formation is analyzed, emphasizing the role of higher-order corrections to scattering amplitudes and cross-sections in shaping the evolution of dark matter.