Two-Component Dark Matter and Cosmology in the TQF Framework (v2)

We investigate the dark matter and cosmological implications of the Timeless Quantum Field (TQF), formulated as a scale-invariant extension of a grand unified gauge theory based on SU (5) symmetry. The model contains an extended scalar sector including an adjoint field responsible for grand unified symmetry breaking together with additional singlet scalars. Within this setup, a real scalar field X, stabilized by a discrete Z₂ symmetry, emerges as a viable Higgs-portal dark matter candidate. The dark matter particle interacts with the visible sector through portal interactions of the form (H†H) X2, which govern the annihilation processes responsible for setting the thermal relic abundance. Using analytic freeze-out estimates and a numerical scan of the parameter space, we identify regions consistent with the observed dark matter relic density and current direct-detection constraints. The framework also naturally admits a multi-component dark matter scenario in which the scalar particle X provides a WIMP component while an axion-like particle associated with the scale-invariant sector may contribute a dominant fraction of the cosmological dark matter density. The gravitational sector of the model includes quadratic curvature terms together with nonminimal couplings between scalar fields and gravity. Inflation is driven primarily by the scalaron generated by the R² term, while scalar nonminimal couplings influence the inflationary dynamics. In this setup, inflationary normalization leads to an approximate scaling relation linking the dark matter mass with the nonminimal coupling appearing in the gravitational sector. The TQF framework therefore provides a unified scenario connecting grand unified symmetry breaking, dark matter phenomenology, and inflationary cosmology within a single scale-invariant theory. The resulting parameter space predicts dark matter masses near the electroweak scale and can be probed by current and upcoming direct detection experiments as well as collider searches.