A Scale-Invariant Fully Conformal Cosmological Model and Generalization of Schwarzschild Solution and Equation of State

This paper presents a further step in the development of scale invariant fully conformal cosmology (FCC), formulated in our previous study. Whereas the previous paper focused mainly on the global cosmological consequences of the fully conformal metric and their confrontation with selected astrophysical data, here we analyze its local gravitational and background consequences. On the background of the fully conformal metric we formulate an effective generalization of the weak Schwarzschild field in the corresponding FCC global coordinates and derive from it the associated modified intensity of the Newtonian central field. We further derive the cosmological state/constitutive equation p = − ε/3 as a direct consequence of the fully conformal metric rather than as an ad hoc additional postulate. Likewise, within the fully conformal metric, spatial flatness and the critical density ρcrit are understood as direct consequences of this metric structure rather than as independently postulated inputs. From the condition of global equilibrium between negative cosmological pressure and the gravitational cohesive pressure of homogeneously distributed matter, the effective particulate fraction is obtained as β ≈ 0.45 of the total critical density ρcrit. For the relatively well-confirmed baryonic matter fraction Ω¯bar ≈0.05, this stable-equilibrium condition then leads to the corresponding particulate fraction of collisionless dark matter Ω¯FCCdm ≈0.40, which is in principle determined by the global cosmological equilibrium within this framework. Because direct identification of the entire dark fraction with standard collisionless cold dark matter would very probably be incompatible with the main structural observables, we discuss an effective phenomenological decomposition into a structuring cold dark matter component (cdm) and an almost homogeneous residual warm-dark-matter-like component (wdm). In this interpretation, the paper preserves the previously introduced global FCC framework while simultaneously providing a concrete background prediction for the matter content and a physically motivated basis for further testing of structure formation within scale invariant fully conformal cosmology.