ΛCDM cosmology from visible matter only

Abstract

We discuss physical interpretation of ΛCDM cosmology from a Machian model of the universe containing nothing but visible matter (ordinary matter, radiation). The Friedmann equation can be derived from a Machian definition of energy, whereby both kinetic and potential energy of a particle are related to all cosmic matter-energy within the particle's gravitational horizon. The distance to this horizon thus appears as a parameter in all forms of matter-energy density. From conservation of Machian energy it follows that all different types of matter-energy are uniformly characterized by ρ\propto 1/a, i.e., by a constant deceleration q=-1/2. This coincides with relative densities \varOmega_{m}=1/3 and Ω_Λ=2/3 of ΛCDM. Thus the Machian cosmological model matches present relative densities of ΛCDM, without invoking dark components.

Revised version,6 pages