A conformal basis for cosmology with energy conservation

Abstract

In the standard FRW formalism, the scale factor is assumed to describe the expansion of the universe. However, by examining empty space with a positive cosmological constant (i.e., a de Sitter space), we find that this assumption is incorrect. When described in conformal time, the associated conformal metric exhibits a big bang singularity where the effective vacuum energy density diverges, dominating the early universe. The corresponding FRW scale factor decreases after the big bang, so that it does not describe the universe's expansion. Instead, the expansion is driven by global energy conservation: as the effective vacuum energy density decreases over time, space must expand to compensate. This leads to a linearly expanding universe, which agrees well with various cosmological observations - such as the red shifts of supernovae; the temperature dependence of the CMB radiation; and the near equality of the Hubble time and the age of the universe. Thus, the conformal vacuum metric can serve as a dominant background metric in cosmology, especially during the big bang era when it suggests new explanations for the creation of the initial energy and the first particles in the universe. Due to this dominance of vacuum energy, matter and radiation can be treated perturbatively. Even in their presence, the linear expansion remains the leading behavior, with the effective matter and radiation densities decreasing like $1/t^3$, just like the vacuum energy density. However, changes in their relative abundance can cause slight deviations from the linear expansion. Matter and radiation change the vacuum metric, thereby generating big secondary terms which could be responsible for the phenomenon of dark matter and for the acceleration of the expansion.