What is flat ΛCDM, and may we choose it?

Abstract

The Universe is neither homogeneous nor isotropic, but it is close enough that we can reasonably approximate it as such on suitably large scales. The inflationary-Λ-Cold Dark Matter (ΛCDM) concordance cosmology builds on these assumptions to describe the origin and evolution of fluctuations. With standard assumptions about stress-energy sources, this system is specified by just seven phenomenological parameters, whose precise relations to underlying fundamental theories are complicated and may depend on details of those fields. Nevertheless, it is common practice to set the parameter that characterizes the spatial curvature, Ω K , exactly to zero. This parameter-fixed ΛCDM is awarded distinguished status as separate model, “flat ΛCDM.” Ipso facto this places the onus on proponents of “curved ΛCDM” to present sufficient evidence that Ω K ≠ 0, and is needed as a parameter. While certain inflationary model Lagrangians, with certain values of their parameters, and certain initial conditions, will lead to a present-day universe well-described as containing zero curvature, this does not justify distinguishing that subset of Lagrangians, parameters and initial conditions into a separate model. Absent any theoretical arguments, we cannot use observations that suggest small Ω K to enforce Ω K = 0. Our track record in picking inflationary models and their parameters a priori makes such a choice dubious, and concerns about tensions in cosmological parameters and large-angle cosmic-microwave-background anomalies strengthens arguments against this choice. We argue that Ω K must not be set to zero, and that ΛCDM remains a phenomenological model with at least 7 parameters.

Evidence of dynamical dark energy in a non-flat universe: current and future observations

“…It has been observed that the curvature term if plugged into the gravitational equations, then it could significantly affect the cosmological parameters [79]. So, the small values of the curvature density parameter obtained from different observational data [73][74][75][76], do not justify the assumption of the spatial flatness of the universe as there is no strong theoretical background available in this regard [80]. In fact, it is very natural to consider the curvature of the universe into the cosmic picture for completeness and then investigate its consequences on the dynamics of the universe.…”

“…In fact, it is very natural to consider the curvature of the universe into the cosmic picture for completeness and then investigate its consequences on the dynamics of the universe. Thus, based on the facts that, the non-zero spatial curvature of the universe is indicated by recent observations [69][70][71][72]78]; no solid theoretical background is available to avoid the curvature of the universe [80]; the presence of a spatial curvature of the universe in the gravitational equations could affect the cosmological parameters [79]; one can infer that a thorough cosmological description might be obtained by allowing the spatial curvature in the gravitational equations and test the underlying cosmological scenario with the available data even if the resulting picture becomes complicated. According to the past and current records in the literature, the curvature of our…”

Why is zero spatial curvature special?

“…This means that the flat universe case corresponds to a set of measure zero among all possible spatial geometries. Therefore, an exactly spatially flat Universe has zero probability to be selected among all possible FRLW models (a point that was recently argued in [21]). This raises the question whether ΛCDM with Ω k = 0 should be considered at all.…”