Matching the observational value of the cosmological constant

Abstract

A simple model is introduced in which the cosmological constant is interpreted as a true Casimir effect on a scalar field filling the universe (e.g. $\mathbf{R} \times \mathbf{T}^p\times \mathbf{T}^q$, $\mathbf{R} \times \mathbf{T}^p\times \mathbf{S}^q, ...$). The effect is driven by compactifying boundary conditions imposed on some of the coordinates, associated both with large and small scales. The very small -but non zero- value of the cosmological constant obtained from recent astrophysical observations can be perfectly matched with the results coming from the model, by playing just with the numbers of -actually compactified- ordinary and tiny dimensions, and being the compactification radius (for the last) in the range $(1-10^3) l_{Pl}$, where $l_{Pl}$ is the Planck length. This corresponds to solving, in a way, what has been termed by Weinberg the {\it new} cosmological constant problem. Moreover, a marginally closed universe is favored by the model, again in coincidence with independent analysis of the observational results.