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., R×Tp×Tq, R×Tp×Sq,…). The effect is driven by compactifying boundary conditions imposed on some of the coordinates, associated with large and with small scales (the total number of large spatial coordinates being always three). 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 just fixing the numbers of — actually compactified — ordinary and tiny dimensions to be very common ones, and being the compactification radius (for the last) in the range (1–103) lPl, where lPl is the Planck length. This corresponds to solving, in a way, what has been termed by Weinberg the new cosmological constant problem. Moreover, a marginally closed universe is favored by the model, again in coincidence with independent analysis of the observational results.
