Can we have a stringy origin behind $Ω_Λ(t)\propto Ω_m(t)$?

Inspired by the current observations that the ratio of the abundance of dark energy $Ω_Λ$, and the matter density, $Ω_{m}$, is such that $Ω_{m}/Ω_Λ\sim 0.37$, we provide a string inspired phenomenological model where we explain this order one ratio, the smallness of the cosmological constant, and also the recent cosmic acceleration. We observe that any effective theory motivated by a higher dimensional physics provides radion/dilaton couplings to the standard model and the dark matter component with different strengths. Provided radion/dilaton is a dynamical field we show that $Ω_Λ(t)$ tracks $Ω_{m}(t)$ and dominates very recently.

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