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We recently presented a series of dark energy theorems that place constraintson the equation of state of dark energy ($\wdark$), the ime-variation ofNewton's constant ($\dot G$), and the violation of energy conditions intheories with extra dimensions. In this paper, we explore how current andfuture measurements of $\wdark$ and $\dot G$ can be used to place tight limitson large classes of these theories (including some of the most well-motivatedexamples) independent of the size of the extra dimensions. As an example, weshow that models with conformally Ricci-flat metrics obeying the null energycondition (a common ansatz for Kaluza-Klein and string constructions) arehighly constrained by current ata and may be ruled out entirely by future darkenergy and pulsar observations.

Exploring extra dimensions through observational tests of dark energy and varying Newton's constant