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The Standard Model of elementary particles and their interactions does notinclude the gravitational interaction and faces problems in understanding ofthe dark matter, dark energy, strong CP violation etc. In continuing attemptsto solve these problems, many predictions of new light elementary particles andhypothetical interactions beyond the Standard Model have been made. Thesepredictions can be constrained by many means and, specifically, by measuringthe Casimir force arising between two closely spaced bodies due to thezero-point and thermal fluctuations of the electromagnetic field. After a briefsurvey in the theory of the Casimir effect, the strongest constraints on thepower-type and Yukawa-type corrections to Newtonian gravity, following frommeasuring the Casimir force at short distances, are considered. Next,theproblems of dark matter, dark energy and their probable constituents arediscussed. This is followed by an analysis of constraints on the dark matterparticles, and, specifically, on axions and axionlike particles, obtained fromthe Casimir effect. The question of whether the Casimir effect can be used forconstraining the spin-dependent interactions is also considered. Then theconstraints on the dark energy particles, like chameleons and symmetrons, areexamined. In all cases the subject of our treatment is not only measurements ofthe Casimir force but some other relevant table-top experiments as well. Inconclusion, the prospects of the Casimir effect for constraining theoreticalpredictions beyond the Standard Model at short distances are summarized.

Testing Gravity and Predictions Beyond the Standard Model at Short Distances: The Casimir Effect