Searching for scalar dark matter in atoms and astrophysical phenomena: variation of fundamental constants

We propose to search for scalar dark matter via its effects on the electromagnetic finestructure constant and particle masses. Scalar dark matter that forms an oscillating classical field produces 'slow' linear-in-Time drifts and oscillating variations of the fundamental constants, while scalar dark matter that forms topological defects produces transient-intime variations of the constants of Nature. These variations can be sought for with atomic clock, laser interferometer and pulsar timing measurements. Atomic spectroscopy and Big Bang nucleosynthesis measurements already give improved bounds on the quadratic interaction parameters of scalar dark matter with the photon and light quarks by up to 15 orders of magnitude, while Big Bang nucleosynthesis measurements provide the first such constraints on the interaction parameters of scalar dark matter with the massive vector bosons