Search for Variations of Fundamental Constants

The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the fundamental theory and their value is instead determined, for example, by the background value of some new field or the size of extra dimensions. So far, most studies have been devoted to constrain possible temporal variations of the electromagnetic fine structure constant $\alpha$, the proton to electron mass ratio $\mu = m_p/m_e$, and the gravitational constant $G_{\rm N}$. Apart some claims of the detection of a temporal or spatial variation of $\alpha$ and $\mu$, so far there is no clear observational evidence of any variation of our fundamental constants.