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We compute the time variation of the fundamental constants (such as the ratioof the proton mass to the electron mass, the strong coupling constant, the finestructure constant and Newton's constant) within the context of the so-calledrunning vacuum models (RVM's) of the cosmic evolution. Recently, compellingevidence has been provided showing that these models are able to fit the maincosmological data (SNIa+BAO+H(z)+LSS+BBN+CMB) significantly better than theconcordance $\Lambda$CDM model. Specifically, the vacuum parameters of the RVM(i.e. those responsible for the dynamics of the vacuum energy) prove to benonzero at a confidence level $\gtrsim3\sigma$. Here we use such remarkablestatus of the RVM's to make definite predictions on the cosmic time variationof the fundamental constants. It turns out that the predicted variations areclose to the present observational limits. Furthermore, we find that the timevariation of the dark matter particles should be crucially involved in thetotal mass variation of our Universe. A positive measurement of this kind ofeffects could be interpreted as strong support to the "micro and macroconnection" (viz. the dynamical feedback between the evolution of thecosmological parameters and the time variation of the fundamental constants ofthe microscopic world), previously proposed by two of us (HF and JS).

Running vacuum in the Universe and the time variation of the fundamental constants of Nature