In classical works, equations for fields are proposed without derivation of the right-hand sides. Here we give a derivation of the right-hand sides of the Maxwell and Einstein equations in the framework of the Vlasov-Maxwell-Einstein equations from the classical, but more general principle of least action. Moreover, in the case of Friedman's model of the Universe, one possibility is obtained to explain the mysterious accelerated expansion of the Universe. The accelerated expansion of the Universe, marked by the 2011 Nobel Prize in Physics, is receiving close attention. The generally accepted explanation now is the addition of Einstein's lambda term to the relativistic action. And it is well known that in the nonrelativistic theory this corresponds to the addition of a repulsive quadratic potential.
