Cosmological horizon entropy and generalized second law for flat Friedmann universe

We investigate the generalized second law (GSL) and the constraints imposed by it for two types of Friedmann universes. The first one is the Friedmann universe with radiation and a positive cosmological constant, and the second one consists of non-relativistic matter and a positive cosmological constant. The time evolution of the event horizon entropy and the entropy of the contents within the horizon are studied by obtaining the Hubble parameter. It is shown that the GSL constrains the temperature of both the radiation and matter of the Friedmann universe. It is also shown that, even though the net entropy of the radiation (or matter) is decreasing at sufficiently large times as the universe expands, it exhibits an increase during the early times when the universe is decelerating. That is, the entropy of the radiation within the comoving volume is decreasing only when the universe is undergoing an accelerated expansion