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Cosmological fluids with a Generalized Equation of State (GEoS) are hereconsidered, whose corresponding EoS parameter $\omega$ describes a fluid withphantom behavior, namely $\omega<-1$, but leading to universes free ofsingularities at any past or future, finite time. Thus avoiding, in particular,the Big Bang and the Big Rip singularities, the last one considered to betypical in phantom fluid models. More specifically, such GEoS fluid cosmologieslead to regular Little Rip universes. A remarkable new property of thesesolutions is proven here, namely that they avoid the initial singularity atearly times; therefore, they are able to describe emergent universes. Solutionsof this kind had been studied previously, but only either as late time or asearly time solutions; never as solutions covering both epochs simultaneously.Appropriate conditions are proposed here that relate the Little Rip cosmologieswith the initial regular universe, for the future and past regimes,respectively. This is done by taking as starting point the conditions underwhich a given scale factor corresponds to a Little Rip universe.

Linking little rip cosmologies with regular early universes