  We propose an extension of Frank-Oseen's elastic energy for bulk nematic
liquid crystals which is based on the hypothesis that the fundamental
deformations allowed in nematic liquid crystals are splay, twist and bend. The
extended elastic energy is a fourth order form in the fundamental deformations.
The existence of bulk spontaneous modulated or deformed nematic liquid crystal
ground states is investigated. The analysis is limited to bulk nematic liquid
crystals in the absence of limiting surfaces and/or external fields. The non
deformed ground state is stable only when Frank-Oseen's elastic constants are
positive. In case where at least one of them is negative, the ground state
becomes deformed. The analysis of the stability of the deformed states in the
space of the elastic parameters allows to characterize different types of
deformed nematic phases. Some of them are new nematic phases, for instance a
twist -- splay nematic phase is predicted. Inequalities between second order
elastic constants which govern the stability of the twist--bend and splay--bend
state are obtained.
