  Motivated by the growing evidence of the importance of charge fluctuations in
the pseudogap phase in high-temperature cuprate superconductors, we apply a
large-N expansion formulated in a path integral representation of the
two-dimensional t-J model on a square lattice. We study all possible charge
instabilities of the paramagnetic state in leading order of the 1/N expansion.
While the d-wave charge density wave (flux phase) becomes the leading
instability for various choices of model parameters, we find that a d-wave
Pomeranchuk (electronic nematic phase) instability occurs as a next leading
one. In particular, the nematic state has a strong tendency to become
inhomogeneous. In the presence of a large second nearest-neighbor hopping
integral, the flux phase is suppressed and the electronic nematic instability
becomes leading in a high doping region. Besides these two major instabilities,
bond-order phases occur as weaker instabilities close to half-filling. Phase
separation is also detected in a finite temperature region near half-filling.
