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Motivated by the recent STM experiments of J.E. Hoffman et.al. and C. Howaldet.al., we study the effects of weak translational symmetry breaking on thequasiparticle spectrum of a d-wave superconductor. We develop a generalformalism to discuss periodic charge order, as well as quasiparticle scatteringoff localized defects. We argue that the STM experiments in$Bi_2Sr_2CaCu_2O_{8+\delta}$ cannot be explained using a simple charge densitywave order parameter, but are consistent with the presence of a periodicmodulation in the electron hopping or pairing amplitude. We review the effectsof randomness and pinning of the charge order and compare it to the impurityscattering of quasiparticles. We also discuss implications of weaktranslational symmetry breaking for ARPES experiments.Comment: 12 pages, 9 figs; (v2) minor corrections to formalism, discussions of  dispersion, structure factors and sum rules added; (v3) discussion of  space-dependent normalization added. To be published in PR

Translational symmetry breaking in the superconducting state of the cuprates: Analysis of the quasiparticle density of states