The next generation of galaxy surveys will provide highly precise measurements of galaxy clustering, therefore requiring a corresponding accuracy. Current approaches, which rely on approximations and idealized assumptions, may fall short in capturing the level of detail required for high-precision observations. In order to increase the modeling accuracy, recently, unequal-time contributions to the galaxy power spectrum have been introduced in order to include the effects of radial correlations. We present a generalization of the formalism for the observed unequal-time power spectrum, that includes Doppler and local general relativistic corrections, plus local primordial non-Gaussianity. We find that unequal-time corrections can potentially mimic an effective $f_{\mathrm{NL}}$ of order unity. We provide a first assessment of the significance of unequal-time corrections for future galaxy clustering experiments, estimating a signal-to-noise ratio of $\sim 3$ for stage-IV- like surveys.

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• Evolution of the Universe
• General relativity
• Inflation
• Large scale structure of the Universe
• Relativistic aspects of cosmology