Fourier transforming over observer positions yields a diagonal power spectrum for any lightcone observable, from which standard two-point and higher-order statistics follow as projections.
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Relativistic effects dominate large-scale galaxy power spectra and grow with redshift, but are largely insensitive to k-essence microphysics in Fourier space while the angular spectrum shows clearer model distinctions, especially for the tachyon.
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The observer power spectrum for lightcone statistics, integrated relativistic observables and wide angle effects
Fourier transforming over observer positions yields a diagonal power spectrum for any lightcone observable, from which standard two-point and higher-order statistics follow as projections.
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Relativistic effects in k-essence
Relativistic effects dominate large-scale galaxy power spectra and grow with redshift, but are largely insensitive to k-essence microphysics in Fourier space while the angular spectrum shows clearer model distinctions, especially for the tachyon.