Second-order relativistic corrections to the redshift drift are derived; the dominant sub-Hubble term is the squared radial velocity gradient, producing a bispectrum that can exceed the squared power spectrum at low z.
Observed galaxy number counts on the lightcone up to second order: I. Main result
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abstract
We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, including all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects.
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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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Nonlinear Relativistic Effects on Cosmological Redshift Drift
Second-order relativistic corrections to the redshift drift are derived; the dominant sub-Hubble term is the squared radial velocity gradient, producing a bispectrum that can exceed the squared power spectrum at low z.
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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.