A Newtonian Motion Gauge found via Einstein-Boltzmann solver maps linear dynamics with scale-dependent growth and GR corrections to Newtonian equations, enabling consistent nonlinear EFT calculations that are transformed back for accuracy in real and redshift space.
& Dio, E
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abstract
Measurements of the clustering of galaxies in Fourier space, and at low wavenumbers, offer a window into the early Universe via the possible presence of scale dependent bias generated by Primordial Non Gaussianites. On such large scales a Newtonian treatment of density perturbations might not be sufficient to describe the measurements, and a fully relativistic calculation should be employed. The interpretation of the data is thus further complicated by the fact that relativistic effects break statistical homogeneity and isotropy and are potentially divergent in the Infra-Red (IR). In this work we compute for the first time the ensemble average of the most used Fourier space estimator in spectroscopic surveys, including all general relativistic (GR) effects, and allowing for an arbitrary choice of angular and radial selection functions. We show that any observable is free of IR sensitivity once all the GR terms, individually divergent, are taken into account, and that this cancellation is a consequence of the presence of the Weinberg adiabatic mode as a solution to Einstein's equations. We then study the importance of GR effects, including lensing magnification, in the interpretation of the galaxy power spectrum multipoles, finding that they are in general a small, less than ten percent level, correction to the leading redshift space distortions term. This work represents the baseline for future investigations of the interplay between Primordial Non Gaussianities and GR effects on large scales and in Fourier space.
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Neglecting linear GR effects biases f_NL at 1–3σ for Euclid/SPHEREx in SFB forecasts; multi-tracer improves Doppler detection and weakly breaks b_ϕ f_NL degeneracy.
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.
Lensing magnification biases the recovered turnover scale k0 by up to 3.6 sigma in high-z mocks, vanishing above z~3.7 for MegaMapper-like surveys and requiring modeling above z~2.9.
LIGER4GAL finds that omitting the finger-of-the-observer effect biases f_nl by more than 1 sigma in 40% of realizations for k_min=0.0015 h/Mpc scales.
citing papers explorer
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Effective Field Theory of Large Scale Structure and Newtonian Motion Gauges
A Newtonian Motion Gauge found via Einstein-Boltzmann solver maps linear dynamics with scale-dependent growth and GR corrections to Newtonian equations, enabling consistent nonlinear EFT calculations that are transformed back for accuracy in real and redshift space.
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Impact and measurability of linear relativistic effects in galaxy surveys
Neglecting linear GR effects biases f_NL at 1–3σ for Euclid/SPHEREx in SFB forecasts; multi-tracer improves Doppler detection and weakly breaks b_ϕ f_NL degeneracy.
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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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Impact of lensing magnification on the power spectrum turnover
Lensing magnification biases the recovered turnover scale k0 by up to 3.6 sigma in high-z mocks, vanishing above z~3.7 for MegaMapper-like surveys and requiring modeling above z~2.9.
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The impact of our peculiar motion on primordial non-Gaussianity measurements using the LIGER4GAL framework
LIGER4GAL finds that omitting the finger-of-the-observer effect biases f_nl by more than 1 sigma in 40% of realizations for k_min=0.0015 h/Mpc scales.