The Galaxy Power Spectrum and Bispectrum in Redshift Space

TL;DR

This paper derives comprehensive formulas for the galaxy power spectrum and bispectrum in redshift space, incorporating all relevant bias and selection effects within the effective field theory framework.

Contribution

It provides the first complete derivation of 1-loop power spectrum and leading bispectrum including selection effects in redshift space bias expansion.

Findings

22 parameters describe the spectra, reducible to 11 if selection effects are neglected.

Power spectrum contributions can be expressed with 28 independent loop integrals.

Selection effects are degenerate with some redshift-space distortions and must be included for consistency.

Abstract

We present the complete expression for the next-to-leading (1-loop) order galaxy power spectrum and the leading-order galaxy bispectrum in redshift space in the general bias expansion, or equivalently the effective field theory of biased tracers. We consistently include all line-of-sight dependent selection effects. These are degenerate with many, but not all, of the redshift-space distortion contributions, and have not been consistently derived before. Moreover, we show that, in the framework of effective field theory, a consistent bias expansion in redshift space must include these selection contributions. Physical arguments about the tracer sample considered and its observational selection have to be used to justify neglecting the selection contributions. In summary, the next-to-leading order galaxy power spectrum and leading-order galaxy bispectrum in the general bias expansion are described by 22 parameters, which reduces to 11 parameters if selection effects can be neglected. All contributions to the power spectrum can be written in terms of 28 independent loop integrals.