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We present the one-loop 2-point function of biased tracers in redshift space computed with Lagrangian perturbation theory, including a full resummation of both long-wavelength (infrared) displacements and associated velocities. The resulting model accurately predicts the power spectrum and correlation function of halos and mock galaxies from two different sets of N-body simulations at the percent level for quasi-linear scales, including the damping of the baryon acoustic oscillation signal due to the bulk motions of galaxies. We compare this full resummation with other, approximate, techniques including the moment expansion and Gaussian streaming model. We discuss infrared resummation in detail and compare our Lagrangian formulation with the Eulerian theory augmented by an infrared resummation based on splitting the input power spectrum into "wiggle"and "no-wiggle"components. We show that our model is able to recover unbiased cosmological parameters in mock data encompassing a volume much larger than what will be available to future galaxy surveys. We demonstrate how to efficiently compute the resulting expressions numerically, making available a fast Python code capable of rapidly computing these statistics in both configuration and Fourier space.

We present the one-loop 2-point function of biased tracers in redshift space computed with Lagrangian perturbation theory, including a full resummation of both long-wavelength (infrared) displacements and associated velocities. The resulting model accurately predicts the power spectrum and correlation function of halos and mock galaxies from two different sets of N-body simulations at the percent level for quasi-linear scales, including the damping of the baryon acoustic oscillation signal due to the bulk motions of galaxies. We compare this full resummation with other, approximate, techniques including the moment expansion and Gaussian streaming model. We discuss infrared resummation in detail and compare our Lagrangian formulation with the Eulerian theory augmented by an infrared resummation based on splitting the input power spectrum into "wiggle"and "no-wiggle"components. We show that our model is able to recover unbiased cosmological parameters in mock data encompassing a volume much larger than what will be available to future galaxy surveys. We demonstrate how to efficiently compute the resulting expressions numerically, making available a fast Python code capable of rapidly computing these statistics in both configuration and Fourier space.

The line-of-sight peculiar velocities of galaxies contribute to theirobserved redshifts, breaking the translational invariance of galaxy clusteringdown to a rotational invariance around the observer. This becomes importantwhen the line-of-sight direction varies significantly across a survey, leadingto what are known as `wide angle' effects in redshift space distortions.Wide-angle effects will also be present in measurements of the momentum field,i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocitysurveys. In this work we study how wide-angle effects modify the predictedcorrelation function and power spectrum for momentum statistics, both inauto-correlation and in cross-correlation with the density field. Using bothlinear theory and the Zeldovich approximation, we find that deviations from theplane-parallel limit are large and could become important in data analysis forlow redshift surveys. We point out that even multipoles in thecross-correlation between density and momentum are non-zero regardless of thechoice of line of sight, and therefore contain new cosmological informationthat could be exploited. We discuss configuration-space, Fourier-space andspherical analyses, providing exact expressions in each case rather thanrelying on an expansion in small angles. We hope these expressions will be ofuse in the analysis of upcoming surveys for redshift-space distortions andpeculiar velocities.

The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance of galaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight direction varies significantly across a survey, leading to what are known as 'wide-angle' effects in redshift-space distortions. Wide-angle effects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocity surveys. In this work, we study how wide-angle effects modify the predicted correlation function and power spectrum for momentum statistics, both in autocorrelation and in cross-correlation with the density field. Using both linear theory and the Zel'dovich approximation, we find that deviations from the plane-parallel limit are large and could become important in data analysis for low-redshift surveys. We point out that even multipoles in the cross-correlation between density and momentum are non-zero regardless of the choice of line of sight, and therefore contain new cosmological information that could be exploited. We discuss configuration space, Fourier space, and spherical analyses; providing exact expressions in each case rather than relying on an expansion in small angles. We hope these expressions will be of use in the analysis of upcoming surveys for redshift-space distortions and peculiar velocities.

The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance of galaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight direction varies significantly across a survey, leading to what are known as 'wide-angle' effects in redshift-space distortions. Wide-angle effects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocity surveys. In this work, we study how wide-angle effects modify the predicted correlation function and power spectrum for momentum statistics, both in autocorrelation and in cross-correlation with the density field. Using both linear theory and the Zel'dovich approximation, we find that deviations from the plane-parallel limit are large and could become important in data analysis for low-redshift surveys. We point out that even multipoles in the cross-correlation between density and momentum are non-zero regardless of the choice of line of sight, and therefore contain new cosmological information that could be exploited. We discuss configuration space, Fourier space, and spherical analyses; providing exact expressions in each case rather than relying on an expansion in small angles. We hope these expressions will be of use in the analysis of upcoming surveys for redshift-space distortions and peculiar velocities.

This is an erratum to the paper 'The Zeldovich approximation and wide-angle redshift-space distortions' by Castorina & White (2018). There is a mistake in equation (37) which should read (Equation Presented) where Σ2 and ξij are defined in the main text. The figures and the conclusions are all unchanged, however this mistake propagates to equation (46) which should read (Equation Presented) Equation (51) then becomes (Equation Presented) Equations (52)-(53) are no longer needed. The change affects equation (63) which should read (Equation Presented) Finally, in Appendix C, equations (C10-C13) should read (Equation Presented).

This is an erratum to the paper 'The Zeldovich approximation and wide-angle redshift-space distortions' by Castorina & White (2018). There is a mistake in equation (37) which should read (Equation Presented) where Σ2 and ξij are defined in the main text. The figures and the conclusions are all unchanged, however this mistake propagates to equation (46) which should read (Equation Presented) Equation (51) then becomes (Equation Presented) Equations (52)-(53) are no longer needed. The change affects equation (63) which should read (Equation Presented) Finally, in Appendix C, equations (C10-C13) should read (Equation Presented).

Upcoming 21-cm intensity surveys will use the hyperfine transition in emission to map out neutral hydrogen in large volumes of the universe. Unfortunately, large spatial scales are completely contaminated with spectrally smooth astrophysical foregrounds which are orders of magnitude brighter than the signal. This contamination also leaks into smaller radial and angular modes to form a foreground wedge, further limiting the usefulness of 21-cm observations for different science cases, especially cross-correlations with tracers that have wide kernels in the radial direction. In this paper, we investigate reconstructing these modes within a forward modeling framework. Starting with an initial density field, a suitable bias parameterization and non-linear dynamics to model the observed 21-cm field, our reconstruction proceeds by {combining} the likelihood of a forward simulation to match the observations (under given modeling error and a data noise model) {with the Gaussian prior on initial conditions and maximizing the obtained posterior}. For redshifts z=2 and 4, we are able to reconstruct 21cm field with cross correlation, rc > 0.8 on all scales for both our optimistic and pessimistic assumptions about foreground contamination and for different levels of thermal noise. The performance deteriorates slightly at z=6. The large-scale line-of-sight modes are reconstructed almost perfectly. We demonstrate how our method also provides a technique for density field reconstruction for baryon acoustic oscillations, outperforming standard methods on all scales. We also describe how our reconstructed field can provide superb clustering redshift estimation at high redshifts, where it is otherwise extremely difficult to obtain dense spectroscopic samples, as well as open up a wealth of cross-correlation opportunities with projected fields (e.g. lensing) which are restricted to modes transverse to the line of sight.

This paper introduces the HiddenValley simulations, a set of trillion-particle N-body simulations in gigaparsec volumes aimed at intensity mapping science. We present details of the simulations and their convergence, then specialize to the study of 21-cm fluctuations between redshifts 2 and 6. Neutral hydrogen is assigned to halos using three prescriptions, and we investigate the clustering in real and redshift-space at the 2-point level. In common with earlier work we find the bias of HI increases from near 2 at z=2 to 4 at z=6, becoming more scale dependent at high z. The level of scale-dependence and decorrelation with the matter field are as predicted by perturbation theory. Due to the low mass of the hosting halos, the impact of fingers of god is small on the range relevant for proposed 21-cm instruments. We show that baryon acoustic oscillations and redshift-space distortions could be well measured by such instruments. Taking advantage of the large simulation volume, we assess the impact of fluctuations in the ultraviolet background, which change HI clustering primarily at large scales.

This paper introduces the HiddenValley simulations, a set of trillion-particle N-body simulations in gigaparsec volumes aimed at intensity mapping science. We present details of the simulations and their convergence, then specialize to the study of 21-cm fluctuations between redshifts 2 and 6. Neutral hydrogen is assigned to halos using three prescriptions, and we investigate the clustering in real and redshift-space at the 2-point level. In common with earlier work we find the bias of HI increases from near 2 at z=2 to 4 at z=6, becoming more scale dependent at high z. The level of scale-dependence and decorrelation with the matter field are as predicted by perturbation theory. Due to the low mass of the hosting halos, the impact of fingers of god is small on the range relevant for proposed 21-cm instruments. We show that baryon acoustic oscillations and redshift-space distortions could be well measured by such instruments. Taking advantage of the large simulation volume, we assess the impact of fluctuations in the ultraviolet background, which change HI clustering primarily at large scales.

We study synergies between three promising methods to measure 22 and suffer from interloper problems even for spectroscopic surveys. Intensity mapping of the 21-cm signal can cover large volumes with exquisite fidelity, but is limited both by loss of information to foreground cleaning and by lack of knowledge of the mean signal. Cosmic microwave background (CMB) lensing is theoretically very clean, but ultimately measures just the projected variations in density. We find that cross-correlation between optical and radio can significantly improve the measurement of growth rate. Combining these with the CMB provides a promising avenue to detecting modified gravity at high redshifts, in particular by independently probing the Weyl and Newtonian potentials and by strengthening control of systematics. We find that cross-correlating a Stage ii 21-cm survey with DESI quasars with a reasonable brightness temperature prior could enable measurements of the growth rate fσ8 at sub 3% and sub 8% levels at z = 3, 4, representing a factor of 4 and 8 improvement over constraints obtainable from DESI quasars alone. Similarly, cross-correlating 21-cm data with a futuristic LBG survey to mUV

We study synergies between three promising methods to measure 22 and suffer from interloper problems even for spectroscopic surveys. Intensity mapping of the 21-cm signal can cover large volumes with exquisite fidelity, but is limited both by loss of information to foreground cleaning and by lack of knowledge of the mean signal. Cosmic microwave background (CMB) lensing is theoretically very clean, but ultimately measures just the projected variations in density. We find that cross-correlation between optical and radio can significantly improve the measurement of growth rate. Combining these with the CMB provides a promising avenue to detecting modified gravity at high redshifts, in particular by independently probing the Weyl and Newtonian potentials and by strengthening control of systematics. We find that cross-correlating a Stage ii 21-cm survey with DESI quasars with a reasonable brightness temperature prior could enable measurements of the growth rate fσ8 at sub 3% and sub 8% levels at z = 3, 4, representing a factor of 4 and 8 improvement over constraints obtainable from DESI quasars alone. Similarly, cross-correlating 21-cm data with a futuristic LBG survey to mUV

Line intensity mapping offers a new avenue for constraining cosmological parameters in the high redshift Universe. However measurements of the growth of structure, a sensitive probe of gravity, are affected by a well known degeneracy with astrophysical parameters, encoded in the mean brightness temperature of the specific line. In this work we show how to break this degeneracy, to a level that could allow constraints of the amplitude of cosmological fluctuations at the percent level, using information in the mildly non-linear regime of structure formation as described by Lagrangian Perturbation Theory. We focus on the 21-cm line with forecasts for HIRAX and the proposed Stage II experiment as illustrations.

We explore Lagrangian perturbation theory (LPT) for biased tracers in the presence of two fluids, focusing on the case of cold dark matter (CDM) and baryons. The presence of two fluids induces corrections to the Lagrangian bias expansion and tracer advection, both of which we formulate as expansions in the three linear modes of the Lagrangian equations of motion. We compute the linear-order two-fluid corrections in the Zeldovich approximation, finding that modifications to the bias expansion and tracer advection both enter as percent-level corrections over a large range of wavenumbers at low redshift and draw parallels with the Eulerian formalism. We then discuss nonlinear corrections in the two-fluid picture, and calculate contributions from the relative velocity effect (vr2) at one loop order. Finally, we conduct an exploratory Fisher analysis to assess the impact of two-fluid corrections on baryon acoustic oscillations (BAO) measurements, finding that while modest values of the relative bias parameters can introduce systematic biases in the measured BAO scale of up to 0.5 σ, fitting for these effects as additional parameters increases the error bar by less than 30% across a wide range of bias values.

Line intensity mapping offers a new avenue for constraining cosmological parameters in the high redshift Universe. However measurements of the growth of structure, a sensitive probe of gravity, are affected by a well known degeneracy with astrophysical parameters, encoded in the mean brightness temperature of the specific line. In this work we show how to break this degeneracy, to a level that could allow constraints of the amplitude of cosmological fluctuations at the percent level, using information in the mildly non-linear regime of structure formation as described by Lagrangian Perturbation Theory. We focus on the 21-cm line with forecasts for HIRAX and the proposed Stage II experiment as illustrations.

We explore Lagrangian perturbation theory (LPT) for biased tracers in the presence of two fluids, focusing on the case of cold dark matter (CDM) and baryons. The presence of two fluids induces corrections to the Lagrangian bias expansion and tracer advection, both of which we formulate as expansions in the three linear modes of the Lagrangian equations of motion. We compute the linear-order two-fluid corrections in the Zeldovich approximation, finding that modifications to the bias expansion and tracer advection both enter as percent-level corrections over a large range of wavenumbers at low redshift and draw parallels with the Eulerian formalism. We then discuss nonlinear corrections in the two-fluid picture, and calculate contributions from the relative velocity effect (vr2) at one loop order. Finally, we conduct an exploratory Fisher analysis to assess the impact of two-fluid corrections on baryon acoustic oscillations (BAO) measurements, finding that while modest values of the relative bias parameters can introduce systematic biases in the measured BAO scale of up to 0.5 σ, fitting for these effects as additional parameters increases the error bar by less than 30% across a wide range of bias values.

Upcoming 21-cm intensity surveys will use the hyperfine transition in emission to map out neutral hydrogen in large volumes of the universe. Unfortunately, large spatial scales are completely contaminated with spectrally smooth astrophysical foregrounds which are orders of magnitude brighter than the signal. This contamination also leaks into smaller radial and angular modes to form a foreground wedge, further limiting the usefulness of 21-cm observations for different science cases, especially cross-correlations with tracers that have wide kernels in the radial direction. In this paper, we investigate reconstructing these modes within a forward modeling framework. Starting with an initial density field, a suitable bias parameterization and non-linear dynamics to model the observed 21-cm field, our reconstruction proceeds by {combining} the likelihood of a forward simulation to match the observations (under given modeling error and a data noise model) {with the Gaussian prior on initial conditions and maximizing the obtained posterior}. For redshifts z=2 and 4, we are able to reconstruct 21cm field with cross correlation, rc > 0.8 on all scales for both our optimistic and pessimistic assumptions about foreground contamination and for different levels of thermal noise. The performance deteriorates slightly at z=6. The large-scale line-of-sight modes are reconstructed almost perfectly. We demonstrate how our method also provides a technique for density field reconstruction for baryon acoustic oscillations, outperforming standard methods on all scales. We also describe how our reconstructed field can provide superb clustering redshift estimation at high redshifts, where it is otherwise extremely difficult to obtain dense spectroscopic samples, as well as open up a wealth of cross-correlation opportunities with projected fields (e.g. lensing) which are restricted to modes transverse to the line of sight.

The contribution of line-of-sight (LOS) peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted two-point functions. These 'wide-angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum. In this work, we present the first calculation of wide-angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys.We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multifrequency angular power spectrum. We compare different definitions of the LOS direction and discuss how to translate between them. We show that wide-angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide-angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

Redshift -space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modelling of clustering observables, leading to what are frequently called 'wide-angle effects'.We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide-angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify in an analytical way the biases that enter and clarify the relation between what we measure and the underlying theoretical modelling. The presence of an angular window function is also discussed. Motivated by this analysis, we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients.We show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.

The contribution of line-of-sight (LOS) peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted two-point functions. These 'wide-angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum. In this work, we present the first calculation of wide-angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys.We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multifrequency angular power spectrum. We compare different definitions of the LOS direction and discuss how to translate between them. We show that wide-angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide-angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

Redshift -space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modelling of clustering observables, leading to what are frequently called 'wide-angle effects'.We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide-angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify in an analytical way the biases that enter and clarify the relation between what we measure and the underlying theoretical modelling. The presence of an angular window function is also discussed. Motivated by this analysis, we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients.We show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.