[Paper Review] Cosmological constraints without fingers of God

Mikhail M. Ivanov, Oliver H. E. Philcox+4 more|arXiv (Cornell University)|Sep 30, 2021

Galaxies: Formation, Evolution, Phenomena36 references4 citations

TL;DR

This paper introduces $Q_0$, a new redshift-space statistic that isolates transverse Fourier modes unaffected by 'fingers of God' distortions, enabling accurate perturbation theory modeling up to $k_{\rm max} \simeq 0.4\, h\,\text{Mpc}^{-1}$, significantly improving cosmological constraints with minimal computational cost when added to standard power spectrum likelihoods.

ABSTRACT

Non-linear redshift-space distortions ("fingers of God") are challenging to model analytically, a fact that limits the applicability of perturbation theory in redshift space as compared to real space. We show how this problem can be mitigated using a new observable, $Q_0$, which can be easily estimated from the redshift space clustering data and is approximately equal to the real space power spectrum. The new statistic does not suffer from fingers of God and can be accurately described with perturbation theory down to $k_{ m max}\simeq 0.4~h~ ext{Mpc}^{-1}$. It can be straightforwardly included in the likelihood at negligible additional computational cost, and yields noticeable improvements on cosmological parameters compared to standard power spectrum multipole analyses. Using both simulations and observational data from the Baryon Oscillation Spectroscopic Survey, we show that improvements vary from $10\%$ to $100\%$ depending on the cosmological parameter considered, the galaxy sample and the survey volume.

Motivation & Objective

• To address the challenge of nonlinear redshift-space distortions ('fingers of God') that limit the accuracy of perturbation theory in redshift space.
• To develop a new observable that isolates transverse modes unaffected by line-of-sight distortions, enabling higher $k_{\rm max}$ analysis.
• To provide a computationally efficient method to include small-scale information in cosmological likelihoods without increasing complexity.
• To resolve the issue of high covariance in higher-order multipoles by imposing smoothness priors on them, ensuring stable $Q_0$ estimation.

Proposed method

• Construct $Q_0$ as a linear combination of power spectrum multipoles $P_{2n}(k)$ using a transformation matrix $M^{-1}$ derived from Legendre polynomial expansions.
• Use theoretical error covariance with natural priors on smoothness of higher-order multipoles to suppress their noise contribution while preserving signal.
• Estimate $Q_0$ from standard multipole measurements, avoiding the need for FFT-based wedge estimators or map-level FoG removal.
• Model $Q_0$ using perturbation theory up to $k_{\rm max} \simeq 0.4\, h\,\text{Mpc}^{-1}$, significantly higher than the $k_{\rm max} \simeq 0.25\, h\,\text{Mpc}^{-1}$ limit in standard redshift-space analyses.
• Compute the covariance matrix of $Q_0$ analytically or from mocks, ensuring compatibility with existing likelihood pipelines.
• Validate the method using simulations and real BOSS data, demonstrating improved cosmological constraints across multiple galaxy samples.

Experimental results

Research questions

• RQ1 Can a new statistic be constructed that isolates transverse modes in redshift space and avoids contamination from 'fingers of God'?
• RQ2 To what extent can perturbation theory be extended to higher $k$-modes when FoG effects are removed?
• RQ3 Can $Q_0$ be estimated efficiently with minimal computational overhead and integrated into standard likelihood analyses?
• RQ4 How does the inclusion of $Q_0$ improve cosmological parameter constraints compared to standard multipole analyses?
• RQ5 What is the impact of systematic errors and survey-specific effects (e.g., systematics in transverse modes) on $Q_0$'s performance?

Key findings

• The $Q_0$ statistic is approximately equal to the real space power spectrum, with only small effects from BAO peak broadening, enabling accurate perturbation theory modeling up to $k_{\rm max} \simeq 0.4\, h\,\text{Mpc}^{-1}$.
• Incorporating $Q_0$ into the likelihood improves cosmological constraints by 10% to 100%, depending on the parameter, galaxy sample, and survey volume.
• The method resolves the high-covariance problem of higher-order multipoles by imposing smoothness priors, which suppress noise while preserving signal in $Q_0$.
• The covariance matrix of $Q_0$ can be computed efficiently, either analytically or from mocks, enabling straightforward likelihood integration at negligible computational cost.
• The improvement from $Q_0$ is most significant for tracers with strong 'fingers of God' effects, such as LRGs and bright galaxies in surveys like BOSS and DESI.
• The method is robust and scalable, allowing inclusion of multipoles up to arbitrary $\ell_{\rm max}$ while maintaining optimal error bars on $Q_0$.