How much information can be extracted from galaxy clustering at the field level? (2403.03220v3)

Abstract: We present optimal Bayesian field-level cosmological constraints from nonlinear tracers of the large-scale structure, specifically the amplitude $\sigma_8$ of linear matter fluctuations inferred from rest-frame simulated dark matter halos in a comoving volume of $8\,(h^{-1}\mathrm{Gpc})^3$. Our constraint on $\sigma_8$ is entirely due to nonlinear information, and obtained by explicitly sampling the initial conditions along with bias and noise parameters via a Lagrangian EFT-based forward model, LEFTfield. The comparison with a simulation-based inference analysis employing the power spectrum and bispectrum -- likewise using the LEFTfield forward model -- shows that, when including precisely the same modes of the same data up to $k_{\mathrm{max}}= 0.10\,h\,\mathrm{Mpc}^{-1}$ ($0.12\,h\,\mathrm{Mpc}^{-1}$), the field-level approach yields a factor of 3.5 (5.2) improvement on the $\sigma_8$ constraint, from 20.0% to 5.7% (17.0% to 3.3%). This study provides direct insights into cosmological information encoded in galaxy clustering beyond low-order $n$-point functions.

• The paper introduces the LEFTfield framework to leverage full three-dimensional galaxy clustering data for improved σ8 constraints.
• It demonstrates a reduction in σ8 uncertainty by up to 5.2 times compared to traditional power spectrum and bispectrum methods.
• The approach mitigates the degeneracy between linear bias and σ8, paving the way for refined cosmological parameter estimates.

Insights into Cosmological Information from Nonlinear Galaxy Clustering

The paper "How much information can be extracted from galaxy clustering at the field level?" explores the extraction of cosmological information from galaxy clustering beyond traditional low-order summary statistics. The authors focus primarily on the parameter $\sigma_8$, which quantifies the amplitude of linear matter fluctuations, using data from simulated dark matter halos. Their approach contrasts field-level statistics with power spectrum and bispectrum summary statistics to determine which method provides stronger constraints on $\sigma_8$.

Methodological Advances

The authors employ an advanced field-level inference framework grounded in Lagrangian effective field theory (EFT), termed {LEFTfield}, to model cosmological density fields. This method allows for the exploration of how nonlinear clustering phenomena can break the degeneracy between linear bias and $\sigma_8$, often encountered at linear order. Unlike traditional approaches relying on two-point and three-point functions, this paper leverages the entire three-dimensional tracer field data to derive constraints, thus purportedly offering a fuller capture of cosmological information.

Strong Numerical Results

The findings demonstrate remarkable improvement using field-level approaches, with constraints on $\sigma_8$ significantly tightened when compared to the traditional power spectrum and bispectrum methods. Specifically, when analyzing modes up to $k_ = 0.10 \, Mpc^{-1}$, the field-level method achieves a 3.5-fold improvement, reducing the uncertainty from 20.0% to 5.7%. Extending the analysis to $k_ = 0.12 \, Mpc^{-1}$ further improves the constraint by 5.2 times, enhancing precision from 17.0% to 3.3%. These results underscore the potential of field-level methods in revealing deeper insights into the clustering of galaxies.

Implications and Future Directions

The implications of these findings are profound for cosmological research. This work not only advances the understanding of $\sigma_8$ in relation to both cosmic microwave background and late-universe weak lensing data but also provides a novel methodology that could resolve current tensions in cosmological parameter estimation. By leveraging the information encoded at the field level, this approach could significantly refine constraints on other cosmological parameters and enhance the predictive power of standard cosmological models.

Future research directions might include extending field-level inference methods to incorporate redshift-space distortions (RSD). This would allow for direct estimation of the linear growth rate, $f$, further probing modifications to General Relativity and Dark Energy models. Additionally, as computational resources become more accessible, these methods could be applied to real-world survey data, potentially enhancing the scientific output from upcoming cosmological projects such as DESI, Euclid, and PFS.

In conclusion, the paper presents a compelling case for adopting field-level inference in cosmological analyses of galaxy clustering. The demonstrated improvements in parameter constraints indicate that such methodologies could play a crucial role in furthering our understanding of the Universe's large-scale structure evolution, providing a robust tool for cosmological research in the years to come.