Bias in the Effective Field Theory of Large Scale Structures (1406.7843v2)

Abstract: We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. We describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of $k/k_{\rm NL}$ and $k/k_{\rm M}$, where $k$ is the wavenumber of interest, $k_{\rm NL}$ is the wavenumber associated to the non-linear scale, and $k_{\rm M}$ is the comoving wavenumber enclosing the mass of a galaxy.

• The paper extends the Effective Field Theory framework by incorporating galaxy bias using a systematic perturbative expansion.
• It develops a Lagrangian description and renormalizes bias coefficients to overcome challenges related to non-locality in time.
• The methodology enhances predictive cosmological modeling by accurately computing galaxy correlation functions over an extended range of scales.

Bias in the Effective Field Theory of Large Scale Structures: An Academic Review

The paper presented by Leonardo Senatore explores the intricate field of the Effective Field Theory of Large Scale Structures (EFTofLSS) with a specific focus on describing collapsed astrophysical objects, particularly galaxies. Traditional efforts have mainly concentrated on the two-point functions of dark matter fluctuations. In this work, however, the author extends the framework by addressing the two-point functions involving galaxies, which consequently require a more elaborate understanding of the biased tracers of the underlying dark matter distribution.

Eulerian and Lagrangian Space Descriptions

The paper starts by establishing the need to transition from the common Eulerian representation to a Lagrangian space description when formulating galaxy observables. The Eulerian method is described as perturbatively local in space yet non-local in time, emphasizing observational consequences. Senatore suggests that the Lagrangian approach allows better modeling of galaxy distribution by supposing that their number density at a given location is a consequence of dark matter fields evaluated at an initial position. The Lagrangian perspective focuses on the transformation of dark matter fields and subsequent renormalization of bias coefficients, which are crucial for computing galaxy correlation functions.

Perturbative Scheme and Bias Derivative Expansion

The core contribution of the paper lies in its rigorous analysis of bias derivative expansions for galaxies within the EFTofLSS context. The paper introduces a perturbative expansion that systematically expresses the correlations as a convergent series in powers of the wavenumbers, $k/k_{\text{NL}}$ and $k/k_M$, where $k_{\text{NL}}$ stands for the non-linear scale associated with dark matter fields and $k_M$ characterizes the object's mass. This approach provides a robust framework to describe the galaxy correlation functions up to a propagative scale in a manifestly convergent formulation.

Simultaneously, Senatore addresses the issue of non-locality in time, which can present certain theoretical discrepancies. He navigates this aspect by proposing it to be handled via a quasi-local approximation, advocating for the treatment of bias coefficients as independent numerical constants that multiply different terms at each perturbative order.

Observational Implications and Renormalization

The paper robustly emphasizes the ramifications this advanced understanding has on cosmological surveys and the estimation of various correlation functions for galaxies. In doing so, Senatore elucidates on the necessity of renormalization. By readjusting the bias parameters, the methodology accommodates the potential UV-sensitive contributions that would otherwise infringe on the reliability of our theoretical conclusions. The focus here is to reconstitute these coefficients to ensure insensitivity to the short-distance physics below the nonlinear scale.

Moreover, significant attention is given to the predictive capability of the EFTofLSS when extended to galaxy correlations. Overcoming traditional approaches that stagnate at relatively low wavenumbers such as $k = 0.1 h/\text{Mpc}^{-1}$, Senatore’s formulation theoretically extends this analytical reach significantly, suggesting a potential availability of a factor of 200 more modes.

Future Directions

While the paper provides a rich theoretical landscape, the implications of its findings pave the way for substantial observational and computational endeavors. The techniques outlined in this paper might transform the precision and scope of future large scale structure surveys. The prospect of extending analytic techniques to new observational domains within cosmology is poised to redefine our understanding of the universe’s evolution.

In conclusion, the paper serves as a pivotal resource that rigorously elucidates the complexities of incorporating bias in the context of the EFTofLSS. By refining perturbative expansions and ensuring the renormalization of bias coefficients, it propounds a pathway to greater cosmological insight, demanding further comparative analysis with simulated data in forthcoming research.