We explore and compare different ways largescale structure observables in redshiftspace and real space can be connected. These include direct computation in La grangian space, moment expansions and two formulations of the streaming model. We derive for the first time a Fourier space version of the streaming model, which yields an algebraic relation between the real and redshiftspace power spectra which can be compared to ear lier, phenomenological models. By considering the redshiftspace 2point function in both configuration and Fourier space, we show how to generalize the Gaussian streaming model to higher orders in a systematic and computationally tractable way. We present a closed form solution to the Zeldovich power spectrum in redshift space and use this as a framework for exploring convergence properties of different expansion approaches. While we use the Zeldovich approximation to illustrate these results, much of the formalism and many of the relations we derive hold beyond perturbation theory, and could be used with ingredients measured from Nbody simulations or in other areas requiring decomposition of Cartesian tensors times plane waves. We finish with a discussion of the redshiftspace bispectrum, bias and stochasticity and terms in Lagrangian perturbation theory up to 1loop order.
The Lyα forest flux correlation function: a perturbation theory perspective
Abstract The Lyα forest provides one of the best means of mapping largescale structure at high redshift, including our tightest constraint on the distanceredshift relation before cosmic noon. We describe how the largescale correlations in the Lyα forest can be understood as an expansion in cumulants of the optical depth field, which itself can be related to the density field by a bias expansion. This provides a direct connection between the observable and the statistics of the matter fluctuations which can be computed in a systematic manner. We discuss the way in which complex, smallscale physics enters the predictions, the origin of the muchdiscussed velocity bias and the `renormalization' of the largescale bias coefficients. Our calculations are within the context of perturbation theory, but we also make contact with earlier work using the peakbackground split. Using the structure of the equations of motion we demonstrate, to all orders in perturbation theory, that the largescale flux power spectrum becomes the linear spectrum times the square of a quadratic in the cosine of the angle to the line of sight. Unlike the case of galaxies, both the isotropic and anisotropic pieces receive contributions from smallscale physics.
 Award ID(s):
 1713791
 Publication Date:
 NSFPAR ID:
 10322130
 Journal Name:
 Journal of Cosmology and Astroparticle Physics
 Volume:
 2021
 Issue:
 05
 ISSN:
 14757516
 Sponsoring Org:
 National Science Foundation
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