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Register a new userNoise Estimates for Measurements of Weak Lensing from the Lyman-alpha Forest
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We have proposed a method for measuring weak lensing using the Lyman-alpha forest. Here we estimate the noise expected in weak lensing maps and power spectra for different sets of observational parameters. We find that surveys of the size and quality of the ones being done today and ones planned for the future will be able to measure the lensing power spectrum at a source redshift of z~2.5 with high precision and even be able to image the distribution of foreground matter with high fidelity on degree scales. For example, we predict that Lyman-alpha forest lensing measurement from the Dark Energy Spectroscopic Instrument survey should yield the mass fluctuation amplitude with statistical errors of 1.5%. By dividing the redshift range into multiple bins some tomographic lensing information should be accessible as well. This would allow for cosmological lensing measurements at higher redshift than are accessible with galaxy shear surveys and correspondingly better constraints on the evolution of dark energy at relatively early times.
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The angular positions of quasars are deflected by the gravitational lensing effect of foreground matter. The Lyman-alpha forest seen in the spectra of these quasars is therefore also lensed. We propose that the signature of weak gravitational lensing of the forest could be measured using similar techniques that have been applied to the lensed Cosmic Microwave Background, and which have also been proposed for application to spectral data from 21cm radio telescopes. As with 21cm data, the forest has the advantage of spectral information, potentially yielding many lensed slices at different redshifts. We perform an illustrative idealized test, generating a high resolution angular grid of quasars (of order arcminute separation), and lensing the Lyman-alphaforest spectra at redshifts z=2-3 using a foreground density field. We find that standard quadratic estimators can be used to reconstruct images of the foreground mass distribution at z~1. There currently exists a wealth of Lya forest data from quasar and galaxy spectral surveys, with smaller sightline separations expected in the future. Lyman-alpha forest lensing is sensitive to the foreground mass distribution at redshifts intermediate between CMB lensing and galaxy shear, and avoids the difficulties of shape measurement associated with the latter. With further refinement and application of mass reconstruction techniques, weak gravitational lensing of the high redshift Lya forest may become a useful new cosmological probe.
We demonstrate a method for reconstructing the weak lensing potential from the Lyman-$alpha$ forest data. We derive an optimal estimator for the lensing potential on the sky based on the correlation between pixels in real space. This method effectively deals with irregularly spaced data, holes in the survey, missing data and inhomogeneous noise. We demonstrate an implementation of the method with simulated spectra and weak lensing. It is shown that with a source density of $>sim 0.5$ per square arcminutes and $sim 200$ pixels in each spectrum ($lambda / Deltalambda = 1300$) the lensing potential can be reconstructed with high fidelity if the relative absorption in the spectral pixels is signal dominated. When noise dominates the measurement of the absorption in each pixel the noise in the lensing potential is higher, but for reasonable numbers of sources and noise levels and a high fidelity map the lensing potential is obtainable. The lensing estimator could also be applied to lensing of the Cosmic Microwave Background (CMB), 21 cm intensity mapping (IM) or any case in which the correlation function of the source can be accurately estimated.
We explore the use of Deep Learning to infer physical quantities from the observable transmitted flux in the Lyman-alpha forest. We train a Neural Network using redshift z=3 outputs from cosmological hydrodynamic simulations and mock datasets constructed from them. We evaluate how well the trained network is able to reconstruct the optical depth for Lyman-alpha forest absorption from noisy and often saturated transmitted flux data. The Neural Network outperforms an alternative reconstruction method involving log inversion and spline interpolation by approximately a factor of 2 in the optical depth root mean square error. We find no significant dependence in the improvement on input data signal to noise, although the gain is greatest in high optical depth regions. The Lyman-alpha forest optical depth studied here serves as a simple, one dimensional, example but the use of Deep Learning and simulations to approach the inverse problem in cosmology could be extended to other physical quantities and higher dimensional data.
We provide an analytical description of the line broadening of HI absorbers in the Lyman-alpha forest resulting from Doppler broadening and Jeans smoothing. We demonstrate that our relation captures the dependence of the line-width on column density for narrow lines in z~3 mock spectra remarkably well. Broad lines at a given column density arise when the underlying density structure is more complex, and such clustering is not captured by our model. Our understanding of the line broadening opens the way to a new method to characterise the thermal state of the intergalactic medium and to determine the sizes of the absorbing structures.
We propose a new method for fitting the full-shape of the Lyman-$alpha$ (Ly$alpha$) forest three-dimensional (3D) correlation function in order to measure the Alcock-Paczynski (AP) effect. Our method preserves the robustness of baryon acoustic oscillations (BAO) analyses, while also providing extra cosmological information from a broader range of scales. We compute idealized forecasts for the Dark Energy Spectroscopic Instrument (DESI) using the Ly$alpha$ auto-correlation and its cross-correlation with quasars, and show how this type of analysis improves cosmological constraints. The DESI Ly$alpha$ BAO analysis is expected to measure $H(z_mathrm{eff})r_mathrm{d}$ and $D_mathrm{M}(z_mathrm{eff})/r_mathrm{d}$ with a precision of $sim0.9%$ each, where $H$ is the Hubble parameter, $r_mathrm{d}$ is the comoving BAO scale, $D_mathrm{M}$ is the comoving angular diameter distance and the effective redshift of the measurement is $z_mathrm{eff}simeq2.3$. By fitting the AP parameter from the full shape of the two correlations, we show that we can obtain a precision of $sim0.5-0.6%$ on each of $H(z_mathrm{eff})r_mathrm{d}$ and $D_mathrm{M}(z_mathrm{eff})/r_mathrm{d}$. Furthermore, we show that a joint full-shape analysis of the Ly$alpha$ auto-correlation and its cross-correlation with quasars can measure the linear growth rate times the amplitude of matter fluctuations in spheres of $8;h^{-1}$Mpc, $fsigma_8(z_mathrm{eff})$. Such an analysis could provide the first ever measurement of $fsigma_8(z_mathrm{eff})$ at redshift $z_mathrm{eff}>2$. By combining this with the quasar auto-correlation in a joint analysis of the three high-redshift two-point correlation functions, we show that DESI could be able to measure $fsigma_8(z_mathrm{eff}simeq2.3)$ with a precision of $5-12%$, depending on the smallest scale fitted.
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