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We develop a deep-learning technique to infer the nonlinear velocity field from the dark matter density field. The deep-learning architecture we use is a "U-net" style convolutional neural network, which consists of 15 convolution layers and 2 deconvolution layers. This setup maps the three-dimensional density field of 323 voxels to the three-dimensional velocity or momentum fields of 203 voxels. Through the analysis of the dark matter simulation with a resolution of 2h−1 Mpc, we find that the network can predict the the nonlinearity, complexity, and vorticity of the velocity and momentum fields, as well as the power spectra of their value, divergence, and vorticity and its prediction accuracy reaches the range of k ≃ 1.4 h Mpc−1 with a relative error ranging from 1% to ≲10%. A simple comparison shows that neural networks may have an overwhelming advantage over perturbation theory in the reconstruction of velocity or momentum fields. [ABSTRACT FROM AUTHOR]

We used the mark weighted correlation functions (MCFs), W(s), to study the large-scale structure of the universe. We studied five types of MCFs with the weighting scheme ρα, where ρ is the local density, and α is taken as −1, −0.5, 0, 0.5, and 1. We found that different MCFs have very different amplitudes and scale dependence. Some of the MCFs exhibit distinctive peaks and valleys that do not exist in the standard correlation functions. Their locations are robust against the redshifts and the background geometry; however, it is unlikely that they can be used as "standard rulers" to probe the cosmic expansion history. Nonetheless, we find that these features may be used to probe parameters related with the structure formation history, such as the values of σ8 and the galaxy bias. Finally, after conducting a comprehensive analysis using the full shapes of the W(s)s and WΔs(μ)s, we found that combining different types of MCFs can significantly improve the cosmological parameter constraints. Compared with using only the standard correlation function, the combinations of MCFs with α = 0, 0.5, 1 and α = 0, −1, −0.5, 0.5, 1 can improve the constraints on Ωm and w by ≈30% and 50%, respectively. We find highly significant evidence that MCFs can improve cosmological parameter constraints. [ABSTRACT FROM AUTHOR]

The tomographic Alcock–Paczynski (AP) method is so far the best method in separating the AP signal from the redshift space distortion (RSD) effects and deriving powerful constraints on cosmological parameters using the clustering region. To guarantee that the method can be easily applied to the future large-scale structure surveys, we study the possibility of estimating the systematics of the method using the fast simulation method. The major contribution of the systematics comes from the nonzero redshift evolution of the RSD effects, which is quantified by in our analysis, and estimated using the BigMultidark exact N-body simulation and approximate COmoving Lagrangian Acceleration (COLA) simulation samples. We find about 5%/10% evolution when comparing the measured as z = 0.5/z = 1 to the measurements at z = 0. We checked the inaccuracy in the 2pCFs computed using COLA, and find it 5–10 times smaller than the intrinsic systematics of the tomographic AP method, indicating that using COLA to estimate the systematics is good enough. Finally, we test the effect of halo bias, and find ≲1.5% change in when varying the halo mass within the range of 2 × 1012–1014M⊙. We will perform more studies to achieve an accurate and efficient estimation of the systematics in the redshift range of z = 0–1.5. [ABSTRACT FROM AUTHOR]

The tomographic Alcock–Paczynski (AP) method utilizes the redshift evolution of the AP distortion to place constraints on cosmological parameters. In previous works, it was performed via the anisotropic two-point correlation function statistic. In this work we consider the feasibility of conducting the analysis in the Fourier domain. We use the integrated galaxy power spectrum as a function of direction, , to quantify the magnitude of anisotropy in the large-scale structure clustering, and use its redshift variation to do the AP test. The method is tested on the large, high-resolution Big-MultiDark Planck simulation at redshifts z = 0–1. Testing the redshift evolution of in the true cosmology and cosmologies deviating from the truth with δΩm = 0.1, δw = 0.3, we find that the redshift evolution of the AP distortion overwhelms the redshift space distortions effects by a factor of ∼1.7–3.6. The method works well throughout the range of k ∈ (0.2, 1.8) h Mpc−1. We tune the halo mass within the range 2 × 1013–1014M⊙, and find that the change of halo bias results in ≲5% change in , which is less significant compared with the cosmological effect. Our work shows that it is feasible to conduct the tomographic AP analysis in the Fourier space. [ABSTRACT FROM AUTHOR]

We develop an improved Alcock–Paczynski (AP) test method that uses the redshift-space two-point correlation function (2pCF) of galaxies. Cosmological constraints can be obtained by examining the redshift dependence of the normalized 2pCF, which should not change apart from the expected small nonlinear evolution. An incorrect choice of cosmology used to convert redshift to comoving distance will manifest itself as redshift-dependent 2pCF. Our method decomposes the redshift difference of the two-dimensional correlation function into the Legendre polynomials whose amplitudes are modeled by radial fitting functions. Our likelihood analysis with this 2D fitting scheme tightens the constraints on Ωm and w by ∼40% compared to the method of Li et al. that uses one-dimensional angular dependence only. We also find that the correction for the nonlinear evolution in the 2pCF has a non-negligible cosmology dependence, which has been neglected in previous similar studies by Li et al. With an accurate accounting for the nonlinear systematics and use of full two-dimensional shape information of the 2pCF down to scales as small as 5 h−1 Mpc it is expected that the AP test with redshift-space galaxy clustering anisotropy can be a powerful method to constraining the expansion history of the universe. [ABSTRACT FROM AUTHOR]

The tomographic Alcock–Paczynski (AP) method can result in tight cosmological constraints by using small and intermediate clustering scales of the large-scale structure of the galaxy distribution. By focusing on the redshift dependence, the AP distortion can be distinguished from the distortions produced by the redshift space distortions. In this work, we combine the tomographic AP method with other recent observational data sets of SN Ia+BAO+CMB+H0 to reconstruct the dark energy equation-of-state w in a nonparametric form. The result favors a dynamical DE at z ≲ 1, and shows a mild deviation (≲2σ) from w = −1 at z = 0.5–0.7. We find the addition of the AP method improves the low-redshift (z ≲ 0.7) constraint by ∼50%. [ABSTRACT FROM AUTHOR]

We perform an anisotropic clustering analysis of 1,133,326 galaxies from the Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey Data Release 12 covering the redshift range 0.15 < z < 0.69. The geometrical distortions of the galaxy positions, caused by incorrect assumptions in the cosmological model, are captured in the anisotropic two-point correlation function on scales of 6–40 h−1 Mpc. The redshift evolution of this anisotropic clustering is used to place constraints on the cosmological parameters. We improve the methodology of Li et al. to enable efficient exploration of high-dimensional cosmological parameter spaces, and apply it to the Chevallier–Polarski–Linder parameterization of dark energy, w = w0 + waz/(1 + z). In combination with data on the cosmic microwave background, baryon acoustic oscillations, Type Ia supernovae, and H0 from Cepheids, we obtain Ωm = 0.301 ± 0.008, w0 = −1.042 ± 0.067, and wa = −0.07 ± 0.29 (68.3% CL). Adding our new Alcock–Paczynski measurements to the aforementioned results reduces the error bars by ∼30%–40% and improves the dark-energy figure of merit by a factor of ∼2. We check the robustness of the results using realistic mock galaxy catalogs. [ABSTRACT FROM AUTHOR]

We develop a methodology to use the redshift dependence of the galaxy 2-point correlation function (2pCF) across the line of sight, , as a probe of cosmological parameters. The positions of galaxies in comoving Cartesian space varies under different cosmological parameter choices, inducing a redshift-dependent scaling in the galaxy distribution. This geometrical distortion can be observed as a redshift-dependent rescaling in the measured . We test this methodology using a sample of 1.75 billion mock galaxies at redshifts 0, 0.5, 1, 1.5, and 2, drawn from the Horizon Run 4 N-body simulation. The shape of can exhibit a significant redshift evolution when the galaxy sample is analyzed under a cosmology differing from the true, simulated one. Other contributions, including the gravitational growth of structure, galaxy bias, and the redshift space distortions, do not produce large redshift evolution in the shape. We show that one can make use of this geometrical distortion to constrain the values of cosmological parameters governing the expansion history of the universe. This method could be applicable to future large-scale structure surveys, especially photometric surveys such as DES and LSST, to derive tight cosmological constraints. This work is a continuation of our previous works as a strategy to constrain cosmological parameters using redshift-invariant physical quantities. [ABSTRACT FROM AUTHOR]

We apply the methodology developed in Li et al. to BOSS DR12 galaxies and derive cosmological constraints from the redshift dependence of the Alcock–Paczynski (AP) effect. The apparent anisotropy in the distribution of observed galaxies arise from two main sources, the redshift-space distortion (RSD) effect due to the galaxy peculiar velocities, and the geometric distortion when incorrect cosmological models are assumed for transforming redshift to comoving distance, known as the AP effect. Anisotropies produced by the RSD effect are, although large, maintaining a nearly uniform magnitude over a large range of redshift, while the degree of anisotropies from the AP effect varies with redshift by a much larger magnitude. We split the DR12 galaxies into six redshift bins, measure the two-point correlation function in each bin, and assess the redshift evolution of anisotropies. We obtain constraints of , which are comparable with the current constraints from other cosmological probes such as SNe Ia, cosmic microwave background, and baryon acoustic oscillation (BAO). Combining these cosmological probes with our method yield tight constraints of . Our method is complementary to the other large-scale structure (LSS) probes like BAO and topology. We expect this technique will play an important role in deriving cosmological constraints from LSS surveys. [ABSTRACT FROM AUTHOR]