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Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and environments from the Solar system to merging black holes. However, experimental confirmations of GR on cosmological scales have so far lacked the accuracy one would hope for-its applications on those scales being largely based on extrapolation and its validity there sometimes questioned in the shadow of the discovery of the unexpected cosmic acceleration. Future astronomical instruments surveying the distribution and evolution of galaxies over substantial portions of the observable Universe, such as the Dark Energy Spectroscopic Instrument (DESI), will be able to measure the fingerprints of gravity and their statistical power will allow strong constraints on alternatives to GR. In this paper, based on a set of N-body simulations and mock galaxy catalogs, we study the predictions of a number of traditional and novel summary statistics beyond linear redshift distortions in two well-studied modified gravity models-chameleon f(R) gravity and a braneworld model-and the potential of testing these deviations from GR using DESI. These summary statistics employ a wide array of statistical properties of the galaxy and the underlying dark matter field, including two-point and higher-order statistics, environmental dependence, redshift space distortions and weak lensing. We find that they hold promising power for testing GR to unprecedented precision. The major future challenge is to make realistic, simulation-based mock galaxy catalogs for both GR and alternative models to fully exploit the statistic power of the DESI survey (by matching the volumes and galaxy number densities of the mocks to those in the real survey) and to better understand the impact of key systematic effects. Using these, we identify future simulation and analysis needs for gravity tests using DESI.

The mark weighted correlation function (MCF) W (s , μ) is a computationally efficient statistical measure which can probe clustering information beyond that of the conventional two-point statistics. In this work, we extend the traditional mark weighted statistics using powers of the density field gradient |∇ρ/ρ|α as the weight, and use the angular dependence of the scale-averaged MCFs to constrain cosmological parameters. The analysis shows that the gradient-based weighting scheme is statistically more powerful than the density-based weighting scheme, while combining the two schemes together is more powerful than separately using either of them. Utilizing the density-weighted or the gradient-weighted MCFs with α = 0.5, 1, we can strengthen the constraint on Ωm by factors of 2 or 4, respectively, compared with the standard two-point correlation function, while simultaneously using the MCFs of the two weighting schemes together can be 1.25 times more statistically powerful than using the gradient weighting scheme alone. The mark weighted statistics may play an important role in cosmological analysis of future large-scale surveys. Many issues, including the possibility of using other types of weights, the influence of the bias on this statistics, and the usage of MCFs in the tomographic Alcock–Paczynski method, are worth further investigations. [ABSTRACT FROM AUTHOR]

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]

We propose a method using the redshift dependence of the Alcock-Paczynski (AP) test and volume effect to measure the cosmic expansion history. The galaxy two-point correlation function as a function of angle, ξ (μ), is measured at different redshifts. Assuming an incorrect cosmological model to convert galaxy redshifts to distances, the shape of ξ (μ) appears anisotropic due to the AP effect, and the amplitude is shifted by the change in comoving volume. Due to the redshift dependence of the AP and volume effect, both the shape and amplitude of ξ (μ) exhibit redshift dependence. Similar to Li et al. (2014), we find that the redshift-space distortions (RSD) caused by galaxy peculiar velocities, although significantly distorting ξ (μ), exhibit much less redshift evolution compared to the AP and volume effects. By focusing on the redshift dependence of ξ (μ), we can correctly recover the cosmological parameters despite the contamination of RSD. The method is tested by using the Horizon Run 3 N-body simulation, from which we made a series of 1/8-sky mock surveys having eight million physically self-bound haloes and sampled to have roughly a uniform number density in z = 0-1.5.We find the AP effect results in tight, unbiased constraints on the density parameter and dark energy equation of state, with 68.3% CL intervals δΩm ~ 0.03 and δw ~ 0.1, and the volume effect leads to much tighter constraints of δΩm ~ 0.007 and δw ~ 0.035. [ABSTRACT FROM AUTHOR]

We present the measurements of the redshift-space three-point correlation function (3PCF) for z ~ 0.5 luminous red galaxies of the CMASS sample in the Sloan Digital Sky Survey- III Baryon Oscillation Spectroscopic Survey Data Release 11. The 3PCF measurements are interpreted within the halo occupation distribution framework using high-resolution N-body simulations, and the model successfully reproduces the 3PCF on scales larger than 1 h-1 Mpc. As with the case for the redshift-space two-point correlation functions, we find that the redshiftspace 3PCF measurements also favour the inclusion of galaxy velocity bias in the model. In particular, the central galaxy in a halo is on average in motion with respect to the core of the halo. We discuss the potential of the small-scale 3PCF to tighten the constraints on the relation between galaxies and dark matter haloes and on the phase-space distribution of galaxies. [ABSTRACT FROM AUTHOR]