Abstract: We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations (BAO) in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey, which is part of the Sloan Digital Sky Survey III. Our results come from the Data Release 11 (DR11) sample, containing nearly one million galaxies and covering approximately 8500 square degrees and the redshift range 0.2 < z < 0.7. We also compare these results with those from the publicly released DR9 and DR10 samples. Assuming a concordance A cold dark matter (ACDM) cosmological model, the DR11 sample covers a volume of 13 Gpc(3) and is the largest region of the Universe ever surveyed at this density. We measure the correlation function and power spectrum, including density- field reconstruction of the BAO feature. The acoustic features are detected at a significance of over 7s in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, r(d), which has a value of r(d,fid) = 149.28 Mpc in our fiducial cosmology. We find D-V = (1264 +/- 25 Mpc)(r(d)/r(d,fid)) at z = 0.32 and D-V = (2056 +/- 20 Mpc)(r(d)/r(d,fid)) at z = 0.57. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line of sight yields measurements at z = 0.57 of D-A = (1421 +/- 20 Mpc)(r(d)/r(d,fid)) and H = (96.8 +/- 3.4 kms(-1) Mpc(-1))(r(d),(fid)/r(d)). Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat CDM model with a cosmological constant.

Abstract: We present measurements of galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), which is part of the Sloan Digital Sky Survey III (SDSS-III). These use the Data Release 9 (DR9) CMASS sample, which contains 264 283 massive galaxies covering 3275 square degrees with an effective redshift z = 0.57 and redshift range 0.43 < z < 0.7. Assuming a concordance Lambda CDM cosmological model, this sample covers an effective volume of 2.2 Gpc(3), and represents the largest sample of the Universe ever surveyed at this density, (n) over bar approximate to 3 x 10(-4) h(-3) Mpc(3). We measure the angle-averaged galaxy correlation function and power spectrum, including density-field reconstruction of the baryon acoustic oscillation (BAO) feature. The acoustic features are detected at a significance of 5 sigma in both the correlation function and power spectrum. Combining with the SDSS-II luminous red galaxy sample, the detection significance increases to 6.7 sigma. Fitting for the position of the acoustic features measures the distance to z = 0.57 relative to the sound horizon D-V/r(s) = 13.67 +/ 0.22 at z = 0.57. Assuming a fiducial sound horizon of 153.19 Mpc, which matches cosmic microwave background constraints, this corresponds to a distance D-V (z = 0.57) = 2094 +/- 34 Mpc. At 1.7 per cent, this is the most precise distance constraint ever obtained from a galaxy survey. We place this result alongside previous BAO measurements in a cosmological distance ladder and find excellent agreement with the current supernova measurements. We use these distance measurements to constrain various cosmological models, finding continuing support for a flat Universe with a cosmological constant.

Abstract: We present a novel methodology based on Physics-Informed Neural Networks (PINNs) for solving systems of partial differential equations admitting discontinuous solutions. Our method, called Gradient-Annihilated PINNs (GA-PINNs), introduces a modified loss function that forces the model to partially ignore high-gradients in the physical variables, achieved by introducing a suitable weighting function. The method relies on a set of hyperparameters that control how gradients are treated in the physical loss. The performance of our methodology is demonstrated by solving Riemann problems in special relativistic hydrodynamics, extending earlier studies with PINNs in the context of the classical Euler equations. The solutions obtained with the GA-PINN model correctly describe the propagation speeds of discontinuities and sharply capture the associated jumps. We use the relative l(2) error to compare our results with the exact solution of special relativistic Riemann problems, used as the reference ''ground truth'', and with the corresponding error obtained with a second-order, central, shock-capturing scheme. In all problems investigated, the accuracy reached by the GA-PINN model is comparable to that obtained with a shock-capturing scheme, achieving a performance superior to that of the baseline PINN algorithm in general. An additional benefit worth stressing is that our PINN-based approach sidesteps the costly recovery of the primitive variables from the state vector of conserved variables, a well-known drawback of grid-based solutions of the relativistic hydrodynamics equations. Due to its inherent generality and its ability to handle steep gradients, the GA-PINN methodology discussed in this paper could be a valuable tool to model relativistic flows in astrophysics and particle physics, characterized by the prevalence of discontinuous solutions.