Standard ruler

Abstract: We perform a comprehensive cosmological study of the $H_0$ tension between the direct local measurement and the model-dependent value inferred from the Cosmic Microwave Background. With the recent measurement of $H_0$ this tension has raised to more than $3\sigma$. We consider changes in the early time physics without modifying the late time cosmology. We also reconstruct the late time expansion history in a model independent way with minimal assumptions using distances measures from Baryon Acoustic Oscillations and Type Ia Supernovae, finding that at $z<0.6$ the recovered shape of the expansion history is less than 5 % different than that of a standard LCDM model. These probes also provide a model insensitive constraint on the low-redshift standard ruler, measuring directly the combination $r_s h$ where $H_0=h \times 100$ km/s/Mpc and $r_s$ is the sound horizon at radiation drag (the standard ruler), traditionally constrained by CMB observations. Thus $r_s$ and $H_0$ provide absolute scales for distance measurements (anchors) at opposite ends of the observable Universe. We calibrate the cosmic distance ladder and obtain a model-independent determination of the standard ruler for acoustic scale, $r_s$. The tension in $H_0$ reflects a mismatch between our determination of $r_s$ and its standard, CMB-inferred value. Without including high-l Planck CMB polarization data (i.e., only considering the "recommended baseline" low-l polarisation and temperature and the high l temperature data), a modification of the early-time physics to include a component of dark radiation with an effective number of species around 0.4 would reconcile the CMB-inferred constraints, and the local $H_0$ and standard ruler determinations. The inclusion of the "preliminary" high-l Planck CMB polarisation data disfavours this solution.

Abstract: We present the cosmological distance errors achievable using the baryonic acoustic oscillations as a standard ruler. We begin from a Fisher matrix formalism that is upgraded from earlier Seo and Eisenstein work. We isolate the information from the baryonic peaks by excluding distance information from other less robust sources. Meanwhile, we accommodate the Lagrangian displacement distribution into the Fisher matrix calculation to reflect the gradual loss of information in scale and in time due to nonlinear growth, nonlinear bias, and nonlinear redshift distortions. We then show that we can contract the multidimensional Fisher matrix calculations into a two-dimensional or even one-dimensional formalism with physically motivated approximations. We present the resulting fitting formula for the cosmological distance errors from galaxy redshift surveys as a function of survey parameters and nonlinearity, which saves us going through the 12 dimensional Fisher matrix calculations. Finally, we show excellent agreement between the distance error estimates from the revised Fisher matrix and the precision on the distance scale recovered from N-body simulations.

Abstract: We present the cosmological distance errors achievable using the baryon acoustic oscillations as a standard ruler. We begin from a Fisher matrix formalism that is upgraded from Seo & Eisenstein (2003). We isolate the information from the baryonic peaks by excluding distance information from other less robust sources. Meanwhile we accommodate the Lagrangian displacement distribution into the Fisher matrix calculation to reflect the gradual loss of information in scale and in time due to nonlinear growth, nonlinear bias, and nonlinear redshift distortions. We then show that we can contract the multi-dimensional Fisher matrix calculations into a 2-dimensional or even 1-dimensional formalism with physically motivated approximations. We present the resulting fitting formula for the cosmological distance errors from galaxy redshift surveys as a function of survey parameters and nonlinearity, which saves us going through the 12-dimensional Fisher matrix calculations. Finally, we show excellent agreement between the distance error estimates from the revised Fisher matrix and the precision on the distance scale recovered from N-body simulations.

Abstract: Baryon Acoustic Oscillations (BAOs) provide a standard ruler of known physical length, making it one of the most promising probes of the nature of dark energy (DE). The detection of BAOs as an excess of power in the galaxy distribution at a certain scale requires measuring galaxy positions and redshifts. Transversal (or angular) BAOs measure the angular size of this scale projected in the sky and provide information about the angular distance. Line-of-sight (or radial) BAOs require very precise redshifts, but provide a direct measurement of the Hubble parameter at different redshifts, a more sensitive probe of DE. The main goal of this paper is to show that it is possible to obtain photometric redshifts with enough precision (? z ) to measure BAOs along the line of sight. There is a fundamental limitation as to how much one can improve the BAO measurement by reducing ? z . We show that ? z ~ 0.003(1 + z) is sufficient: a much better precision will produce an oversampling of the BAO peak without a significant improvement on its detection, while a much worse precision will result in the effective loss of the radial information. This precision in redshift can be achieved for bright, red galaxies, featuring a prominent 4000 ? break, by using a filter system comprising about 40 filters, each with a width close to 100 ?, covering the wavelength range from ~4000 to ~8000 ?, supplemented by two broad-band filters similar to the Sloan Digital Sky Survey u and z bands. We describe the practical implementation of this idea, a new galaxy survey project, PAU16Physics of the Accelerating Universe (PAU): http://www.ice.cat/pau., to be carried out with a telescope/camera combination with an etendue about 20 m2 deg2, equivalent to a 2 m telescope equipped with a 6 deg2 field of view camera, and covering 8000 deg2 in the sky in four years. We expect to measure positions and redshifts for over 14 million red, early-type galaxies with L > L and iAB 22.5 in the redshift interval 0.1 < z < 0.9, with a precision ? z < 0.003(1 + z). This population has a number density n 10?3 Mpc?3 h 3 galaxies within the 9 Gpc3 h ?3 volume to be sampled by our survey, ensuring that the error in the determination of the BAO scale is not limited by shot noise. By itself, such a survey will deliver precisions of order 5% in the dark-energy equation of state parameter w, if assumed constant, and can determine its time derivative when combined with future cosmic microwave background measurements. In addition, PAU will yield high-quality redshift and low-resolution spectroscopy for hundreds of millions of other galaxies, including a very significant high-redshift population. The data set produced by this survey will have a unique legacy value, allowing a wide range of astrophysical studies.