The quantity and quality of cosmic structure observations have greatly accelerated in recent years, and further leaps forward will be facilitated by imminent projects. These will enable us to map the ...evolution of dark and baryonic matter density fluctuations over cosmic history. The way that these fluctuations vary over space and time is sensitive to several pieces of fundamental physics: the primordial perturbations generated by GUT-scale physics; neutrino masses and interactions; the nature of dark matter and dark energy. We focus on the last of these here: the ways that combining probes of growth with those of the cosmic expansion such as distance-redshift relations will pin down the mechanism driving the acceleration of the Universe.
One way to explain the acceleration of the Universe is invoke dark energy parameterized by an equation of state w. Distance measurements provide one set of constraints on w, but dark energy also affects how rapidly structure grows; the greater the acceleration, the more suppressed the growth of structure. Upcoming surveys are therefore designed to probe w with direct observations of the distance scale and the growth of structure, each complementing the other on systematic errors and constraints on dark energy. A consistent set of results will greatly increase the reliability of the final answer.
Another possibility is that there is no dark energy, but that General Relativity does not describe the laws of physics accurately on large scales. While the properties of gravity have been measured with exquisite precision at stellar system scales and densities, within our solar system and by binary pulsar systems, its properties in different environments are poorly constrained. To fully understand if General Relativity is the complete theory of gravity we must test gravity across a spectrum of scales and densities. Rapid developments in gravitational wave astronomy and numerical relativity are directed at testing gravity in the high curvature, high density regime. Cosmological evolution provides a polar opposite test bed, probing how gravity behaves in the lowest curvature, low density environments.
There are a number of different implementations of astrophysically relevant modifications of gravity. Generically, the models are able to reproduce the distance measurements while at the same time altering the growth of structure. In particular, as detailed below, the Poisson equation relating over-densities to gravitational potentials is altered, and the potential that determines the geodesics of relativistic particles (such as photons) differs from the potential that determines the motion of non-relativistic particles. Upcoming surveys will exploit these differences to determine whether the acceleration of the Universe is due to dark energy or to modified gravity.
To realize this potential, both wide field imaging and spectroscopic redshift surveys play crucial roles. Projects including DES, eBOSS, DESI, PFS, LSST, Euclid, and WFIRST are in line to map more than a 1000cubic-billion-light-year volume of the Universe. These will map the cosmic structure growth rate to 1% in the redshift range 0<z<2, over the last 3/4 of the age of the Universe.
Large redshift surveys capable of measuring the baryon acoustic oscillation (BAO) signal have proven to be an effective way of measuring the distance–redshift relation in cosmology. Building off the ...work in Zhu et al., we develop a technique to directly constrain the distance–redshift relation from BAO measurements without splitting the sample into redshift bins. We apply the redshift weighting technique in Zhu et al. to the clustering of galaxies from 1000 Quick particle mesh (QPM) mock simulations after reconstruction and achieve a 0.75 per cent measurement of the angular diameter distance D
A at z = 0.64 and the same precision for Hubble parameter H at z = 0.29. These QPM mock catalogues mimic the clustering and noise level of the Baryon Oscillation Spectroscopic Survey Data Release 12 (DR12). We compress the correlation functions in the redshift direction on to a set of weighted correlation functions. These estimators give unbiased DA
and H measurements across the entire redshift range of the combined sample. We demonstrate the effectiveness of redshift weighting in improving the distance and Hubble parameter estimates. Instead of measuring at a single ‘effective’ redshift as in traditional analyses, we report our DA
and H measurements at all redshifts. The measured fractional error of DA
ranges from 1.53 per cent at z = 0.2 to 0.75 per cent at z = 0.64. The fractional error of H ranges from 0.75 per cent at z = 0.29 to 2.45 per cent at z = 0.7. Our measurements are consistent with a Fisher forecast to within 10–20 per cent depending on the pivot redshift. We further show the results are robust against the choice of fiducial cosmologies, galaxy bias models, and redshift–space distortions streaming parameters.
With the largest spectroscopic galaxy survey volume drawn from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), we can extract cosmological constraints from the measurements of redshift ...and geometric distortions at quasi-linear scales (e.g. above 50 h
−1 Mpc). We analyse the broad-range shape of the monopole and quadrupole correlation functions of the BOSS Data Release 12 (DR12) CMASS galaxy sample, at the effective redshift z = 0.59, to obtain constraints on the Hubble expansion rate H(z), the angular- diameter distance D
A
(z), the normalized growth rate f(z)σ8(z), and the physical matter density Ωm h
2. We obtain robust measurements by including a polynomial as the model for the systematic errors, and find it works very well against the systematic effects, e.g. ones induced by stars and seeing. We provide accurate measurements {D
A
(0.59)r
s,fid/r
s
, H(0.59)r
s
/r
s,fid, f(0.59)σ8(0.59), Ωm h
2} = {1427 ± 26 Mpc, 97.3 ± 3.3 km s−1 Mpc−1, 0.488 ± 0.060, 0.135 ± 0.016}, where r
s
is the comoving sound horizon at the drag epoch and r
s,fid = 147.66 Mpc is the sound scale of the fiducial cosmology used in this study. The parameters which are not well constrained by our galaxy clustering analysis are marginalized over with wide flat priors. Since no priors from other data sets, e.g. cosmic microwave background (CMB), are adopted and no dark energy models are assumed, our results from BOSS CMASS galaxy clustering alone may be combined with other data sets, i.e. CMB, SNe, lensing or other galaxy clustering data to constrain the parameters of a given cosmological model. The uncertainty on the dark energy equation of state parameter, w, from CMB+CMASS is about 8 per cent. The uncertainty on the curvature fraction, Ω
k
, is 0.3 per cent. We do not find deviation from flat ΛCDM.
Abstract
We develop a new computationally efficient methodology called double-probe analysis with the aim of minimizing informative priors (those coming from extra probes) in the estimation of ...cosmological parameters. Using our new methodology, we extract the dark energy model-independent cosmological constraints from the joint data sets of the Baryon Oscillation Spectroscopic Survey (BOSS) galaxy sample and Planck cosmic microwave background (CMB) measurements. We measure the mean values and covariance matrix of {R, l
a, Ωb
h
2, n
s, log(A
s), Ωk, H(z), D
A(z), f(z)σ8(z)}, which give an efficient summary of the Planck data and two-point statistics from the BOSS galaxy sample. The CMB shift parameters are
$R=\sqrt{\Omega _{\rm m} H_0^2}\,r(z_*)$
and l
a = πr(z
*)/r
s(z
*), where z
* is the redshift at the last scattering surface, and r(z
*) and r
s(z
*) denote our comoving distance to the z
* and sound horizon at z
*, respectively; Ωb is the baryon fraction at z = 0. This approximate methodology guarantees that we will not need to put informative priors on the cosmological parameters that galaxy clustering is unable to constrain, i.e. Ωb
h
2 and n
s. The main advantage is that the computational time required for extracting these parameters is decreased by a factor of 60 with respect to exact full-likelihood analyses. The results obtained show no tension with the flat Λ cold dark matter (ΛCDM) cosmological paradigm. By comparing with the full-likelihood exact analysis with fixed dark energy models, on one hand we demonstrate that the double-probe method provides robust cosmological parameter constraints that can be conveniently used to study dark energy models, and on the other hand we provide a reliable set of measurements assuming dark energy models to be used, for example, in distance estimations. We extend our study to measure the sum of the neutrino mass using different methodologies, including double-probe analysis (introduced in this study), full-likelihood analysis and single-probe analysis. From full-likelihood analysis, we obtain Σm
ν < 0.12 (68 per cent), assuming ΛCDM and Σm
ν < 0.20 (68 per cent) assuming owCDM. We also find that there is degeneracy between observational systematics and neutrino masses, which suggests that one should take great care when estimating these parameters in the case of not having control over the systematics of a given sample.
In the context of the study of the integrated Sachs–Wolfe (ISW) effect, we construct a template of the projected density distribution up to redshift z ≃ 0.7 by using the luminous galaxies (LGs) from ...the Sloan Digital Sky Survey (SDSS) Data Release 8 (DR8). We use a photometric redshift catalogue trained with more than a hundred thousand galaxies from the Baryon Oscillation Spectroscopic Survey (BOSS) in the SDSS DR8 imaging area covering nearly one-quarter of the sky. We consider two different LG samples whose selection matches that of SDSS-III/BOSS: the low-redshift sample (LOWZ, z ∈ 0.15, 0.5) and the constant mass sample (CMASS, z ∈ 0.4, 0.7). When building the galaxy angular density templates we use the information from star density, survey footprint, seeing conditions, sky emission, dust extinction and airmass to explore the impact of these artefacts on each of the two LG samples. In agreement with previous studies, we find that the CMASS sample is particularly sensitive to Galactic stars, which dominate the contribution to the auto-angular power spectrum below ℓ = 7. Other potential systematics affect mostly the very low multipole range (ℓ ∈ 2, 7), but leave fluctuations on smaller scales practically unchanged. The resulting angular power spectra in the multipole range ℓ ∈ 2, 100 for the LOWZ, CMASS and LOWZ+CMASS samples are compatible with linear Λ cold dark matter (ΛCDM) expectations and constant bias values of b = 1.98 ± 0.11, 2.08 ± 0.14 and 1.88 ± 0.11, respectively, with no traces of non-Gaussianity signatures, i.e.
$f_{\rm NL}^{\rm local}=59\pm 75$
at 95 per cent confidence level for the full LOWZ+CMASS sample in the multipole range ℓ ∈ 4, 100. After cross-correlating Wilkinson Microwave Anisotropy Probe 9-year data with the LOWZ+CMASS LG projected density field, the ISW signal is detected at the level of 1.62–1.69σ. While this result is in close agreement with theoretical expectations and predictions from realistic Monte Carlo simulations in the concordance ΛCDM model, it cannot rule out by itself an Einstein–de Sitter scenario, and has a moderately low signal compared to previous studies conducted on subsets of this LG sample. We discuss possible reasons for this apparent discrepancy, and point to uncertainties in the galaxy survey systematics as most likely sources of confusion.
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