Lawrence Berkeley National Laboratory
Recent Work
Title
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic
Survey: Cosmological analysis of the DR12 galaxy sample
Permalink
https://escholarship.org/uc/item/95g853gv
Journal
Monthly Notices of the Royal Astronomical Society, 470(3)
ISSN
0035-8711
Authors
Alam, S
Ata, M
Bailey, S
et al.
Publication Date
2017-09-21
DOI
10.1093/mnras/stx721
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California
Mon. Not. R. Astron. Soc. 000, 1–38 (2016) Printed 13 July 2016 (MN L
A
T
E
X style file v2.2)
The clustering of galaxies in the completed SDSS-III Baryon
Oscillation Spectroscopic Survey: cosmological analysis of the DR12
galaxy sample
Shadab Alam
1,2
, Metin Ata
3
, Stephen Bailey
4
, Florian Beutler
4
, Dmitry Bizyaev
5,6
, Jonathan A.
Blazek
7
, Adam S. Bolton
8,9
, Joel R. Brownstein
8
, Angela Burden
10
, Chia-Hsun Chuang
11,3
, Johan
Comparat
11,12
, Antonio J. Cuesta
13
, Kyle S. Dawson
8
, Daniel J. Eisenstein
14
, Stephanie Escoffier
15
,
H
´
ector Gil-Mar
´
ın
16,17
, Jan Niklas Grieb
18,19
, Nick Hand
20
, Shirley Ho
1,2
, Karen Kinemuchi
5
, David
Kirkby
21
, Francisco Kitaura
3,4,20
, Elena Malanushenko
5
, Viktor Malanushenko
5
, Claudia Maraston
22
,
Cameron K. McBride
14
, Robert C. Nichol
22
, Matthew D. Olmstead
23
, Daniel Oravetz
5
, Nikhil
Padmanabhan
10
, Nathalie Palanque-Delabrouille
24
, Kaike Pan
5
, Marcos Pellejero-Ibanez
25,26
, Will J.
Percival
22
, Patrick Petitjean
27
, Francisco Prada
11,28,29
, Adrian M. Price-Whelan
30
, Beth A. Reid
4,31,32
, Ser-
gio A. Rodr
´
ıguez-Torres
11,28,12
, Natalie A. Roe
4
, Ashley J. Ross
7,22
, Nicholas P. Ross
33
, Graziano Rossi
34
,
Jose Alberto Rubi
˜
no-Mart
´
ın
25,26
, Ariel G. S
´
anchez
19
, Shun Saito
35,36
, Salvador Salazar-Albornoz
18,19
,
Lado Samushia
37
, Siddharth Satpathy
1,2
, Claudia G. Sc
´
occola
11,38,39
, David J. Schlegel
⋆4
, Donald P.
Schneider
40,41
, Hee-Jong Seo
42
, Audrey Simmons
5
, An
ˇ
ze Slosar
43
, Michael A. Strauss
30
, Molly E. C.
Swanson
14
, Daniel Thomas
22
, Jeremy L. Tinker
44
, Rita Tojeiro
45
, Mariana Vargas Maga
˜
na
1,2,46
, Jose Al-
berto Vazquez
43
, Licia Verde
13,47,48,49
, David A. Wake
50,51
, Yuting Wang
52,22
, David H. Weinberg
53,7
,
Martin White
4,32
, W. Michael Wood-Vasey
54
, Christophe Y
`
eche
24
, Idit Zehavi
55
, Zhongxu Zhai
44
, Gong-
Bo Zhao
52,22
13 July 2016
ABSTRACT
We present cosmological results from the final galaxy clustering data set of the Baryon Oscil-
lation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. Our combined galaxy
sample comprises 1.2 million massive galaxies over an effective area of 9329 deg
2
and vol-
ume of 18.7 Gpc
3
, divided into three partially overlapping redshift slices centred at effective
redshifts 0.38, 0.51, and 0.61. We measure the angular diameter distance D
M
and Hubble
parameter H from the baryon acoustic oscillation (BAO) method after applying reconstruc-
tion to reduce non-linear effects on the BAO feature. Using the anisotropic clustering of the
pre-reconstruction density field, we measure the product D
M
H from the Alcock-Paczynski
(AP) effect and the growth of structure, quantified by f σ
8
(z), from redshift-space distortions
(RSD). We combine individual measurements presented in seven companion papers into a set
of consensus values and likelihoods, obtaining constraints that are tighter and more robust
than those from any one method; in particular, the AP measurement from sub-BAO scales
sharpens constraints from post-reconstruction BAO by breaking degeneracy between D
M
and
H. Combined with Planck 2015 cosmic microwave background measurements, our distance
scale measurements simultaneously imply curvature Ω
K
= 0.0003 ± 0.0026 and a dark en-
ergy equation of state parameter w = −1.01 ± 0.06, in strong affirmation of the spatially flat
cold dark matter model with a cosmological constant (ΛCDM). Our RSD measurements of
fσ
8
, at 6 per cent precision, are similarly consistent with this model. When combined with
supernova Ia data, we find H
0
= 67.3 ± 1.0 km s
−1
Mpc
−1
even for our most general dark
energy model, in tension with some direct measurements. Adding extra relativistic species as
a degree of freedom loosens the constraint only slightly, to H
0
= 67.8 ± 1.2 km s
−1
Mpc
−1
.
Assuming flat ΛCDM we find Ω
m
= 0.310 ± 0.005 and H
0
= 67.6 ± 0.5 k m s
−1
Mpc
−1
,
and we find a 95% upper limit of 0.16 eV/c
2
on the neutrino mass sum.
Key words: cosmology: observations, distance scale, large-scale structure
⋆
BOSS PI: djschlegel@lbl.gov
c
2016 RAS
arXiv:1607.03155v1 [astro-ph.CO] 11 Jul 2016
2 S. Alam et al.
1
Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213,
USA
2
The McWilliams Center for Cosmology, Carnegie Mellon University, 5000 Forbes Ave.,
Pittsburgh, PA 15213, USA
3
Leibniz-Institut f
¨
ur Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam,
Germany
4
Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
5
Apache Point Observatory and New Mexico State University, P.O. Box 59, Sunspot, NM 88349,
USA
6
Sternberg Astronomical Institute, Moscow State University, Universitetski pr. 13, 119992
Moscow, Russia
7
Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, Ohio, USA
8
Department Physics and Astronomy, University of Utah, 115 S 1400 E, Salt Lake City, UT 84112,
USA
9
National Optical Astronomy Observatory, 950 N Cherry Ave, Tucson, AZ 85719, USA
10
Department of Physics, Yale University, 260 Whitney Ave, New Haven, CT 06520, USA
11
Instituto de F
´
ısica Te
´
orica (UAM/CSIC), Universidad Aut
´
onoma de Madrid, Cantoblanco,
E-28049 Madrid, Spain
12
Departamento de F
´
ısica Te
´
orica M8, Universidad Aut
´
onoma de Madrid, E-28049 Cantoblanco,
Madrid, Spain
13
Institut de Ci
`
encies del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Mart
´
ı i
Franqu
`
es 1, E08028 Barcelona, Spain
14
Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA
15
CPPM, Aix-Marseille Universit
´
e, CNRS/IN2P3, CPPM UMR 7346, 13288, Marseille, France
16
Sorbonne Universit
´
es, Institut Lagrange de Paris (ILP), 98 bis Boulevard Arago, 75014 Paris,
France
17
Laboratoire de Physique Nucl
´
eaire et de Hautes Energies, Universit
´
e Pierre et Marie Curie, 4
Place Jussieu, 75005 Paris, France
18
Universit
¨
ats-Sternwarte M
¨
unchen, Scheinerstrasse 1, 81679 Munich, Germany
19
Max-Planck-Institut f
¨
ur Extraterrestrische Physik, Postfach 1312, Giessenbachstr., 85748
Garching, Germany
20
Department of Astronomy, University of California at Berkeley, Berkeley, CA 94720, USA
21
Department of Physics and Astronomy, UC Irvine, 4129 Frederick Reines Hall, Irvine, CA
92697, USA
22
Institute of Cosmology & Gravitation, Dennis Sciama Building, University of Portsmouth,
Portsmouth, PO1 3FX, UK
23
Department of Chemistry and Physics, King’s College, 133 North River St, Wilkes Barre, PA
18711, USA
24
CEA, Centre de Saclay, IRFU/SPP, F-91191 Gif-sur-Yvette, France
25
Instituto de Astrof
´
ısica de Canarias (IAC), C/V
´
ıa L
´
actea, s/n, E-38200, La Laguna, Tenerife,
Spain
26
Dpto. Astrof
´
ısica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain
27
Institut d’Astrophysique de Paris, Universit
´
e Paris 6 et CNRS, 98bis Boulevard Arago, 75014
Paris, France
28
Campus of International Excellence UAM+CSIC, Cantoblanco, E-28049 Madrid, Spain
29
Instituto de Astrof
´
ısica de Andaluc
´
ıa (CSIC), E-18080 Granada, Spain
30
Department of Astrophysical Sciences, Princeton University, Ivy Lane, Princeton, NJ 08544,
USA
31
Hubble Fellow
32
Department of Physics, University of California, 366 LeConte Hall, Berkeley, CA 94720, USA
33
Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ, UK
34
Department of Astronomy and Space Science, Sejong University, Seoul 143-747, Korea
35
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo
Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
36
Max Planck Institut f
¨
ur Astrophysik, Karl-Schwarzschild-Straße 1, D-85740 Garching bei
M
¨
unchen, Germany
37
Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506, USA
38
Facultad de Ciencias Astron
´
omicas y Geof
´
ısicas - Universidad Nacional de La Plata. Paseo del
Bosque S/N, (1900) La Plata, Argentina
39
CONICET, Rivadavia 1917, (1033) Buenos Aires, Argentina
40
Department of Astronomy and Astrophysics, The Pennsylvania State University, University
Park, PA 16802, USA
41
Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park,
PA 16802, USA
42
Department of Physics and Astronomy, Ohio University, 251B Clippinger Labs, Athens, OH
45701, USA
43
Brookhaven National Laboratory, Bldg 510, Upton, New York 11973, USA
44
Center for Cosmology and Particle Physics, New York University, New York, NY 10003, USA
45
School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, UK
46
Instituto de F
´
ısica, Universidad Nacional Aut
´
onoma de M
´
exico, Apdo. Postal 20-364, M
´
exico
47
ICREA (Instituci
´
o Catalana de Recerca i Estudis Avanc¸ats) Passeig Llu
´
ıs Companys 23,
E-08010 Barcelona, Spain
48
Radcliffe Institute for Advanced Study & ITC, Harvard-Smithsonian Center for Astrophysics,
Harvard University, MA 02138, USA
49
Institute of Theoretical Astrophysics, University of Oslo, 0315 Oslo, Norway
50
Department of Astronomy, University of Wisconsin-Madison, 475 N. Charter Street, Madison,
WI, 53706, USA
51
Department of Physical Sciences, The Open University, Milton Keynes, MK7 6AA, UK
52
National Astronomy Observatories, Chinese Academy of Science, Beijing, 100012, P.R. China
53
Department of Astronomy, Ohio State University, Columbus, Ohio, USA
54
PITT PACC, Department of Physics and Astronomy, University of Pittsburgh, 3941 O’Hara
Street, Pittsburgh, PA 15260, USA
55
Department of Astronomy, Case Western Reserve University, Cleveland, OH 44106, USA
1 INTRODUCTION
Observations and theoretical studies over the past four decades
have led to the emergence of a standard cosmological model,
ΛCDM, based on a spatially flat universe, cold dark matter, a cos-
mological constant that drives accelerated expansion at late times,
and structure seeded by quantum fluctuations during an epoch of
inflation at very early times. The goals of “precision cosmology”
are to test the underlying assumptions of this model and to mea-
sure its parameters with sufficient precision to yield new physi-
cal insights, such as the mass scale of neutrinos, the presence of
unknown relativistic species, possible small departures from flat-
ness, and the physics of inflation or alternative scenarios of the
early universe. Observations on galactic and sub-galactic scales can
test the hypothesis that dark matter is weakly interacting and cold
(in the sense that its primordial velocity dispersion was too small
to affect structure formation). The biggest question of contempo-
rary cosmology is the origin of cosmic acceleration: does it arise
from a constant vacuum energy as assumed in ΛCDM, or from an-
other form of dark energy that varies in time and space, or from
a breakdown of General Relativity (GR) on cosmological scales?
This question can be addressed by precisely measuring the cosmic
expansion history over a wide span of redshift and by comparing
measurements of the growth of matter clustering to the predictions
of Λ CDM+GR.
This paper presents cosmological results from the final galaxy
clustering data set of the Baryon Oscillation Spectroscopic Survey
(BOSS; Dawson et al. 2013), conducted as part of the Sloan Digi-
tal Sky Survey III (SDSS-III; Eisenstein et al. 2011). As the name
suggests, the defining goal of BOSS is to measure the cosmic ex-
pansion history by means of baryon acoustic oscillations (BAO),
which imprint a characteristic scale detectable in the clustering of
galaxies and of intergalactic Lyα forest absorption. BOSS is the
premier current data set for measurements of large scale galaxy
clustering, which can also be used to constrain cosmological pa-
rameters through the full shape of the galaxy power spectrum and
the anisotropy induced by redshift-space distortions (RSD). As dis-
cussed further below, this paper draws on results from a number
of supporting papers, which present analyses of BAO, RSD, and
full shape constraints using a variety of measurement and mod-
elling techniques and provide the infrastructure to derive statisti-
cal uncertainties and test for systematic effects. Here we synthe-
size these results into “consensus” cosmological constraints from
BOSS galaxy clustering, in combination with a variety of external
data sets. The galaxy data set that underpins these measurements
comes from SDSS Data Release 12 (DR12; Alam et al. 2015a) and
the large scale structure catalogue with the additional information
(masks, completeness, etc.) required for clustering measurements
appears in Reid et al. (2016).
The first direct evidence for cosmic acceleration came from
surveys of Type Ia supernovae (SNe) in the late 1990s (Riess et
al. 1998; Perlmutter et al. 1999). This evidence had immediate
impact in part because studies of cosmic microwave background
(CMB) anisotropy and large scale structure (LSS) already favoured
ΛCDM as an economical explanation for observed cosmic struc-
ture (see, e.g., Efstathiou, Sutherland, & Maddox 1990; Krauss &
Turner 1995; Ostriker & Steinhardt 1995). The case for ΛCDM
sharpened quickly with balloon-based CMB measurements that
found the first acoustic peak at the angular location predicted for
a flat universe (de Bernardis et al. 2000; Hanany et al. 2000; see
Netterfield et al. 1997 for earlier ground-based results pointing in
this direction). Today the web of evidence for cosmic acceleration
c
2016 RAS, MNRAS 000, 1–38
Cosmological Analysis of BOSS galaxies 3
is extremely strong, and nearly all observations remain consistent
with a cosmological constant form of dark energy. CMB measure-
ments from the Wilkinson Microwave Anisotropy Probe (WMAP;
Bennett et al. 2013), ground-based experiments such as the Ata-
cama Cosmology Telescope (Das et al. 2014) and the South Pole
Telescope (George et al. 2015), and, especially, the Planck satel-
lite (Planck Collaboration I 2015) now provide strong constraints
on the cosmic matter and radiation density, the angular diameter
distance to the surface of last scattering, and the shape and am-
plitude of the matter power spectrum at the recombination epoch
z
rec
≈ 1090. These measurements also probe lower redshift matter
clustering through gravitational lensing and the integrated Sachs-
Wolfe (ISW; Sachs & Wolfe 1967) effect. Within ΛCDM, CMB
data alone are sufficient to provide tight parameter constraints, but
these weaken considerably when non-zero curvature or more flex-
ible forms of dark energy are allowed (Planck Collaboration XIII.
2015, hereafter Planck2015). Supernova measurements of the ex-
pansion history have improved dramatically thanks to large ground-
based surveys that span the redshift range 0.2 < z < 0.8, im-
proved local calibrator samples, Hubble Space Telescope searches
that extend the Hubble diagram to z ≈ 1.5, and major efforts
by independent groups to place different data sets on a common
scale and to identify and mitigate sources of systematic error (see
Suzuki et al. 2012; Betoule et al. 2014; and references therein).
BAO measurements, now spanning z = 0.1 − 0.8 and z ≈ 2.5,
complement the SN measurements by providing an absolute dis-
tance scale, direct measurement of the expansion rate H( z), and
robustness to systematic errors (see discussion and references be-
low). Direct “distance ladder” measurements of H
0
constrain the
present day expansion rate, providing the longest lever arm against
the CMB (Riess et al. 2011, 2016; Freedman et al. 2012). RSD and
weak gravitational lensing measurements provide complementary
probes of structure growth that have somewhat different parame-
ter sensitivity and very different systematics. Consistency of RSD
and weak lensing can also test modified gravity models that predict
different effective potentials governing light-bending and acceler-
ation of non-relativistic tracers. At present, these structure growth
measurements are substantially less precise than expansion history
measurements (∼ 5 − 10% vs. ∼ 1 − 2%), so they serve pri-
marily to test departures from GR and constrain neutrino masses
rather than measure dark energy parameters. This situation is likely
to change in next-generation experiments. Observational probes of
dark energy are reviewed by, e.g., Albrecht et al. (2006), Frieman,
Turner, & Huterer (2008), Blanchard (2010), Astier & Pain (2012),
and more comprehensively by Weinberg et al. (2013). Reviews fo-
cused more on theories of dark energy and modified gravity include
Copeland, Sami, & Tsujikawa (2006), Jain & Khoury (2010), and
Joyce, Lombriser, & Schmidt (2016). Reviews focused on future
observational facilities include LSST Science Collaboration et al.
(2009), Kim et al. (2015), Huterer et al. (2015), and Amendola et
al. (2016).
While acoustic oscillations were already incorporated in early
theoretical calculations of CMB anisotropies (Peebles & Yu 1970;
Sunyaev & Zel’dovich 1970), interest in using the BAO feature as
a “standard ruler” in galaxy clustering grew after the discovery of
cosmic acceleration (Eisenstein, Hu, & Tegmark 1998; Blake &
Glazebrook 2003; Seo & Eisenstein 2003). The physics of BAO
and contemporary methods of BAO analysis are reviewed at length
in Ch. 4 of Weinberg et al. (2013), and details specific to our anal-
yses appear in the supporting papers listed below. In brief, pressure
waves in the pre-recombination universe imprint a characteristic
scale on late-time matter clustering at the radius of the sound hori-
zon,
r
d
=
Z
∞
z
d
c
s
(z)
H(z)
dz , (1)
evaluated at the drag epoch z
d
, shortly after recombination, when
photons and baryons decouple (see Aubourg et al. 2015 for more
precise discussion). This scale appears as a localized peak in the
correlation function or a damped series of oscillations in the power
spectrum. Assuming standard matter and radiation content, the
Planck 2015 measurements of the matter and baryon density de-
termine the sound horizon to 0.2%. An anisotropic BAO analysis
that measures the BAO feature in the line-of-sight and transverse
directions can separately measure H(z) and the comoving angular
diameter distance D
M
(z), which is related to the physical angu-
lar diameter distance by D
M
(z) = (1 + z)D
A
(z) (Padmanabhan
et al. 2008). Adjustments in cosmological parameters or changes
to the pre-recombination energy density (e.g., from extra relativis-
tic species) can alter r
d
, so BAO measurements really constrain
the combinations D
M
(z)/r
d
, H(z)r
d
. An angle-averaged galaxy
BAO measurement constrains a combination that is approximately
D
V
(z) =
czD
2
M
(z)/H(z)
1/3
. (2)
An anisotropic BAO analysis automatically incorporates the so-
called Alcock-Paczynski (1979; AP) test, which uses the require-
ment of statistical isotropy to constrain the parameter combination
H(z)D
M
(z).
The localized three-dimensional nature of the BAO feature
makes BAO measurements robust to most observational system-
atics (see Ross et al. 2012, 2016), which tend to introduce only
smooth distortions in clustering measurements. Similarly, non-
linear evolution and galaxy bias are expected to produce smooth
rather than localized distortions of clustering. Our BAO analy-
sis methods introduce parametrized templates to marginalize over
smooth distortions of observational or astrophysical origin, and re-
sults are insensitive to details of these templates and to many other
analysis details (Vargas-Maga
˜
na et al. 2014, 2016). Non-linear evo-
lution broadens the BAO peak in the correlation function (or damps
high-k oscillations in the power spectrum), and simulations and
perturbation theory calculations indicate that non-linear evolution
and galaxy bias can shift the location of the BAO peak at a level
of 0.2 − 0.5% (Eisenstein et al. 2007b; Padmanabhan & White
2009; Seo et al. 2010; Mehta et al. 2011; Sherwin & Zaldarriaga
2012). Measurements of the BAO scale using samples with consid-
erable differences in galaxy bias that share the same volume have
obtained results consistent with such small shifts (Ross et al. 2014;
Beutler et al. 2016a). A key element of recent BAO analyses is re-
construction, which attempts to reverse non-linear effects so as to
sharpen the BAO peak and thereby restore measurement precision
(Eisenstein et al. 2007; Padmanabhan et al. 2012; Burden, Percival
& Howlett 2015; Schmittfull et al. 2015). Simulation tests and per-
turbation theory calculations show that reconstruction also removes
the small shifts induced by non-linearity and galaxy bias, to a level
of ≈ 0.1% or better (Padmanabhan, White, & Cohn 2009; Noh,
White, & Padmanabhan 2009; Seo et al. 2010; Mehta et al. 2011;
Tassev & Zaldarriaga 2012; White 2015). The combination of pre-
cision, complementarity to SNe, and robustness to systematics has
made BAO a pillar of contemporary cosmology.
Early analyses of the power spectrum of the 2-Degree Field
Galaxy Redshift Survey (2dFGRS; Colless et al. 2003) showed
strong hints of baryonic features (Percival et al. 2001), but the first
clear detections of BAO came in 2005 with analyses of the final
c
2016 RAS, MNRAS 000, 1–38
4 S. Alam et al.
2dFGRS data set (Cole et al. 2005) and the SDSS DR3 data set
(Eisenstein et al. 2005). These detections were already sufficient to
yield 3 − 4% distance scale constraints. The SDSS measurement
was based on the luminous red galaxy (LRG) sample, constructed
to provide sparse but relatively uniform sampling over a large vol-
ume (Eisenstein et al. 2001). Subsequent milestones in BAO mea-
surement include: isotropic BAO analyses of the final (DR7) SDSS-
I/II LRG and main galaxy redshift surveys (Percival et al. 2007);
detection of BAO in clustering of SDSS galaxies with photomet-
ric redshifts (Padmanabhan et al. 2007); analyses of anisotropic
BAO signals in SDSS-I/II (Okumura et al. 2008; Gazta
˜
naga et al.
2009; Chuang & Wang 2012; Chuang et al. 2013a; Chuang & Wang
2013b); the first BAO measurements at z > 0. 5 from the WiggleZ
survey (Blake et al. 2011a); a low redshift (z ≈ 0.1) BAO measure-
ment from the 6-degree Field Galaxy Survey (6dFGS; Beutler et al.
2011); improved measurements from applying reconstruction to the
SDSS LRG survey (Padmanabhan et al. 2012) and main galaxy sur-
vey (MGS; Ross et al. 2015); BAO measurements from the BOSS
DR9 and DR11 galaxy redshift surveys (Anderson et al. 2012,
2014a,b; Tojeiro et al. 2014); and BAO measurements at z ≈ 2.5
in the BOSS Lyα forest using auto-correlations in DR9 (Busca et
al. 2013; Slosar et al. 2013) and both auto-correlations and quasar-
Lyα cross-correlations in DR11 (Font-Ribera et al. 2014; Delubac
et al. 2015). The BOSS DR11 measurements achieve distance scale
precision of 2.0% at z = 0.32, 1.0% at z = 0.57, and ≈ 2% at
z = 2.5 (where the best constrained combination is D
0.3
M
H
−0.7
rather than D
V
). Aubourg et al. (2015) present cosmological con-
straints and model tests derived from these measurements in con-
cert with other data, and they provide a high-level discussion of the
interplay between BAO measurements and complementary probes.
Section 9 of this paper updates these constraints and model tests
to our final DR12 galaxy clustering results. The DR12 Lyα forest
BAO measurements are in process and will be reported in future
work (J. Bautista et al., in prep.).
The linear theory description of RSD is three decades old
(Kaiser 1987), but progress on high-precision RSD constraints has
been slow because a variety of non-linear effects influence RSD
signals even out to very large scales (Cole, Fisher, & Weinberg
1994; Scoccimarro 2004; Tinker, Weinberg, & Zheng 2006). RSD
constraints thus require both large survey volumes and analytic or
numerical models for non-linear evolution and galaxy bias. Mile-
stones in large scale RSD analysis include measurements from the
1.2-Jy (Cole, Fisher, & Weinberg 1995) and PSCz (Tadros et al.
1999) IRAS redshift surveys, the Stromlo-APM redshift survey
(Loveday et al. 1996), the 2dFGRS (Peacock et al. 2001; Hawkins
et al. 2003; Percival et al. 2004b), the VVDS (Guzzo et al. 2008),
VIPERS (de la Torre et al. 2013), the SDSS LRG sample (Okumura
et al. 2008; Chuang et al. 2013a; Chuang & Wang 2013b; Oka et al.
2014) and main galaxy redshift survey (Howlett et al. 2015), and
the 6dFGS (Beutler et al. 2012) and WiggleZ (Blake et al. 2012)
surveys. RSD measurements from earlier BOSS data releases, us-
ing a variety of technical approaches, include Reid et al. (2012,
2014); Tojeiro et al. (2012); Chuang et al. (2013a); Samushia et al.
(2013, 2014); S
´
anchez et al. (2013, 2014); Beutler et al. (2014a);
Gil-Mar
´
ın et al. (2016b); Alam et al. (2015b). Modern RSD analy-
ses usually frame their results in terms of constraints on f(z)σ
8
(z),
where σ
8
(z) describes the normalization of the linear theory matter
power spectrum at redshift z (via the rms fluctuation in 8 h
−1
Mpc
spheres) and
f(z) ≡
d ln G
d ln a
(3)
is the logarithmic growth rate of the linear fluctuation amplitude
G(t) with respect to expansion factor a(t) = (1 + z)
−1
(see Per-
cival & White 2009; Song & Percival 2009; §7.2 of Weinberg et
al. 2013 and references therein). The papers above adopt a variety
of approaches to RSD measurement and, crucially, to modelling
non-linear effects. There is frequently a trade-off between decreas-
ing statistical errors and increasing theoretical systematics as one
probes to smaller scales. There is also partial degeneracy between
clustering caused by peculiar velocities and the geometric distor-
tion from the AP effect. Analyses that reach to BAO scales, or that
include BAO as an external constraint, can achieve better fσ
8
con-
straints because the BAO themselves constrain the AP distortion.
Conversely, AP constraints from anisotropic clustering analysis on
sub-BAO scales can help break the degeneracy between D
M
(z)
and H(z) in BAO. Thus, the potential gains from combining BAO
analyses with analyses of the full shape of the galaxy power spec-
trum or correlation function are large.
This paper derives cosmological constraints from the com-
bination of BAO-only measurements that incorporate reconstruc-
tion and full shape (FS) measurements of galaxy clustering without
reconstruction. FS measurements do not have the precision gains
available from reconstruction at the BAO scale, and their interpre-
tation relies more heavily on non-linear modelling. However, FS
analyses take advantage of the rich information on cosmological
parameters encoded in the broad band power spectrum, they use
broad band information to improve measurement of the AP effect,
and, most importantly for purposes of this paper, they yield con-
straints on structure growth through RSD. The input measurements
for our analysis are summarized in this paper and detailed in seven
supporting papers (Table 1). The BAO scale is measured using the
anisotropic two-point correlation function in Ross et al. (2016) and
Vargas-Maga
˜
na et al. (2016) and using the anisotropic power spec-
trum in Beutler et al. (2016b). The full shape of the anisotropic two-
point correlation function is computed and analysed using multi-
poles in Satpathy et al. (2016) and using µ -wedges in S
´
anchez et al.
(2016a). The equivalent measurements in Fourier space are made
using power-spectrum multipoles in Beutler et al. (2016c) and µ-
wedges in Grieb et al. (2016). Other key supporting papers are Reid
et al. (2016), who describe the LSS catalogues used for all of these
analyses, Kitaura et al. (2016), who describe the MultiDark-Patchy
mock catalogues used to test analysis methods and derive covari-
ance matrices, Tinker et al. (2016), who present high-resolution
mock catalogues and use them to test the RSD performance of our
FS methods, and S
´
anchez et al. (2016b), who describe and test our
statistical methodology for combining results from these analyses.
The resulting final consensus likelihoods are publicly available
1
.
While each of these analyses is individually a major endeav-
our, this multi-faceted approach has two key virtues. First, we ob-
tain results from several groups working semi-independently with a
variety of analysis tools and modelling assumptions, allowing pow-
erful cross checks for errors or for systematic effects that might in-
fluence one method more than another. Second, even though they
are applied to the same data set, these methods extract information
in different ways that are not entirely redundant, even within the
BAO-only or FS subsets. We evaluate the covariance of their re-
sults using mock catalogues, and even though the covariances are
often strong, the combined precision is higher than that of any indi-
1
https://sdss3.org/science/boss_publications.php.
The MCMC chains used to infer cosmological parameters will be made
available after acceptance of the paper.
c
2016 RAS, MNRAS 000, 1–38