New neutrino mass
bounds from BOSS
photometric luminous
galaxies
Elena Giusarma
IFIC, University of Valencia-CSIC
in collaboration with:
Roland De Putter, IFIC of Valencia, ICC of Barcelona
Olga Mena, IFIC of Valencia
Introduction
(0.36 eV). Σmν < 0.90 W
of adding supernova and
, Θs , τ, nsoscillation
, log[1010 Aexperiments
{Ωb h2 , Ωc h2Neutrino
ment,
but when the HS
s ], fν , ASZ , bhave
i , ai }adduced
robust
additions lower the upp
evidence for a non-zero neutrino mass but they are not
Combining the CMASS data with a CMB prior from
only model). Consideri
sensitive
the
scaleΣm
of neutrino
the WMAP7 survey,
weto
find
anabsolute
upper bound
< 0.6 masses.
pole range, characterize
•
•
ν
eV (0.90 eV) at 95% confidence level for "max = 200 in the
we find that a significan
Cosmology
provides
meansthe
to tackle
thelargest multipoles
and of
ai ).theAdding
in the
model with free
parameters
bi (bi one
absolute
scale
of neutrino
masses.
current"max
limit=on
thethe galaxy
HST measurement
of the
Hubble
parameter,
the A
prob150,
ability distribution
and
we find
neutrino
sum oftightens
neutrino
masses
is Σmν < 0.6 eV at 95%
CL, mass.
depending on the cosmological data and on the
cosmological model.
•
We derive neutrino mass constrains from the angular
power spectra of galaxy density at different redshifts,
in combination with priors from the CMB and from
measurements of the Hubble parameter.
owave Backconstraints on the sum of the neutrino masses and other
n anisotropy
parameters for several data combinations in section 6.
ased experiFinally, we discuss these results and conclude in section
of the stan7.
eigh neutri- Imaging data from DR8
2. DATA
eutrinos can (Aihara et al, APJS ’11)
e formation
The data and the method for obtaining angular spectra
Sloan
Digital
Skyin detail in Ref. Ross et al. (2011)
ogical data ofhave
been
described
mordial rela- Survey
and in III,
Ho etSDSS-III
al. (2012). Here we provide a brief descriper-radiation
tion of the main properties and refer the reader to those
etfor
al,details.
APJ ’00)
tropies. Af- (York
papers
Our galaxy sample is obtained from
ming nature
imaging data from DR8 Aihara et al. (2011) of SDSSthe growth The
III first
York etdata
al. (2000).
This
survey mapped about 15, 000
release
of
ecting both
square degrees of the sky in five pass bands (u, g, r, i and
in the low- the
z) Baryon
FukugitaOscillation
et al. (1996) using a wide field CCD camera
). MeasureGunn et al. (1998)
on the 2.5 meter Sloan telescope at
Spectroscopic
Survey,
sed to place
Apache Point Observatory Gunn et al. (2006) (the subogy Elgaroy BOSS
(Eisenstein
al,
sequent
astrometric et
calibration
of these imaging data is
tad (2003);
described in Pier et al. (2003)). A sample of 112, 778
APJ
’11)
Barger et al.
galaxy spectra from BOSS Eisenstein et al. (2011) were
Ross et al.
t al. (2004);
used as a training sample for the photometric redshift
5); Hannescatalog, as described in Ross et al. (2011).
t al. (2007);
focus of
on luminous
the approximately
mass-limited
CMASSWe
sample
galaxiesstellar
(White
et al APJ ’11) is divided
matsu et al.
CMASS sample of luminous galaxies, detailed in White
into four
bins
, four photometric
a); Thomas
et al.photometric
(2011), whichredshift
are divided
into
t al. (2011);
redshift bins, zphoto = 0.45 − 0.5 − 0.55 − 0.6 − 0.65.
2011); BenThe photometric redshift error lies in the range σz (z) =
It covers
an0.06,
area
of 10,000
degree
and Figure
consists of 900,000
sum of neu0.04 −
increasing
fromsquare
low to high
redshift.
Reid et al.
1 shows the estimated true redshift distribution of each
galaxies.
ion of data
bin, determined using the methods described in section
del.
5.3 of Ross et al. (2011).
rom the fiThe calculation of the angular power spectrum for each
Data
•
•
Angular power spectra of the galaxy density
The showing
theoretical
is given by:15 . It then folthat power
this is aspectra
safe approximation
lows from the above (see Fisher et al. (1994); Heavens &
Taylor (1995); Padmanabhan et al. (2007)) that
�
�
�2
2
(ii)
(i)
RSD,(i)
C� = b2i
k 2 dk Pm (k, z = 0) ∆� (k) + ∆�
(k) ,
π
(9)
where Pm (k, z = 0) is the matter power spectrum at
redshift zero and
�
(i)
∆� (k) = dz gi (z) T (k, z) j� (k d(z)) .
(10)
large non-line
stricted to low
modes per uni
many modes a
ure 3 (left pan
value of � abov
dimensional p
lar spectrum b
considering va
kNL (z). Given
range z = 0.45
comes inadequ
Here, j� is the spherical Bessel function and T (k, z) the
a conservative
150 and 200.
matter transfer function relative to redshift zero16 . The
Alternativel
contribution due to redshift space distortions is
�
portance of no
�
2
(2l + 2l − 1)
RSD,(i)
non-lin
∆l
(k) = βi
dz gi (z) T (k, z)
jl (kd(z)) fect of
(2l + 3)(2l − 1)
trum18 (which
panel in Figur
l(l − 1)
Angular power spectra of the galaxy density
The showing
theoretical
is given by:15 . It then folthat power
this is aspectra
safe approximation
lows from the above (see Fisher et al. (1994); Heavens &
Taylor (1995); Padmanabhan et al. (2007)) that
�
�
�2
2
(ii)
(i)
RSD,(i)
C� = b2i
k 2 dk Pm (k, z = 0) ∆� (k) + ∆�
(k) ,
π
(9)
where Pm (k, z = 0) is the matter power spectrum at
redshift zero and
�
galaxy bias. We add
(i)
four free bias, one
∆� (k) = dz gi (z) T (k, z) j� (k d(z)) .
(10)
large non-line
stricted to low
modes per uni
many modes a
ure 3 (left pan
value of � abov
dimensional p
lar spectrum b
considering va
kNL (z). Given
range z = 0.45
for each bin
comes inadequ
Here, j� is the spherical Bessel function and T (k, z) the
a conservative
150 and 200.
matter transfer function relative to redshift zero16 . The
Alternativel
contribution due to redshift space distortions is
�
portance of no
�
2
(2l + 2l − 1)
RSD,(i)
non-lin
∆l
(k) = βi
dz gi (z) T (k, z)
jl (kd(z)) fect of
(2l + 3)(2l − 1)
trum18 (which
panel in Figur
l(l − 1)
Angular power spectra of the galaxy density
The showing
theoretical
is given by:15 . It then folthat power
this is aspectra
safe approximation
lows from the above (see Fisher et al. (1994); Heavens &
Taylor (1995); Padmanabhan et al. (2007)) that
�
�
�2
2
(ii)
(i)
RSD,(i)
C� = b2i
k 2 dk Pm (k, z = 0) ∆� (k) + ∆�
(k) ,
π
(9)
where Pm (k, z = 0) is the matter power spectrum at
redshift zero and
�
galaxy bias. We add
(i)
four free bias, one
∆� (k) = dz gi (z) T (k, z) j� (k d(z)) .
(10)
large non-line
stricted to low
modes per uni
many modes a
ure 3 (left pan
value of � abov
dimensional p
lar spectrum b
considering va
kNL (z). Given
range z = 0.45
for each bin
comes inadequ
matter power spectrum at
Here, j� is the spherical Bessel function and T (k, z) the
a conservative
redshift zero
150 and 200.
matter transfer function relative to redshift zero16 . The
Alternativel
contribution due to redshift space distortions is
�
portance of no
�
2
(2l + 2l − 1)
RSD,(i)
non-lin
∆l
(k) = βi
dz gi (z) T (k, z)
jl (kd(z)) fect of
(2l + 3)(2l − 1)
trum18 (which
panel in Figur
l(l − 1)
Angular power spectra of the galaxy density
The showing
theoretical
is given by:15 . It then folthat power
this is aspectra
safe approximation
large non-line
lows from the above (see Fisher et al. (1994); Heavens &
stricted to low
Taylor (1995); Padmanabhan et al. (2007)) that
modes per uni
�
many modes a
�
�
2
(ii)
(i)
RSD,(i)
2 2
C � = bi
k 2 dk Pm (k, z = 0) ∆� (k) + ∆�
(k) , ure 3 (left pan
π
value of � abov
(9)
showing that this is a safe approximation15 . It then follarge
non-linear p
co
dimensional
(see matter
Fisher etpower
al. (1994);
Heavens &
stricted
to low �.b
where Plows
z =the0)above
is the
spectrum
at
m (k,from
lar spectrum
(1995); Padmanabhan et al. (2007)) that
modes per unit � i
redshift Taylor
zero and
considering
va
�
many
modes
as
pos
�
�
�2
galaxy bias. We add
2
(ii)
(i)
RSD,(i)
kNL
(z).panel)
Given
2
ure
3
(left
d
(i)= b2i
C∆
k
dk
P
(k,
z
=
0)
∆
(k)
+
∆
(k)
,
m
four free bias, one
�
�
�
dz gi (z) T (k, z) j� (k d(z)) .
(10)
π
range
= 0.45
� (k) =
value
of � zabove
wh
for each bin
(9)
dimensional
power
comes inadequ
matter
power
spectrum
atis the matter power spectrum at
where
P
(k,
z
=
0)
m
lara spectrum
becom
Here, j� is the spherical Bessel function and T (k, z) the
conservative
redshift
zero and
redshift
zero
considering various
150
and
200.
matter transfer function�relative to redshift zero16 . The
k
(z).
Given
that
NL
(i)
contribution due
redshift
distortions
∆�to(k)
= dz gspace
z) j� (k d(z))is.
(10)
i (z) T (k,
rangeAlternativel
z = 0.45 − 0.
�
portance
of noa
�
comes
inadequate
2
(2l +and
2l T−(k,
1)z) the
RSD,(i)Here, j� is the spherical Bessel function
a conservative
choi
fect
of
non-lin
∆l
(k) = βi
dz gi (z) T (k, z)
j
(kd(z))
l
150
and18
200.
matter transfer function relative to
zero
(2lredshift
+ 3)(2l
−161). The
trum
(which
Alternatively,
we
contribution due to redshift space distortions is
panel
in
Figur
l(l�− 1)
�
portance of non-lin
2
Angular power spectra of the galaxy density
The showing
theoretical
is given by:15 . It then folthat power
this is aspectra
safe approximation
large non-line
lows from the above (see Fisher et al. (1994); Heavens &
stricted to low
Taylor (1995); Padmanabhan et al. (2007)) that
modes per uni
�
many modes a
�
�
2
(ii)
(i)
RSD,(i)
2 2
C � = bi
k 2 dk Pm (k, z = 0) ∆� (k) + ∆�
(k) , ure 3 (left pan
π
value of � abov
(9)
showing that this is a safe approximation15 . It then follarge
non-linear p
co
dimensional
(see matter
Fisher etpower
al. (1994);
Heavens &
stricted
to low �.b
where Plows
z =the0)above
is the
spectrum
at
m (k,from
lar spectrum
(1995); Padmanabhan et al. (2007)) that
modes per unit � i
redshift Taylor
zero and
considering
va
�
many
modes
as
pos
�
�
�2
galaxy bias. We add
2
(ii)
(i)
RSD,(i)
kNL
(z).panel)
Given
2
ure
3
(left
d
(i)= b2i
C∆
k
dk
P
(k,
z
=
0)
∆
(k)
+
∆
(k)
,
m
four free bias, one
�
�
�
dz gi (z) T (k, z) j� (k d(z))
.
(10)
π
range
= 0.45
� (k) =
value
of � zabove
wh
contribution
due
to
the
for each bin
(9)
dimensional
power
comes inadequ
redshift
space
distortions
matter
power
spectrum
atis the matter power spectrum at
where
P
(k,
z
=
0)
m
lara spectrum
becom
Here, j� is the spherical Bessel function and T (k, z) the
conservative
redshift
zero and
redshift
zero
considering various
150
and
200.
matter transfer function�relative to redshift zero16 . The
k
(z).
Given
that
NL
(i)
contribution due
redshift
distortions
∆�to(k)
= dz gspace
z) j� (k d(z))is.
(10)
i (z) T (k,
rangeAlternativel
z = 0.45 − 0.
�
portance
of noa
�
comes
inadequate
2
(2l +and
2l T−(k,
1)z) the
RSD,(i)Here, j� is the spherical Bessel function
a conservative
choi
fect
of
non-lin
∆l
(k) = βi
dz gi (z) T (k, z)
j
(kd(z))
l
150
and18
200.
matter transfer function relative to
zero
(2lredshift
+ 3)(2l
−161). The
trum
(which
Alternatively,
we
contribution due to redshift space distortions is
panel
in
Figur
l(l�− 1)
�
portance of non-lin
2
for an approach based on perturbation theory and the
local bias model McDonald (2006), and Swanson et al.
(2010)
for a cross-comparison
of a number
methods),
Angular
power spectra
of ofthe
galaxy density
we consider it appropriate, given the multipole range we
include, to use the simple model described in Eq. (9),
characterized by bias parameters bi . In addition to this
The
theoretical
power
is givenmodel
by:15 . with
model,
we also
an alternative
more
showing
that consider
this is aspectra
safe
approximation
It then
follarge non-line
lows from
the above
Fisher et
al. (1994);aHeavens
&
stricted to low
freedom,
by adding
shot(see
noise-like
parameters
i (see also
(1995);papers),
Padmanabhan et al. (2007)) that
modes per uni
ourTaylor
companion
� �
many
modes
a
�
�
�
�
2
2
RSD,(i)
2
(ii)(ii) 2 22 2
(i)(i)
RSD,(i)
2
ure
3 (left pan
(k)
+
∆
(k)
,
m (k,
C� C� = b=i bi π k kdkdk
PmP(k,
z z==0)0) ∆∆
(k)
+
∆
(k)
+a
.
�
�
i
�
�
value of � abov
π
(9)
showing that this is a safe approximation15 . It then(12)
follarge
non-linear p
co
dimensional
the0)above
(see matter
Fisher etpower
al. (1994);
Heavens &
stricted
to low �.b
where
Plows
z =
is
the
spectrum
at
m (k,from
lar
spectrum
The
parameters
a
serve
to
mimic
effects
of
scalei
Taylor
(1995);
Padmanabhan et al. (2007)) that
modes per unit � i
redshift
zero
and
considering
va
dependent
galaxy
bias
and
to
model
the
effect
of
poten�
many
modes
as
pos
�
�
�2
galaxy bias. We add
2
(ii)
(i)
RSD,(i)
kNL
(z).panel)
Given
2
2
ure
3
(left
d
noise
subtraction.
This
model
is
a
(i)=shot
C∆
b
k
dk
P
(k,
z
=
0)
∆
(k)
+
∆
(k)
,
m
fourtial
freeinsufficient
bias, one
i
�
�
�
(k) =
dz gi (z) T (k, z) j� (k d(z))
.
(10)
π
range
= 0.45
�
value
of � zabove
wh
contribution
due
to
the
version
of
what
is
sometimes
referred
to
as
the
“P-model”
for each bin
(9)
dimensional
power
comes inadequ
redshift
space
distortions
(e.g. Hamann
et
al.
(2008);
Swanson
et
al.
(2010))
and
is
matter
power
spectrum
atis the matter power spectrum at
where
P
(k,
z
=
0)
m
lara spectrum
becom
Here,
j
is
the
spherical
Bessel
function
and
T
(k,
z)
the
conservative
�
independently
motivated
(2000,
redshift
zero and by the halo model Seljak 16
redshift
zero
considering various
�relative to redshift zero . The
150
and
200.
matter
transfer
function
k
(z).
Given
that
2001); Schulz & White
(2006);
Guzik
et
al.
(2007)
and
NL
(i)
Alternativel
contribution
due
redshift
distortions
∆�to(k)
= dz gspace
z) j� (k d(z))is.
(10)
i (z) T (k,
range
z = 0.45 − 0.
the local bias ansatz
Scherrer
&
Weinberg
(1998);
Coles
�
portance of no
�
comes inadequate a
(2l +and
2l T−(k,
1)z) the
RSD,(i)Here, j� is the spherical Bessel function
18 However,
a conservative
choi
fect
of
non-lin
must
keep
in
mind
that
this
may
underestimate
∆l
(k)one
=β
dz
g
(z)
T
(k,
z)
j
(kd(z))
i
i
l
16
150
and18
200.
matter
transfer
function
relative
to
redshift
zero
.
The
(2l
+
3)(2l
−
1)
trum
(which
the effect of non-linear galaxy bias, as galaxies are more strongly
Alternatively,
we
contribution
due
tothus
redshift
space
distortions
is
clustered than
matter and
are
prone
to
larger
non-linear
corpanel
in
Figur
l(l�− 1)
�
portance of non-lin
2
rections.
2
for an approach based on perturbation theory and the
local bias model McDonald (2006), and Swanson et al.
(2010)
for a cross-comparison
of a number
methods),
Angular
power spectra
of ofthe
galaxy density
we consider it appropriate, given the multipole range we
include, to use the simple model described in Eq. (9),
characterized by bias parameters bi . In additionshot-noise
to this that serves to mimic
The
theoretical
power
is givenmodel
by:15 . with
model,
we also
an alternative
more
showing
that consider
this is aspectra
safe
approximation
It effects
then
folnon-line
of scale large
dependent
lows from
the above
Fisher et
al. (1994);aHeavens
&
stricted to low
freedom,
by adding
shot(see
noise-like
parameters
also
i (see
galaxy
bias
(1995);papers),
Padmanabhan et al. (2007)) that
modes per uni
ourTaylor
companion
� �
many
modes
a
�
�
�
�
2
2
RSD,(i)
2
(ii)(ii) 2 22 2
(i)(i)
RSD,(i)
2
ure
3 (left pan
(k)
+
∆
(k)
,
m (k,
C� C� = b=i bi π k kdkdk
PmP(k,
z z==0)0) ∆∆
(k)
+
∆
(k)
+a
.
�
�
i
�
�
value of � abov
π
(9)
showing that this is a safe approximation15 . It then(12)
follarge
non-linear p
co
dimensional
the0)above
(see matter
Fisher etpower
al. (1994);
Heavens &
stricted
to low �.b
where
Plows
z =
is
the
spectrum
at
m (k,from
lar
spectrum
The
parameters
a
serve
to
mimic
effects
of
scalei
Taylor
(1995);
Padmanabhan et al. (2007)) that
modes per unit � i
redshift
zero
and
considering
va
dependent
galaxy
bias
and
to
model
the
effect
of
poten�
many
modes
as
pos
�
�
�2
galaxy bias. We add
2
(ii)
(i)
RSD,(i)
kNL
(z).panel)
Given
2
2
ure
3
(left
d
noise
subtraction.
This
model
is
a
(i)=shot
C∆
b
k
dk
P
(k,
z
=
0)
∆
(k)
+
∆
(k)
,
m
fourtial
freeinsufficient
bias, one
i
�
�
�
(k) =
dz gi (z) T (k, z) j� (k d(z))
.
(10)
π
range
= 0.45
�
value
of � zabove
wh
contribution
due
to
the
version
of
what
is
sometimes
referred
to
as
the
“P-model”
for each bin
(9)
dimensional
power
comes inadequ
redshift
space
distortions
(e.g. Hamann
et
al.
(2008);
Swanson
et
al.
(2010))
and
is
matter
power
spectrum
atis the matter power spectrum at
where
P
(k,
z
=
0)
m
lara spectrum
becom
Here,
j
is
the
spherical
Bessel
function
and
T
(k,
z)
the
conservative
�
independently
motivated
(2000,
redshift
zero and by the halo model Seljak 16
redshift
zero
considering various
�relative to redshift zero . The
150
and
200.
matter
transfer
function
k
(z).
Given
that
2001); Schulz & White
(2006);
Guzik
et
al.
(2007)
and
NL
(i)
Alternativel
contribution
due
redshift
distortions
∆�to(k)
= dz gspace
z) j� (k d(z))is.
(10)
i (z) T (k,
range
z = 0.45 − 0.
the local bias ansatz
Scherrer
&
Weinberg
(1998);
Coles
�
portance of no
�
comes inadequate a
(2l +and
2l T−(k,
1)z) the
RSD,(i)Here, j� is the spherical Bessel function
18 However,
a conservative
choi
fect
of
non-lin
must
keep
in
mind
that
this
may
underestimate
∆l
(k)one
=β
dz
g
(z)
T
(k,
z)
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.
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the effect of non-linear galaxy bias, as galaxies are more strongly
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contribution
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portance of non-lin
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2
Angular power spectra of the galaxy
density
Xiv:1201.1909v1 [astro-ph.CO] 9 Ja
4
form of massive neutrinos. A new bound on the sum of neu
confidence level (CL), is obtained after combining our sampl
with WMAP 7 year Cosmic Microwave Background (CMB)
of the Hubble parameter from the Hubble Space Telescope (H
conservative multipole range choice of 30 < � < 200 in order
bias parameter in each of the four redshift bins. We study th
bias model using mock catalogs, and find that this model cau
For this reason, we also quote neutrino bounds based on a con
additional, shot�noise-like free parameters. In this conserva
weakened, e.g.
mν < 0.36 eV (95% confidence level) for WM
also study the dependence of the neutrino bound on multipol
on which combination of data sets is included as a prior. Th
Acoustic Oscillation data does not significantly improve the n
is included.
A companion paper (Ho et al. 2012) describes the constru
detail and derives constraints on a general cosmological mode
state w and the spatial curvature ΩK , while a second compa
measurement of the scale of baryon acoustic oscillations from
based on the catalog by Ross et al. (2011).
scription
at least t
During the last several years, experiments involving sothe two
lar, atmospheric, reactor and accelerator neutrinos have
2
∆m
23 =
adduced robust evidence for flavor change, implying non(2011),
zero neutrino mass, see Ref. Gonzalez-Garcia & Maltoni
tions. D
(2008) and references therein. The most economical deoscillatio
1 ICC, University of Barcelona (IEEC-UB), Marti i Franques
future se
1, Barcelona 08028, Spain
ve
2 Instituto de Fisica Corpuscular, University of ValenciaDe Putter etDirac
al.
1. INTRODUCTION
Effect of massive neutrinos on the angular
power spectra
We assume that there are
three degenerate species of
massive neutrinos with
Fig. 4.— Effect of neutrinos on the angular power spectra. The so
respectively.
the input values
(although
the parameter most affected
De Putter
et al.
by the mock CMASS data, ΩDM h2 , is higher than the
In the presence of massive neutrinos
theto
angular
power spectra are suppressed at
bylessclose
1σ).is dominated
input values (although the parameter most affected input
significantly
(as their reconstruction
by
the
mock
CMB
prior).
the mock
data, Ω hand
, is higher
thansuppression
the
anyCMASS
redshift,
this
could be partially
increasing
Unfortunately,
do compensate
have by
mocks
basedtheon
Adding the nuisance parameter awe
, we obtain
thenot
red
ut by close to 1σ).
points and curves in Fig. 6. The effect of marginalizing
nfortunately, we do not have mocks based on
a
with biasof
non-zero
Σm
. lower
Onethe
check
cold
dark
matter
energy
density.
Thetheeffect
the
is νto
powerwe
overcosmology
a is to diminish
parameter
so that
Ω bias
h
osmology with non-zero Σm .
One check we
is typically reconstructed to well within 1σ. We atdo, however, is to fit a model with parameters
can
however,
to fit
spectra
at
any
multipole
range.
tribute do,
this change
to a accounting is
for a possible
scale-a model with parameters
h , Ω h , θ, A , n , τ, Σm , b } to our Σm = 0
2 in galaxy bias
2 on quasilinear scales. The
dependence
ck spectra. The parameters affected by far the most
{Ω
b h , ΩDM h , θ, As , ns , τ, Σmν , b0 } to our Σmν = 0
g. 4.— Effect of neutrinos on the angular power spectra. The solid and dashed curves depict the massless and Σmν = 0.3 eV cases,
ectively.
DM
2
0
0
ν
2
DM
2
s
s
ν
0
ν
2
DM
0
2
bound which would only apply if neutrinos are Majospectra of the galaxy density at different 1
redsh
rana particles Gomez-Cadenas et al. (2011). Forthcomcombination with priors from the CMB and
1 fro
ing ββ(0ν) experiments aim for sensitivity approaching
surements of the Hubble parameter, supernov
�meff � < 0.05 eV Gomez-Cadenas et al. (2011).
tances and the BAO scale. The spectra and the
2
2
10
Cosmology
of the
means
a minimal
ΛCDM cosmology are described in d
,provides
τ, ns ,one
log[10
As ],toftackle
Athe
, bi , aofof
ΛCDM
+ sneutrino
mass
fraction
Sunyaev-Zel’dovich
bh , Ω
ch , Θ
ν ,, Amplitude
SZ abi }the
solute
our companion paper Ho et al. (2012) and the m
10
2 scale2of neutrino masses. Some
10of the earliest cosog[10
A
],
f
,
A
,
b
,
a
}
, four
bias
parameters
fourfrom
nuisance
{Ωbmological
hspectrum
,Ω
,onτ,
log[10
As ],
fνfrom
, ASZ
ai }(optionally)
s c hbounds
ν, Θs
SZ
ins , igalaxy
neutrino
masses
followed
the, bi ,and
ment
of the BAO scale
the spectra is prese
relic neutrinos, present today
a separate companion paper Seo et al. (2012).
As ], frequirement
, ASZ , that
bi , amassive
νparameters
i}
in the expected numbers, do2 not saturate
the critical den-10
often refer to these works for details and focus
2
, Ωthe
, Θs , τ, mass
ns , log[10
fν ,neutrino
ASZ , bibound.
, ai }
sity of the Universe, {Ω
i.e.,b hthat
energy As ],the
c h neutrino
density given by
The structure of the paper is as follows. In se
we describe the data set and the derived angular
�
mν
We then discuss our theoretical model for the spec
Ων =
(1)
We derive
their cosmology dependence in section 3. In secti
93.1h2 eV
explain the specific signature of neutrino mass on
satisfies Ων ≤ 1. The Universe therefore offers a new labclustering data. We test our model for the angula
oratory for testing neutrino masses and neutrino physics.
spectra against mock data in section 5 and pres
Accurate measurements of the Cosmic Microwave Backconstraints on the sum of the neutrino masses an
ground (CMB) temperature and polarization anisotropy
parameters for several data combinations in se
from satellite, balloon-borne and ground-based experiFinally, we discuss these results and conclude in
ments have fully confirmed the predictions of the stan7.
dard cosmological model and allow us to weigh neutri2. DATA
nos Lesgourgues & Pastor (2006). Indeed, neutrinos can
ect ofplay
neutrinos
on therole
angular
power spectra.
Theformation
solid and dashedThe
curves
the
massless
and Σmν angular
= 0.3 e
a relevant
in large-scale
structure
datadepict
and the
method
for obtaining
and leave key signatures in several cosmological data
have been described in detail in Ref. Ross et al
sets. More the
specifically,
the amount
of primordial relaand inless
Ho (as
et al.
(2012).
Here we provide
a brief
ues (although
parameter
most
affected
significantly
their
reconstruction
is
domina
tivistic neutrinos changes
the epoch of matter-radiation
tion of the main properties and refer the reader t
2
the
mock
CMB prior).
CMASS
data,
ΩDM
, is higher
than
the
equality,
leaving
anhimprint
on CMB
anisotropies.
Afpapers for details. Our galaxy sample is obtain
Adding
the nuisance
, we
obtainof
e to ter
1σ).
becoming non-relativistic, their free-streaming nature
imaging
data fromparameter
DR8 Aiharaa0et
al. (2011)
points and
curves
in(2000).
Fig. 6.This
The
effect
of margin
power
small scales,
ely, damps
we do
noton have
mockssuppressing
based onthe growth
III York
et al.
survey
mapped
about
of matter
density
fluctuations
thus affecting
both
square
degrees ofthe
the parameter
sky in five pass
bands
(u, g,
over a0 is
to diminish
bias
so that
with
non-zero
Σm
Oneandcheck
we
ν.
CMB
and agalaxy
clustering
observables in the is
low-typically
z) Fukugita
et al. (1996)
wide field1σ.
CCD
reconstructed
tousing
wella within
ever,the
is
to
fit
model
with
parameters
redshift universe Lesgourgues & Pastor (2006). MeasureGunnchange
et al. (1998)
on
the 2.5 meter
Sloan
teles
2
tribute
this
to
a
accounting
for
a
possibl
, θ, ments
As , nsof, τ,
Σm
,
b
}
to
our
Σm
=
0
0
ν
0
ν
all of these observations have been used to place
Apache Point Observatory Gunn et al. (2006) (t
dependence
in astrometric
galaxy bias
on quasilinear
scales
. The
affected
by far
the
most Elgaroy
newparameters
bounds on neutrino
physics
from
cosmology
sequent
calibration
of
these
imaging
2
MCMC Analysis and Results
1redsh
bound
which would
only
apply
if neutrinos
are Majospectra
the galaxy
at ±
different
0.975
± 0.026
−
1.002
± 0.004
0.949 ± 0.004
0.991 ± 0.004
1.001of
± 0.003
0.954 ±density
0.004 1.007
0.004 0.972
±
MCMC Analysis and Results
rana particles Gomez-Cadenas et al. (2011). Forthcomcombination with priors from the CMB and
1 fro
— ββ(0ν) experiments
—
−0.035
−0.026 ±
0.005 −0.008 ± 0.005
—
—
—
ing
aim ±
for0.005
sensitivity
approaching
surements— of the Hubble
parameter,
supernov
�meff � < 0.05 eV Gomez-Cadenas et al. (2011).
tances and the BAO scale. The spectra and the
2 —
2
10
—
— ΛCDM cosmology
—
−1.19
0.10 −1.06
Cosmology
of—the
means
tackle
a minimal
are ±
described
in ±
d
,provides
τ, ns ,one
log[10
As ],tof—
Athe
, bi—, aofof
ΛCDM
+ sneutrino
mass
fraction
Sunyaev-Zel’dovich
bh , Ω
ch , Θ
ν ,, Amplitude
SZ abi }the
solute
our companion paper Ho et al. (2012) and the m
10
2 scale2of neutrino masses. Some
10of the earliest cosog[10
A
],
f
,
A
,
b
,
a
}
, four
bias
parameters
four
nuisance
{Ωbmological
h—spectrum
,Ω
,onτ,
log[10
As ],
, ASZ
ai }(optionally)
—s
—
— fνfrom
— BAO scale
— from
0.77spectra
± 0.23 is0.40
±
s c hbounds
ν, Θ
SZ
ins , igalaxy
neutrino
masses
followed
the, —bi ,and
ment
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the
prese
relic neutrinos, present today
a separate companion paper Seo et al. (2012).
As ], frequirement
, ASZ , that
bi , amassive
νparameters
i}
the expected
do2 not
saturate
theeach
critical
den-10
ofteninrefer
to these
details
focusc
LE I. in
Constraints
on numbers,
cosmological
parameters
for
model
described
the text.
We works
report for
both
68% and 95%
2
, Ωthe
, Θstandard
nsdeviation
, log[10
Asthe
],the
fposterior
ASZ , distribution
bibound.
, ai }
sity of parameters
the Universe,
i.e.,
that
neutrino
energy of
bh
c hand
s , τ, mass
ν ,neutrino
he neutrino
and{Ω
the
mean
for the others cosmologic
density given by
The structure of the paper is as follows. In se
meters.
we describe the data set and the derived angular
�
mν
We then discuss our theoretical model for the spec
Ων =
(1)
We derive
their cosmology dependence in section 3. In secti
93.1h2 eV
explain the specific signature of neutrino mass on
satisfies Ων ≤ 1. The Universe therefore offers a new labclustering data. We test our model for the angula
oratory for testing neutrino masses and neutrino physics.
spectra against mock data in section 5 and pres
Accurate measurements of the Cosmic Microwave Backconstraints on the sum of the neutrino masses an
ground (CMB) temperature and polarization anisotropy
parameters for several data combinations in se
from satellite, balloon-borne
and ground-based experi!
Finally, we discuss these results and conclude in
95%
CL
m
[eV]
prior
only
prior+CMASS,!
=
150 prior+CMASS,!max = 200
ν
max
ments have fully confirmed the predictions of the stan7.
WMAP7
prior and allow
1.1 us to weigh
0.74
(0.92)
0.56 (0.90)
dard cosmological
model
neutri2. DATA
nos Lesgourgues & Pastor (2006). Indeed, neutrinos can
ect ofplay
neutrinos
on therole
angular
power spectra.
Theformation
solid and dashedThe
curves
the
massless
and Σmν angular
= 0.3 e
a relevant
in large-scale
structure
datadepict
and the
method
for obtaining
and leave key signatures in several cosmological data
have been described in detail in Ref. Ross et al
sets. More the
specifically,
the amount
of primordial relaand inless
Ho (as
et al.
(2012).
Here we provide
a brief
ues (although
parameter
most
affected
significantly
their
reconstruction
is
domina
tivistic neutrinos changes
the epoch of matter-radiation
tion of the main properties and refer the reader t
2
the
mock
CMB prior).
CMASS
data,
ΩDM
, is higher
than
the
equality,
leaving
anhimprint
on CMB
anisotropies.
Afpapers for details. Our galaxy sample is obtain
Adding
the nuisance
, we
obtainof
e to ter
1σ).
becoming non-relativistic, their free-streaming nature
imaging
data fromparameter
DR8 Aiharaa0et
al. (2011)
points and
curves
in(2000).
Fig. 6.This
The
effect
of margin
power
small scales,
ely, damps
we do
noton have
mockssuppressing
based onthe growth
III York
et al.
survey
mapped
about
!
of matter
density
fluctuations
and
thus prior+CMASS,!
affecting
both
square
degrees ofthe
the parameter
sky
in five pass
bands
(u, g,
over max
a0 =
is
to diminish
bias
so that
with
non-zero
Σm
. ν [eV]One
check
we
95%
CL
prior
only
150
prior+CMASS,!
νm
max = 200
CMB
and agalaxy
clustering
observables in the is
low-typically
z) Fukugita
et0.26
al. (1996)
wide field1σ.
CCD
reconstructed
wella within
ever,the
is
to
fit
model
with
parameters
WMAP7
+ HST prior
0.44
0.31 (0.40)
(0.36)tousing
redshift universe Lesgourgues & Pastor (2006). MeasureGunnchange
et al. (1998)
on
the 2.5 meter
Sloan
teles
2
tribute
this
to
a
accounting
for
a
possibl
, θ, ments
As , nsof, τ,
Σm
,
b
}
to
our
Σm
=
0
0
ν
0
ν
all of these observations have been used to place
Apache Point Observatory Gunn et al. (2006) (t
dependence
in astrometric
galaxy bias
on quasilinear
scales
. The
affected
by far
the
most Elgaroy
newparameters
bounds on neutrino
physics
from
cosmology
sequent
calibration
of
these
imaging
2
1redsh
bound
which would
only
apply
if neutrinos
are Majospectra
the galaxy
at ±
different
0.975
± 0.026
−
1.002
± 0.004
0.949 ± 0.004
0.991 ± 0.004
1.001of
± 0.003
0.954 ±density
0.004 1.007
0.004 0.972
±
MCMC Analysis and Results
rana particles Gomez-Cadenas et al. (2011). Forthcom-2
combination with priors from the CMB and
1 fro
Fig. 6.— Left panel: Recovered values of ΩDM h from averaged mock spectrum together with CMB prior. W
— ββ(0ν) experiments
—
−0.035 ±
−0.026 ±
0.005 −0.008 ± 0.005
—
—
—
—
ing
for0.005
sensitivity
approaching
thevalues
Hubble
parameter,
supernov
different lines ofaim
sight.
The
points with
error bars show surements
the posteriorofmean
and 1σ
error bars after
the
�meff � < 0.05
eV Gomez-Cadenas
et al.
(2011).
and the
BAO
scale.
The spectra
and the
the i
scenarios:
varying Σmν 10
with
(red)
and without (blue) a0 tances
marginalized.
The
vertical
magenta
lines indicate
2 —
2
—
—parameter
—
−1.19
0.10the−1.06
Cosmology
of—the
tackle
the
a minimal
ΛCDM uncertainty
cosmology
are ±
described
in ±
d
input
±means
one
=, 0.0032
is the
based
on
data
,provides
τ,and
nsthe
,one
log[10
Asand
],totwo
f—
Awhere
, σbi—
aofof
ΛCDM
+(solid)
mass
fraction
Amplitude
Sunyaev-Zel’dovich
bh , Ω
ch , Θ
sneutrino
ν ,,σ,
SZ abi }the
(ai = masses.
0 fixed). Some
There
is athe
bias
of about
1σ without
nuisance parameter,
which
disappears
a
solute
of neutrino
earliest
cosour the
companion
paper Ho et
al. (2012)
andwhen
the m
10
2 scale2spectra
10of
og[10
A
],
f
,
A
,
b
,
a
}
, four
bias
parameters
four
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h—spectrum
,Ω
,Θ
,onτ,
log[10
A
fνfrom
, ASZ
bithe
,and
atwo
—s
—
—distributions
—
— discussed
— from
0.77
± 0.23
±a
panel:
The
posterior
neutrino
mass
cases
above.
The
mock
constraints
s c hbounds
ν
SZ
ins , igalaxy
s ],
i }(optionally)
neutrino
masses
followed
the,for
ment
of
the
BAO scale
the
spectra
is0.40
prese
cosmology
of Σmrelic
Other parameters
are
all reconstructed
to close
to their input
values
and
are
not stro
ν = 0.
that
massive
neutrinos,
present
today
a
separate
companion
paper
Seo
et
al.
(2012).
As ], frequirement
,
A
,
b
,
a
}
parameters
ν
SZ spectra.
i
i
the expected
do2 not
saturate
theeach
critical
den-10
ofteninrefer
to these
details
focusc
LE I. in
Constraints
on numbers,
cosmological
parameters
for
model
described
the text.
We works
report for
both
68% and 95%
2
, Ωthe
, Θstandard
nsdeviation
, log[10
Asthe
],the
fposterior
ASZ , distribution
bibound.
, ai }
sity of parameters
the Universe,
i.e.,
that
neutrino
energy of
bh
c hand
s , τ, mass
ν ,neutrino
he neutrino
and{Ω
the
mean
for the others cosmologic
�
95% CL
mν [eV]
prior only The
prior+CMASS,�
150 isprior+CMASS,�
m
density given by
structure of max
the =
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as follows. In se
meters.
the (0.92)
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the specific
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1
satisfies Ων ≤The
1. The
therefore
offers alimits
new labclustering
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test our
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95%Universe
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on the sum
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ν . The top row inv
oratory for testing
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an
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.
ground (CMB) temperature and polarization anisotropy
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for severalaidata
combinations in se
from satellite, balloon-borne
and ground-based experi!
Finally, we discuss these results and conclude in
95%
CL
m
[eV]
prior
only
prior+CMASS,!
=
150 prior+CMASS,!max = 200
ν
max
ments have fully confirmed the predictions of the stan7.
WMAP7
prior1,
1.1
0.74
0.56the
(0.90)
dard cosmological
model
and
allow
to weigh
neutrirow
of Table
with
theusresults
with
a(0.92)
WMAP7+HST bound is so
i marginalized in
2. DATA
nos Lesgourgues
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(2006).
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parentheses.
bound
improves
fromcan
1.1 eV for CMB
WMAP7-only
one, i.e. Σmν <
ect ofplay
neutrinos
on
the
angular
power
spectra.
The
solid
and
dashed
curves
depict
the
massless
andAdding
Σmν angular
=the
0.3 eC
a relevant
role
in eV
large-scale
formation
The
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theνmethod
obtaining
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0.56
for CMBstructure
with CMASS
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200).
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and leave key
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detail
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Ross et al
by Reid
etinal,the
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Thissignatures
constraintinisseveral
comparable
to the limit
tightens
bound
significantly
ν < 0.62
sets. MoreeV
specifically,
theReid
amount
of(2010)
primordial
inless
Ho (as
et al.
(2012).
Here
we provide
a brief
derived
by
et al.
from relathe DR7and
spectroper
bound
of Σm
0.26
eV is
ues (although
the
parameter
most
affected
significantly
their
reconstruction
domina
ν < is
tivistic neutrinos
changes
theItepoch
of
matter-radiation
tion of the
main
properties
and refer
the reader
t
2
scopic
sample.
thus
appears
that
the
advantage
of
(in
the
bias-only
model),
as
is
s
the
mock
CMB
prior).
CMASS
data,
ΩDM
, is higher
than
the
equality,
leaving
anhimprint
on CMB
anisotropies.
Afpapers
for details.
Our 1.
galaxy
sample
ismargin
obtain
spectroscopic
redshifts
(providing
information
on
clusof
Table
The
effect
of
Adding
the
nuisance
parameter
a
,
we
obtain
e to ter
1σ).
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al. (1996)
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that the
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in
Fig.
8. InSloan
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Lesgourgues
& Pastor
(2006).
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al.
(1998)
on
the
2.5
meter
teles
2
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this
change
to
a
accounting
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, θ, ments
As , nsof, τ,
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,
b
}
to
our
Σm
=
0
0
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0
ν
deteriorates
significantly
for Σmν , summarized
Table
allconstraint
of these observations
have
been used towhen
place marginalizing
Apache Point Observatory
Gunn et al. in
(2006)
(t
dependence
in
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bias
on
quasilinear
scales
. The
affected
by parameters
far
the
most
the
nuisance
ai . InElgaroy
this case, sequent
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ors are
worth noting.
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effe
newparameters
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2
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bound
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only
apply
if neutrinos
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0.975
± 0.026
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1.002
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— with priors
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—
rana
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(2011).
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Fig. 6.— Left panel: Recovered values of ΩDM h from averaged mock spectrum together with CMB prior. W
— ββ(0ν) experiments
—
−0.035
±
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0.005 −0.008 ± 0.005
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(2012)
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panel:
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SZ
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masses
followed
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ment
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the
BAO scale
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spectra
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= 0.neutrinos,
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text.
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today
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companion
paper
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et
al.
(2012).
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1
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focusc
LE neutrino
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the text.
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+ HST prior (1)
0.44
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their cosmology dependence in section 3. In secti
explain TABLE
the specific
signature of neutrino mass on
1
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1. The
therefore
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new labclustering
data. Wemasses
test our
model
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on the sum
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oratory for testing
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masses
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physics.to a WMAP
spectra prior
against
mock
in section
5 and
pres
adding
the CMASS
galaxy
power spectra
while
thedata
bottom
row uses
WMAP
Accurate measurements
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a prior.
parentheses
we show constraints
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the
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!
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aidata
.
ground (CMB)
temperature
anisotropy = 150
parameters
for several
combinations in se
95% CL
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priorpolarization
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prior+CMASS,!
max
max = 200
from satellite, balloon-borne
and ground-based experi!
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discuss
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prior
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0.74 (0.92)
(0.90)
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CL
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prior
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150
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ments have fully confirmed the predictions of the stan7.
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of Table
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i marginalized in
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& PastorThe
(2006).
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bound
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ect ofplay
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angular
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for CMBstructure
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Ross et al
by Reid
etinal,the
JCAP’10
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tightens
bound
significantly
ν < 0.62
sets. MoreeV
specifically,
theReid
amount
of(2010)
primordial
inless
Ho (as
et al.
(2012).
Here
we provide
a brief
derived
by
et al.
from relathe DR7and
spectroper
bound
of Σm
0.26
eV is
ues (although
the
parameter
most
affected
significantly
their
reconstruction
domina
ν < is
tivistic neutrinos
changes
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of
matter-radiation
tion of the
main
properties
and refer
the reader
t
2
scopic
sample.
thus
appears
that
the
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as well.
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that the
shown
in
Fig.
8. InSloan
addition
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& Pastor
(2006).
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al.
(1998)
on
the
2.5
meter
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2
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change
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b
}
to
our
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=
0
0
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0
ν
deteriorates
significantly
for Σmν , summarized
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allconstraint
of these observations
have
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(2006)
(t
dependence
in
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on
quasilinear
scales
. The
affected
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far
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nuisance
ai . InElgaroy
this case, sequent
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ors are
worth noting.
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effe
newparameters
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of
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bound
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only
apply
if neutrinos
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± 0.026
−
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± 0.004
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± 0.003
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— with priors
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—
rana
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(2011).
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— ββ(0ν) experiments
—
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±
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ment
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oratory for testing
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5 and
pres
adding
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power spectra
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max
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from satellite, balloon-borne
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discuss
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150
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ments have fully confirmed the predictions of the stan7.
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been described
detail
in Ref.
Ross et al
by Reid
etinal,the
JCAP’10
Thissignatures
constraintinisseveral
comparable
to the limit
tightens
bound
significantly
ν < 0.62
sets. MoreeV
specifically,
theReid
amount
of(2010)
primordial
inless
Ho (as
et al.
(2012).
Here
we provide
a brief
derived
by
et al.
from relathe DR7and
spectroper
bound
of Σm
0.26
eV is
ues (although
the
parameter
most
affected
significantly
their
reconstruction
domina
ν < is
tivistic neutrinos
changes
theItepoch
of
matter-radiation
tion of the
main
properties
and refer
the reader
t
2
scopic
sample.
thus
appears
that
the
advantage
of
(in
the
bias-only
model),
as
is
s
the
mock
CMB
prior).
CMASS
data,
ΩDM
, is higher
than
the
equality,
leaving
anhimprint
on CMB
anisotropies.
Afpapers
for details.
Our 1.
galaxy
sample
ismargin
obtain
spectroscopic
redshifts
(providing
information
on
clusof
Table
The
effect
of
Adding
the
nuisance
parameter
a
,
we
obtain
e to ter
1σ).
0et al. (2011) of
becoming non-relativistic,
their free-streaming nature
imaging
data from
DR8the
Aihara
!
tering
along
the
line
of
sight)
in
that
sample
is
offset
to
bring
constraint
back
to c
points
and
curves
in
Fig.
6.
The
effect
of
margin
power
on
small
scales,
suppressing
the growth
95%
CLhave
mν [eV]
prior
only prior+CMASS,!
=
150
prior+CMASS,!
=
200
ely, damps
we do
not
mocks
based
on
This survey mapped about
max III York et al. (2000).max
by
the
advantage
of
the
current
sample
having
a
larger
bound.
!
of matter
density
and
thus prior+CMASS,!
affecting
WMAP7
+ fluctuations
HST
prior
0.44
0.31both
(0.40)
0.26
(0.36)
square
degrees
ofthe
the
sky
in
bands
(u, g,
over
abetween
is
to diminish
parameter
bias
so that
with
non-zero
Σm
.
One
check
we
0 =
95%
CL
m
[eV]
prior
only
150
prior+CMASS,!
= five
200 pass
ν
ν
max
max
volume,
although
there
are
other
differences
the
The
posteriors
for
all
cosm
CMB
and agalaxy
clustering
observables in the is
low-typically
z) Fukugita
et0.26
al. (1996)
using
a within
wide field1σ.
CCD
reconstructed
to
well
ever,the
is
to
fit
model
with
parameters
WMAP7
+
HST
prior
0.44
0.31
(0.40)
(0.36)
samples
and analyses
as well.
Note,
however, Gunn
that the
shown
in
Fig.
8. InSloan
addition
redshift universe
Lesgourgues
& Pastor
(2006).
Measureet
al.
(1998)
on
the
2.5
meter
teles
2
tribute
this
change
to
a
accounting
for
a
possibl
, θ, ments
As , nsof, τ,
Σm
,
b
}
to
our
Σm
=
0
0
2
2
10
ν
0
ν
deteriorates
significantly
marginalizing
for
Σm
Table
νi,, summarized
allconstraint
of these observations
place
Apache
Point
Observatory
Gunn
et al. in
(2006)
(t
{Ωhave
Ωc hused
, Θsto
,when
τ,
n
,
log[10
A
],
f
,
A
,
b
a
}
marginalization
over
the
parameters
b h , been
s
s
ν
SZ
i
dependence
in
galaxy
bias
on
quasilinear
scales
. The
affected
by parameters
far
the
most
the
nuisance
ai . InElgaroy
this case, sequent
the massastrometric
ors are
worth noting.
The
effe
newparameters
boundsover
on neutrino
physics
from
cosmology
calibration
of
these
imaging
2
93.1h2 eV
Posterior probability for all cosmological
parameters
CMB+H
0
CMB+H0 with
CMASS spectra
in theprior.
rangeWe show th
Fig. 8.— Cosmological constraints with a WMAP7 CMB and Hubble parameter
for CMB + H0 only (black), CMB + H0 with CMASS spectra in the range � = 30 − 150 (blue dash
spectra in the range � = 30 − 200 (blue solid). The red curves represent the constraints in the conser
over a set of nuisance parameters ai . While this marginalization degrades the neutrino bound, simulat
CMB+H0 with
in ΩDM h2 (see section 5).
CMASS spectra
on the sum of neutrino masses. We have used Fig.
mock
(0.36 eV).constraints
We have with
alsoac
8.— Cosmological
in
the
range
forHOD
CMB + H0supernova
only (black),
+ H0red
w
galaxy catalogs based on N-body simulations and
andCMB
a (lower
spectra
in the when
range � the
= 30HST
− 200 prior
(blue solid
modeling to test two models for the angular galaxy
specis
over a set of nuisance parameters ai . While
tra. Based on these tests, we decided to compare
theh2 (seetions
lower
lim
in ΩDM
section
5). the upper
Constraints
in the
data to theoretical spectra based on the non-linear matmodel). Considering the
conservative
model
on bias
the sum range,
of neutrino
masses.
ter power spectrum augmented by a linear galaxy
characterized
byWe
a
N-body
sim
where
we
marginalize
factor. However, since this model does result ingalaxy
a biascatalogs
findbased
that aon
significant
am
2
2
10
2
modeling
test
two
h , Ωwe
, Θs , also
τ, nfitted
As ], fνto, the
ASZlargest
, bi ,models
aimultipoles
} for the�an
over
in ΩDM h of ∼ 1{Ω
− b1.5σ,
the
data
=
c h have
s , log[10
on
tests,thewegalaxy
decide
to a more conservative model, with an additionaltra.
set Based
of
�maxthese
= 150,
spectra
based
on m
t
shot noise-like fitting parameters, in which this data
bias to
is theoretical
on neutrino
mass.
Our
virtually absent. The tests also motivated us to ter
use power
the spectrum
Table 1. augmented by a
factor.
this model
do
multipole range � = 30 − 200, but we quoted results
for However,
It issince
interesting
to compa
2
in Ω
1−
1.5σ, we
al
DM h ofof∼an
the more conservative choice � = 30 − 150 as well.
The
analysis
of ahave
simila
a more conservative
model, with
added advantage is that this analysis provides to
insight
SDSS photometric
cataloa
shot noise-like
parameters,
in
into the range of scales that yields the galaxy clustering
et fitting
al. (2007).
In Thoma
virtually absent.
tests isalso
motivC
information.
boundThe
quoted
a 95%
multipole
� = SN
30 −and
200,BAO
but we
Combining the CMASS data with a CMB prior
from range
cluding
da
more conservative
choice
� = 30
the WMAP7 survey, we find an upper bound Σmνthe
< 0.56
and MegaZ.
However,
thi−
is thatrange
this with
analysi
eV (0.90 eV) at 95% confidence level for �max =added
200 inadvantage
a multipole
�m
into the
the range
of scales
yields
the model with free parameters bi (bi and ai ). Adding
rameters
ai .that
As we
havethe
d
De
Putter
et
al.
HST measurement of the Hubble parameter, theinformation.
proba�max = 200 (or even sligh
Correlations between parameters
{Ωb h2 , Ωc h2 , Θs , τ, ns , log[1010 As ],
CMB+H0+CMASS
fspectra
b i , ai }
ν , ASZ ,with
{Ωb h2 , Ωc h2 , Θs , τ, ns , log[1010 As ], fCMB+H
b i , ai }
0 ,with
ν , ASZ
{Ωb h2 , Ωc h2 , Θs , τ,
CMB+H0+CMASS
ns , log[1010 As ],
fν , Awithout
spectra
SZ , bi , ai }
{Ωb h2 , Ωc h2 , Θs , τ, ns , log[1010 AsCMB+H
], fν , 0Awithout
SZ , bi , ai }
De Putter et al.
Correlations between parameters
{Ωb h2 , Ωc h2 , Θs , τ, ns , log[1010 As ],
CMB+H0+CMASS
fspectra
b i , ai }
ν , ASZ ,with
{Ωb h2 , Ωc h2 , Θs , τ, ns , log[1010 As ], fCMB+H
b i , ai }
0 ,with
ν , ASZ
{Ωb h2 , Ωc h2 , Θs , τ,
CMB+H0+CMASS
ns , log[1010 As ],
fν , Awithout
spectra
SZ , bi , ai }
{Ωb h2 , Ωc h2 , Θs , τ, ns , log[1010 AsCMB+H
], fν , 0Awithout
SZ , bi , ai }
De Putter et al.
We also add supernova and BAO data to the CMB+HST+CMASS data set,
and consider the neutrino mass bound in the bias only. We find negligible
improvement (from 0.26 eV to 0.25 eV) relative to the case without these
additional data set.
Conclusions
(0.36 eV). We have
supernova and a (low
2 exploited
2
10
We
angular
power
h
,
Ω
h
,
Θ
,
τ,
n
,
log[10
As spectra
], fν , ASZfrom
, bi , athe
{Ωhave
when the HST prior
b
c
s
s
i } SDSS-III
(0.36 eV). We have also considered
the effect of addi
lower the upper limit
DR8 sample photometric
galaxy
sample
CMASS
to
put
supernova and a (lower redshift) BAO measurement, b
Combiningonthe
CMASS
data
with amasses.
CMB prior from
Considering the depe
10
constraints
the
sum
of
neutrino
10 As ],the
fν ,WMAP7
ASZ , bi survey,
, ai } we find
when
HST
priorΣm
is included
already,
these
additio
<
0.90
(0.36
eV).
Σm
ν
anthe
upper
bound
<
0.56
acterized
by
a
maxim
ν
lower thelevel
upper
limit
to
0.25
eV
(in
the
bias-only
mode
of
adding
supernova
an
eV (0.90
eV)
at
95%
confidence
for
"
significant
amount
o
=
200
in
max
2
2
10
Combining
the
CMASS
data
with
CMB
data
we
find
an
upper
a with athe
CMB
prior
from
the
on thement,
multipole
range,
h , Ω
h , Θ
ns ,Considering
log[10bi A
fν , adependence
A
, bi , ai }the
{Ω
but when
thech
H
bmodel
cwith
s , τ,
SZAdding
(bsi],and
multipoles
" = 150
−
free
parameters
i ).
eVthe
at
95% CLparameter,
model
with
free
bias
additions
lower
the
up
upperbound
bound
Σmν < 0.56of
, we
find
that
acterized
byinathe
maximum
multipole
"max
HST measurement
Hubble
the probathe
galaxy
spectra
Combining
the CMASS
data
with
a CMB
prior
from
model).
Conside
ce levelparameter.
for
"max
amount
resides
larg
=Adding
200
intightens
thesignificant
HST
eV
95%
CL. in the
bility
distribution
andwe
wefind
find
Σmνof
<information
0.26
eV at only
mass.
the WMAP7
survey,
an upper"bound
pole
range,
ν < 0.56
ai ). Adding
the we find
multipoles
= 150Σm
− 200,
but that
even
for characteri
"max = 15
bi (bi and
eV (0.90 the
eV) aprobaatconservative
95% confidence
level spectra
for "max
we find
thaton
a signific
= 200
ble parameter,
the galaxy
place
ainstrong
bound
neutri
Considering
galaxy
bias
model
containing
in the largest multipol
the Σm
model<with
free
parameters
bi (bi and ai ). Adding the
d we find
0.26
eV
mass.
ν
additional
shot noise
parameters
the bounds
are weakened,
0.90
We
(0.36"max
eV).=Σm
ν <
HST measurement
of the
Hubble parameter,
the proba150,
the
galax
supernova
eV
at distribution
95% CL fortightens
CMB+CMASS
and Σmν < 0.36eV
atadding
95%
CL
for
bility
and we find
eVof
neutrino
mass. and a
, Ωc h2 , Θs , τ, ns , log[1010 As ], fν , ASZ , bi , ai }
{Ωb h2CMB+HST+CMASS.
ment, but when the HST
additions lower the upper
Combining the CMASS data with a CMB prior from
only model). Considering
the WMAP7 survey, we find an upper bound Σmν < 0.56
pole range, characterized
eV (0.90 eV) at 95% confidence level for "max = 200 in
we find that a significant
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•
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