Have Baryonic Acoustic Oscillations in the galaxy distribution really been measured?

0.39 MB·English

by  Anna Cabre

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed19January2011 (MNLATEXstylefilev2.2)
Have Baryonic Acoustic Oscillations in the galaxy
distribution really been measured?
Anna Cabr´e1, Enrique Gaztan˜aga2
1 1Department of Physics and Astronomy, University of Pennsylvania, 209, South 33rd Street, Philadelphia, PA 19104-6396, USA
1 2Instituto de Ciencias del Espacio (IEEC/CSIC), F. de Ciencias, Torre C5- Par-2a, Bellaterra, 08193 Barcelona, Spain.
0
2

n
a Accepted—.Received—;inoriginalform—
J

8
1 ABSTRACT
Recent publications claim that there is no convincing evidence for measurements of

] thebaryonicacoustic(BAO)featureingalaxysamplesusingeithermonopoleorradial
O
information.Differentclaimsseemcontradictory:dataiseithernotconsistentwiththe
C BAO model or data is consistent with both the BAO model and featureless models
. withoutBAO.Weinvestigatethispointwithasetof216realisticmockgalaxycatalogs
h
extracted from MICE7680, one of the largest volume dark matter simulation run to
p
date, with a volume of 1300 cubical gigaparsecs. Our mocks cover similar volume,
-
o densities and bias as the real galaxies and provide 216 realizations of the Lambda
r or ω = −1 Cold Dark Matter (ωCDM) BAO model. We find that only 20% of the
t
s mocks show a statistically significant (3 sigma) preference for the true (input) ωCDM
a BAOmodelascomparedtoafeatureless(non-physical)modelwithoutBAO.Thusthe
[
volumeofcurrentgalaxysamplesisnotyetlargeenoughtoclaimthattheBAOfeature

3 has been detected. Does this mean that we can not locate the BAO position? Using a
v simple(nonoptimal)algorithmweshowthatin50%(100%)ofthemockswecanfind
9 the BAO position within 5% (20%) of the true value. These two findings are not in
2 contradiction:theformerisaboutmodelselection,thelaterisaboutparameterfitting
7 within a model. We conclude that current monopole and radial BAO measurements
2 can be used as standard rulers if we assume ωCDM type of models.
.
1
Key words: galaxies: statistics, cosmology: theory, large-scale structure.
1
0
1
:
v
i 1 INTRODUCTION Reid et al 2010, Kazin et al 2010a and references therein).
X
Different studies use different ways to extract the BAO sig-
r Primordial fluctuations generated acoustic waves in the nal and quantify the significance of the measurements (see
a
early universe photon-baryon plasma. Those waves were Sanchezetal2008).Forexample,Eisensteinetal2005and
frozen at decoupling, z ∼ 1100, then baryon acoustic os- Sanchez et al 2009 used the full shape of the 2-point cor-
cillations (BAO) were imprinted in the cosmic microwave relation to ωCDM class of models and found constraints to
background (CMB) at the sound horizon scale, as a series thecombinationdistanceD (z)=(D2/H)1/3 tothegalaxy
v A
of peaks in the power spectrum or a single peak in the 2- samplemeanredshiftbasedonaglobalχ2fitting,whilePer-
pointcorrelationfunction(seeegPeeblesandYu,1970and cival et al 2010 used a fit to the oscillatory components in
Komatsuetal2010forthelatestmeasurementsbyWMAP). the power spectrum to find constraints on D (z).
v
BAO can also be seen at the present in matter power These previous analysis used the monopole component
spectrum, and its position, r can be used as a stan- ofthecorrelationfunction,whereallpairsareaveragedwith
BAO
dard cosmological ruler. Measurements in the radial (red- independenceoftheirorientation.Okumuraetal2008dida
shift direction), ∆z, can be used to estimate the Hubble separate analysis of pairs as a function of orientation but
rate as H(z) = c∆z/r , while angular measurements, avoiding the radial direction. Gaztanaga, Cabr´e and Hui
BAO
∆θ, can be used to estimate the angular diameter distance: (2009, GCH hereafter) presented constraints to H(z) based
D (z) = r /∆θ. Baryon acoustic oscillations in the ontheradialcorrelation,whichusesonlythosepairsaligned
A BAO
galaxy correlations of the Sloan Digital Sky Survey (SDSS) with the redshift direction. This reduces the number of ob-
luminous red galaxy (LRG) sample have been used to con- servational data but boost the contrast on the BAO peak
strain cosmological parameters (eg Eisenstein et al 2005, becauseofredshiftspacedistortions.Atintermediatescales,
Hutsi et al 2006, Sanchez et al 2009, Percival et al 2010, lowerthan BAO, thecorrelation functionbecomesnegative
(cid:13)c 0000RAS
2 A. Cabr´e & E. Gaztan˜aga
in the line-of-sight direction, creating a better contrast in can we constrain the parameters of the ωCDM model, and
the BAO position, easier to detect than in real space. Also, in particular the BAO position with current data?
non-linearities, magnification and bias can boost the peak Wewillinvestigatethesepointswithasetof216mock
(see GCH and Tian et al 2010 for further details). galaxycatalogsextractedfromMICE7680(seeFosalbaetal
2008,Crocceetal2009),oneofthelargestvolumedarkmat-
GCHpresentedtwowaystoanalyzetheBAOdata:the
ter simulation run to date. The mocks are made to match
peak and the shape method. In the peak method they find
the SDSS LRG DR6 sample and should therefore provide a
thelocationofthepeakanduseitasstandardrulertomea-
sureH(z).Intheshapemethodtheyuseaχ2 fittothefull good representation of biased ωCDM realizations. We will
use these mocks to explore the peak and the shape method
shape of the correlation and find the best shift in the dis-
appliedtothemonopole.Weusethemonopolehere(rather
tance H(z)/H . The shape method was also used to test if
0
than radial BAO) for several reasons: shape measurements
thedatawascompatiblewiththeshapeofthecorrelationex-
havelargersignal-to-noise,theoreticalmodelingofmonopole
pectedinωCDM.Theycomparedifferentclassesofmodels:
isbetterunderstood(seeGCH)andthemonopoleBAOhas
the standard BAO ωCDM model, a similar class of models
been more widely used to test cosmological models. Rather
withoutBAO(socalledno-wigglemodelinEisenstein&Hu
than comparing the ωCDM with some add-hoc correlation
1998)andamodelwithzerocorrelationξ=0.Theno-BAO
modelhas∆χ2 =10withrespecttothebestfittingωCDM (power-law,constantorsomecombination)wechoosetofo-
model while a model with ξ = 0 has ∆χ2 = 4. Kazin et cus on comparing BAO and no-BAO models. This has the
advantageofbeingawelldefinedprocedure(quitestandard
al(2010b)didanindependentanalysisoftheSDSScatalog
intheliterature)wherewehavethesamenumberofparam-
and found similar results for the correlation measurements
etersineachcase,whichsimplifiestheinterpretationofthe
and errors. In their interpretation they did not explore the
statisticalsignificancewhencomparingtwodifferentmodels
parameterspaceofωCDMbutconcludethatthereisnocon-
with different number of parameters (eg see Liddle 2009).
vincing evidence for radial BAO because the ξ = 0 model
fit the data better than ωCDM. They argue that there are Throughoutweassumeastandardcosmologicalmodel,
no parameters in the ξ = 0 model while for ωCDM sev- withΩM =0.25,ΩΛ =0.75,Ωb =0.044,ns =0.95,σ8 =0.8
eral parameters where fitted in GCH. After including the and h≡H0/(100kms−1Mpc−1)=0.7.
penaltyforaddingparameters,theyfindthatωCDMisnot
significantly better than ξ=0.
But a similar argument could be extended to the BAO
monopole measurements. For example, if one fits a con- 2 BAO IN GALAXY MOCKS
stant correlation to the LRG correlation function in Fig.17
Appendix A in Cabr´e & Gaztanaga 2009 (CG09 from now
of Sanchez etal (2009) to scales larger than 70 Mpc/h one
on) describes how our mocks were built and also how the
findsthatthismodelcannotbedistinguishedfromaωCDM
correlationfunctionisestimated.1 Weincludebothbiasand
model with free parameters. The original Eisenstein etal
redshift distortions in the mocks. We will focus here on the
(2005) results can also be well fitted with a power-law
monopolecorrelationforhaloz=0mockswithabiasb(cid:39)2,
model1.DoesthismeanthattheBAOfeaturehasnotbeen
similartoLRGgalaxies.Thecorrelationfunctionforour216
detected at all? These are important points to clarify as it
mocks, its mean and errors are displayed in Fig.1. These
iscommonpracticetoincludeBAOmeasurementswhenfit-
mocks are realistic as they cover similar volume, densities
tingcosmologicalmodelstoprovideevidencefordarkenergy
andbiasastherealLRGgalaxies,buttheyhavesomelimi-
models (eg Sanchez et al 2009; Komatsu et al 2010; Kazin
tations.Ingeneral,oneneedsfirsttoexploretheparameters
et al 2010a; Gaztanaga, Miquel & Sanchez 2009).
inωCDM(andbiasmodel)togetagoodmatchtodata.Our
Otherrecentstudiesseemtoreachasimilarconclusion,
simulations have β ≡f(Ω )/b(cid:39)0.25 and z =0, which are
m
that the BAO feature has not been detected, but using an
different from the values in real data β (cid:39) 0.34±0.03 and
argumentthatseemstogointheoppositedirection.Rather
z = 0.35 (the difference in β comes from the difference in
than finding that data is too noisy and compatible with
redshift,asbiasissimilar,seeCG09).Dependingonthetest
featurelessmodels,theyfindthatthedataisnotconsistent
used, this could result in a poor fit of models to data. De-
with ωCDM (eg see Labini et al 2009, Labatie et al 2010).
spitetheselimitations,wewillfindbelowagoodfitofdata
Also see Martinez et al 2009 for a study of peak detection
tothemockswhenweallowtheamplitudetovaryinthefit.
using DR7 monopole. We will investigate this here to find,
Thisindicatesthatourmocksprovideagoodrepresentation
as in previous analysis (eg GCH, Sanchez et al 2009, Kazin
of the data, given the errors, at least for the questions we
et al 2010a) that data is in good agreement with ωCDM
want to address here.
although we should stress that this statement will depend
In our analysis we will pretend that each mock is a
on the specific test we use.
realizationoftherealLRGdata.Ourmocksarecloseenough
We will argue that there are two separate questions to the real data to provide a realistic representation of how
mixed up in the above line of argumentation: model selec- much variation there is from one realization of real data to
tion and parameter fitting. We will find that while current theother.Indeedthejack-knife(JK)errors(andcovariance
datacannotbeusedtoselectωCDM,onecanstillconstrain matrix) in the real data are similar to the JK errors in our
theparametersofωCDMifthismodelisassumed.Toshow mocks and to the ensemble variation from mock to mock.
this, we will set out to address two main questions: 1) can ThiswasshowninCG09andcanalsobeseeninFig.1where
we use current BAO data to favor ωCDM? In other words: we compare the ensemble variation in mocks (short dashed
is the volume of current data large enough to pass a null lines)totheJKerrorsintheDR6SDSSLRGmeasurements
detection test to choose ωCDM over some other model? 2) from CG09 (note that we show DR6 to be consistent with
(cid:13)c 0000RAS,MNRAS000,000–000
Have Baryonic Acoustic Oscillations been measured? 3
Figure 2. Histogramsshowingthedistributionofdifferencesin
χ2 values for different LRG mocks. The correlation function in
eachmockisfittedwithboththestandardωCDMBAOcorrela-
tionandwiththeno-BAOclassofmodels.Thedifferencebetween
Figure 1. Thin (black) lines show the correlation function ξ(r)
thetwoχ2 valuesineachmockisaccumulatedinthehistogram.
(scaledbyr2)ineachofour216mocks.Solid(green)lineshows
ThereareN =20databinsineachfit,butonlyoneparameter
the BAO model (the mean of the mocks). Short dashed (green) b
isfitted(theoverallamplitude).Thefigureshowsthatonly20%
linesencompass1-sigmaerrorbarsfromthemean(thesearemock
√ of the cases show a significant preference at 3σ (ie ∆χ2 < −9)
to mock errors, the error of the mean would be 1/ 216 better).
fortheBAOmodelovertheno-BAOmodel.Themeanformocks
Longdashed(blue)lineshowstheno-BAOmodel.The(red)er-
is ∆χ2 =−5. A fit to the real LRG data gives also ∆χ2 =−5,
rorbarscorrespondtotherealLRGdatashiftedasshowninEq.1.
closetothemaximum.
themocks,butsimilarresultsarefoundforDR7,seeGCH). 1987). We use the correlation function ξ (r ) measured in
i j
TocomparetosimulationswehavescaledtheLRGdataas: the i-th mock at separation r to perform a χ2 fit and find
j
thebestfitamplitudeA foreitherBAOorno-BAOmodels
ξ(r)→A[ξ(r)+K] (1) i
(which are labeled generically as ξ ):
m
with A = 1.2 and K = −0.005. The value of A accounts χ2 =(cid:88)[ξ (r )−A ξ (r )]C−1[ξ (r )−A ξ (r )] (2)
forthedifferencesbetweenthesimulationandLRGdatain i i j i m j jk i k i m k
β, growth and bias. The value of K represents a possible, jk
but quite minor (0.25%), error (contamination or sampling The indexes j and k run over the Nb =20 bin separations,
fluctuation)intheoverallmeandensityofthesample.This ie ν =19 degrees of freedom. Bins are linearly spaced with
has little impact in the fit of models to data (covariance ∆r=5 Mpc/h between 30 and 130 Mpc/h (we find similar
allows for a constant shift in the data) but improves the results in the range 20-150 Mpc/h). The covariance matrix
visual comparison in the figure (see Fig.17 in Sanchez et al Cjk is estimated from the mocks:
2009).AsindicatedbyFig.1themocksrepresentquitewell
216
the variation seen in the observational data. C = 1 (cid:88)(cid:2)ξ (r )−ξ¯(r )(cid:3)(cid:2)ξ (r )−ξ¯(r )(cid:3) (3)
jk 215 i j j i k k
i=1
where ξ¯(r )≡ 1 (cid:80) ξ (r ) is the mean value in bin j.
2.1 The shape method: null test j 216 i i j
The resulting distribution of values of χ2 for the BAO
i
We use two models to fit the correlation ξ(r): 1) the BAO modelpeaksaroundχ2 (cid:39)ν =19andisquitebroad(∆χ2 (cid:39)
√ i
model: it uses the mean of all the mocks in order to have 2ν (cid:39)6, as expected). The no-BAO model peaks at larger
a perfect BAO model (with bias, redshift space and non- values (χ2 (cid:39) 24) and is slightly broader (∆χ2 (cid:39) 7.7). The
i
linearities effects included). 2) the no-BAO model: a non- real LRG data produces χ2 = 20 for the BAO model and
physical model that imitates well the broad band corre- χ2 =25fortheno-BAOmodel,wellwithinthevaluesfound
lation but does not include a BAO peak. We use the no- for most of the mocks. Thus, given the large errorbars, the
wigglepowerspectrumofEisenstein&Hu(2001)withsame real data seems to match quite well our mocks, despite the
ωCDM parameters as the simulation. Fig.1 compares the differencesinthemodeledvaluesofβ,biasandzmentioned
BAO(solidline)withtheno-BAOmodel(long-dashedline). above.
Our null test is: does the data prefer the BAO to the no- InFig.2weplotthehistogramofthedifferencesbetween
BAO model at 3-sigma confidence level (CL)? the χ2 values in the fits to the BAO and no-BAO models
i
To simplify the analysis and interpretation, the only for each mock. Negative values mean that the mock prefers
free parameter that we fit is the global amplitude A of the theBAOmodeloverno-BAOmodel.Adifferenceat3σ CL
correlation, which includes a possible bias (as we are us- between both models, ie ∆χ2 < −9, only happens in the
ing halos) and a constant redshift distortion boost (Kaiser 20% of cases (up to 30% when we explore other range of
(cid:13)c 0000RAS,MNRAS000,000–000
4 A. Cabr´e & E. Gaztan˜aga
fects. For WMAP parameters, very similar to MICE simu-
lation, the sound horizon scale is at 107.3Mpc/h.
We find similar results when we use a fixed power-law
for all mocks, the one fitted for the mean correlation func-
tion,orwhenusingthebestpower-lawforeachmock,asone
would do in real data. When we apply the same method to
the real DR6 data we find r = 112Mpc/h, well within
BAO
the bulk of our mocks.
WehavealsotriedthemethodtolocatetheBAOposi-
tionpropposedbyKazinetal(2010a).Themocks(ordata)
are fitted using a χ2 likelihood (including covariance) to a
BAOmodelwhichconsistsinthemeanofthemocks,ξ (r),
m
shiftedbytwofreeparameters:theamplitudeAandascale
shiftα,ieAξ (αr).Wefindaverysimilarhistogramtothat
m
inFig.3butwithsmallererrorbar:6%insteadof8%.Kazin
et al (2010a) further reduced this error to 3−4% by using
onlythemockswhichhaveaclearBAOasintheDR6data.
Wewillobviuslygetsmallererrorsbyremovingsuchoutliers
Figure 3.HistogramshowingthedistributionofpeakBAOpo-
in our mocks but this later step involves more assumptions
sition measured in LRG mocks. This distribution has rBAO =
107.2±8.8 Mpc/h as compared to rBAO =107.5 Mpc/h in the than just the existance of a peak. It not only assumes that
meanmodel.Thedistributionisquitegaussian,asshownbythe we live in ωCDM, but selects in a subjective way (a poste-
linecrossingthehistograms.ThesamemeasurementinrealLRG riori) within a subset of realizations. Also note that in this
DR6datayieldsrBAO =112Mpc/h. method we are using a priori knowledge of the shape of the
input model to locate the peak. In the peak method, used
in Fig.3, we do not need to make such assumption and so
scales). This means than in 80% of the cases one does not we think this makes a stronger case for the point we want
expecttobeabletodistinguishbetweenthetwomodels(at to demostrate, even when the error is larger.
more than 3σ CL). This result is not surprising. The mean Itismorerobustandself-consistenttolocatetheBAO
difference in χ2 between the BAO and no-BAO model is and error using the full shape of ξ(r) and a larger family of
only ∆χ2 (cid:39) −5, which in comparable to the width of the cosmological models, eg as shown in Sanchez et al (2009),
χ2 distribution with 19 degrees of freedom. In other words, avoiding any dependence on a particular cosmology in the
current errors are still too large to claim a BAO detection. algorithmtolocatethepeak.Thepointdemonstratedhereis
thattheBAOpositionisimprintedinthemocksdespitethe
factthattheydonotpassanulldetectiontest.Acomparison
2.2 The peak method: BAO position
between methods is left for future analysis.
In the peak method, we assume that we live in a ωCDM
universeandtrytolocatetheBAOposition.Tokeepthings
simple, here we locate the position of the peak by search-
3 CONCLUSION
ing the maximum in the correlation function in the BAO
scale, between 80-135Mpc/h (results are similar when we Thefirstquestionwesetouttoaddresswasifthevolumeof
move around 70-150Mpc/h). The BAO feature is modified current BAO data is large enough to pass a null detection
bythepresenceofthebroadband(CDM)correlationfunc- testforωCDM.Theanswertothisquestionseemsnegative.
tion, which can be modeled approximately by a power law. We have shown in Fig.2 that the distribution of χ2 differ-
We fit a power law to each correlation function at small encesisquitebroadandonecouldfindmocksforwhichthe
scales(10-70Mpc/h)andsubtractthecorrelationfunction null test is passed or failed. In fact 80% of the mocks have
fromthebestpowerlawbeforelocatingthepeak.GCHuse ∆χ2 > −9, which indicates no statistically significant (at
averysimilarpeakmethodbutdonotneedtosubtractthe 3-sigma CL) preference for the true BAO input model as
power-law because the correlation is quite flat (and close compared to the featureless no-BAO family. Current SDSS
to zero) in the radial direction. Sanchez et al (2010) use a (DR6-DR7)dataseemstolieclosetothepeakofthisdistri-
similarbutmoreelaboratedversion,wheretheyfitsimulta- bution,∆χ2 (cid:39)−5,butaccordingtoFig.2thisdoesnotpro-
neouslyapower-law,aconstantshiftandagaussian(BAO) vide convincing evidence for the BAO model. As expected,
peak.Thiswouldprovidemoreaccurateerrorsforthepeak. the DR3 results in Eisenstein et al 2005 (about half of the
Fig. 3 shows the distribution of recovered BAO posi- DR6volume)isevenlesssignificant:∆χ2 (cid:39)−1.1.Whenwe
tionsforindividualmocks.Thisdistributioniswellapprox- compare the BAO model to a power-law fit (with 2 param-
imated by a Gaussian (also shown in the figure). The mean eters) we find χ2 −χ2 (cid:39)0.4.1
BAO power−law
BAOpositionis107.2Mpc/hwithadispersionof8.8Mpc/h, Ourmockshaveslightlydifferentvaluesofβandzthan
compared to mocks mean value position at 107.5Mpc/h the DR6 data (see Fig.1) and we wonder if this could af-
(note that the resolution in the position of the peak is of fect the above conclusion. The important point to notice is
5Mpc/h). The position of the peak can differ slightly (less that the BAO and no-BAO model also have a similar dif-
than 2%) from the sound horizon scale at decoupling (see ference of ∆χ2 (ie (cid:39) −5) when we compare to the DR6
Sa´nchez, Baugh and Angulo 2008 and Sa´nchez et al 2010) data (using the same bins and covariance as in the mocks).
depending on the cosmology, non-linearities, and other ef- Models with other cosmological parameters within the un-
(cid:13)c 0000RAS,MNRAS000,000–000
Have Baryonic Acoustic Oscillations been measured? 5
certaintiesofωCDMalsoproducesimilar∆χ2.Butavalue modelswhichproducesimilarclustering(anderrors)tothe
of∆χ2 (cid:39)−5iscomparabletothewidthofaχ2distribution ones in ωCDM. 1
with19degreesoffreedom(whichis∆χ2 (cid:39)6).Thisiswhy
the result is not significant. Our conclusion is quite robust
and mostly relays in the size of the errors and covariance ACKNOWLEDGEMENTS
between bins. The covariance estimate is consistent in the
data (ie from Jack-knife subsamples), in our mocks and in We would like to thank Carlton Baugh, Pablo Fosalba,
other mocks produced by several groups (eg Eisenstein et Ramon Miquel and Ariel Sanchez for their comments on
√
al 2005, CG2009, Kazin et al 2010a). We would need 1.8 earlier versions of this manuscript. The MICE simulations
timessmallererrors,ie1.8timesmoredataorsomeoptimal have been developed at the MareNostrum supercomputer
weighting (Hamaus et al. 2010, Cai etal 2010), than DR6 (BSC-CNS) thanks to grants AECT-2006-2-0011 through
(so that ∆χ2 increases from 5 to 9) to be able to claim a 3 AECT-2010-1-0007. Data products have been stored at the
sigma BAO detection in the monopole. Port d’Informacio´ Cient´ıfica (PIC). This work was par-
tially supported by the Spanish Ministerio de Ciencia e In-
For the radial BAO analysis, GCH reach similar con-
novacion (MICINN), projects AYA2009-13936, Consolider-
clusions. They find that the difference ∆χ2 (cid:39) −10 in DR6
Ingenio CSD2007- 00060 and research project 2009-SGR-
for 20 degrees of freedom (5Mpc/h radial bins within 40-
1398 from Generalitat de Catalunya.
140Mpc/h)whencomparingBAO(plusmagnification)and
no-BAO models (without magnification the difference is
∆χ2 (cid:39)−6).Thisseemsmoresignificantthanthemonopole,
REFERENCES
probablybecausetheradialBAOpeakisboostedbyredshift
space distortions and magnification. Cabr´e,A.andGaztan˜aga,E.,2009,MNRAS,393,1183
Does this mean that the BAO position can’t be mea- CaiY.-C.,BernsteinG.,ShethR.K.,2010,arXiv:1007.3500
sured? If we assume the ωCDM model, we can locate the Crocce,M.,etal.2009,MNRAS,403,1353
Eisenstein,D.J.,&Hu,W.1998,ApJ,496,605
BAO position to better than 8% of the true value, as illus-
EisensteinD.J.,etal.,2005,ApJ,633,560
trated in Fig.3. We show that in 50% (100%) of the mocks
Fosalba,P.,etal.2008,MNRAS,391,435
we can find the BAO position within 5% (20%) of the true
Gaztan˜aga, E. and Cabr´e, A. and Hui, L., 2009, MNRAS, 399,
value. This error is an upper bound as we have not tried
1663
to optimize the method to locate the peak. We have com- Gaztan˜aga,E.andMiquel,R.andS´anchez,E.,2009,PhyRevLet,
pared the mocks with the real data and found no evidence 103,9
fordeviationsawayfromtheωCDM.Noneofthe216ωCDM Gaztan˜aga E., Cabr´e A., Castander F., Crocce M., Fosalba P.,
realizations is identical to the measurements (or in fact to 2009,MNRAS,399,801
each other), but observations produce values that lie well Hamaus N., Seljak U., Desjacques V., Smith R. E., Baldauf T.,
within thehistograms in Fig.2 andFig.3 for the two simple 2010,PhRvD,82,043515
KaiserN.,1987,MNRAS,227,1
but generic tests that we have explored here.
Kazin,E.etal.,2010a,ApJ,710,1444
Lessons learned in this study can be applied to the Kazin,E.etal.,2010b,ApJ,719,1032
monopole BAO analysis (eg Eisenstein et al 2005, Sanchez Komatsu,E.,etal.,2010,astro-ph/1001.4538
et al 2009, Percival et al 2010, Kazin et al 2010a) and the LabatieA.,etal.,2010,astro-ph/1009.1232
radial BAO in GCH (or the BAO in the 3-point function Labini,S.etal2009A&A,505,981-990
by Gaztanaga et al 2009). Kazin et al (2010b) have argued LiddleA.,2009,Ann.Rev.Nucl.Part.Sci.59,95
thatbecauseωCDMdoesnotfittheradialBAOdatasignif- Martinez,V.etal.,2009,ApJ,696,L93
icantlybetterthanamodelwithξ=0(nulltest),theH(z) Okumura,T.,etal.,2008,ApJ,676,889
Peebles,P.J.E.andYu,J.T.,1970,ApJ,162,815
measurements presented by CGH based on the location of
PercivalW.,etal.,2010,MNRAS401,2148
the radial BAO peak can not be regarded as a detection.
Reid,B.A.,etal.,2010,MNRAS,404,60
We have shown here that his argument is not necessarily
S´anchez A. G., Crocce M., Cabr´e A., Baugh C. M., Gaztan˜aga
correct. If we apply such argument to the monopole BAO E.,2009,MNRAS,400,1643
measurements previously cited we would conclude that we S´anchez A. G., Baugh C. M., Angulo R., 2008, MNRAS, 390,
cannotlocatethepeakpositionincurrentdatabecauseac- 1470
cording to Fig.2 there is no significant BAO detection. But SanchezE.,etal,2010,arXiv,arXiv:1006.3226
we have shown here that we can locate the BAO position Tian, H. J. and Neyrinck, M. C. and Budav´ari, T. and Szalay,
with reasonable accuracy even with data that fails the null A.S.,2010,arXiv,1011.2481
BAOdetectiontest.AsimilaranalysiswasdonewithMonte
Carlo mocks in GCH for the radial BAO position. Even if
the shape method gives low significance, the peak method
can still be used to detect the position of the peak.
Tianetal2010reachessimilarconclusionsfortheradial
BAO peak using different simulations. They use a wavelet
techniquetodetectthepeakandassesthesignificanceofthe
detection, splitting SDSS into slices in various rotations.
CurrentBAOmeasurementscannotyetbeusedtose- 1 Data and mocks used in this paper, together with co-
lectωCDM,buttheycanbeusedtolocatetheBAOposition variance matrix and additional figures can be found in
(orothercosmologicalparameters)ifoneassumesωCDMor http://www.ice.csic.es/mice/baodetection.
(cid:13)c 0000RAS,MNRAS000,000–000