Baryon Acoustic Oscillations and the Expansion History of the Universe Antonio J. Cuesta (on behalf of the BOSS collaboration) Institut de Ciències del Cosmos Universitat de Barcelona Outline • Motivation: The distance - redshift relation • Physics of Baryon Acoustic Oscillations (BAO) • Reconstruction of the linear density field • Anisotropies in the galaxy distribution • BAO measurements from BOSS (SDSS-III) Baryon Oscilation Spectroscopic Survey • The correlation function of galaxies: the LOWZ and CMASS samples • The correlation function of neutral Hydrogen: the Lyman-Alpha Forest • Cosmological results from BAO measurements The relation between distances and redshifts Fundamental quantities
a(t) = R(t)/R0 Scale factor å(t)/a(t) = H(t) Hubble parameter
D(z)=∫cdz/H(z) Comoving distance
a = 1/(1+z) Fundamental quantities
a(t) = R(t)/R0 Expansion history å(t)/a(t) = H(t) Expansion rate Distance-redshift D(z)=∫cdz/H(z) relation
a = 1/(1+z) Fundamental quantities
a(t) = R(t)/R0 Expansion history å(t)/a(t) = H(t) Expansion rate Distance-redshift D(z)=∫cdz/H(z) relation z is observable! z = (λ-λ0)/λ0 D is hard to measure at high z
a = 1/(1+z) Why do we want to constrain the Distance-redshift relation?
D(z)=∫cdz/H(z)
2 2 3 H (z) = H0 [ Ωm(1+z) +Ω� ]
Friedmann’s equation (�CDM model) We can constrain the matter content of the Universe Ωm , the dark energy content ΩΛ , the spatial geometry of the Universe Ωk , the equation of state of dark energy �0 , and its time dependence �a Why do we want to constrain the Distance-redshift relation?
D(z)=∫cdz/H(z)
2 2 3 2 H (z) = H0 [ Ωm(1+z) +Ωk(1+z) +Ω� ]
Friedmann’s equation (O�CDM model) We can constrain the matter content of the Universe Ωm , the dark energy content ΩΛ , the spatial geometry of the Universe Ωk , the equation of state of dark energy �0 , and its time dependence �a Why do we want to constrain the Distance-redshift relation?
D(z)=∫cdz/H(z)
2 2 3 2 H (z) = H0 [ Ωm(1+z) +Ωk(1+z) + 3(1+w ) +Ω�(1+z) 0 ] Friedmann’s equation (owCDM model)
We can constrain the matter content of the Universe Ωm , the dark energy content ΩΛ , the spatial geometry of the Universe Ωk , the equation of state of dark energy �0 , and its time dependence �a Why do we want to constrain the Distance-redshift relation?
D(z)=∫cdz/H(z)
2 2 3 2 H (z) = H0 [ Ωm(1+z) +Ωk(1+z) + 3(1+w +w ) w z/(1+z) +Ω�(1+z) 0 a e a ] Friedmann’s equation (ow0waCDM model)
We can constrain the matter content of the Universe Ωm , the dark energy content ΩΛ , the spatial geometry of the Universe Ωk , the equation of state of dark energy �0 , and its time dependence �a What are Baryon Acoustic Oscillations? The physics behind BAO
1 Inflation seeds the Universe with primordial perturbations
2 The photon-baryon fluid, reacts to the perturbation creating a spherical sound wave
3 The sound wave stops propagating shortly after Credit: Daniel Eisenstein (Harvard CfA) electron/proton recombination leaving an overdensity at the same fixed scale, everywhere The physics behind BAO
1 Inflation seeds the Universe with primordial perturbations
2 The photon-baryon fluid, reacts to the perturbation creating a spherical sound wave
3 The sound wave stops propagating shortly after Credit: Daniel Eisenstein (Harvard CfA) electron/proton recombination leaving an overdensity at the same fixed scale, everywhere The physics behind BAO
1 Inflation seeds the Universe with primordial perturbations
2 The photon-baryon fluid, reacts to the perturbation creating a spherical sound wave
3 The sound wave stops propagating shortly after Credit: Daniel Eisenstein (Harvard CfA) electron/proton recombination It can be used as a leaving an overdensity standard ruler at the same fixed scale, to measure the Universe everywhere Propagation of the baryon acoustic wave
Credit: Daniel Eisenstein (Harvard CfA) Propagation of the baryon acoustic wave
Credit: Daniel Eisenstein (Harvard CfA) How long is the BAO standard ruler? The Cosmic Microwave background (CMB) 2 2 measures the matter and baryon densities (Ωbh , Ωmh ) which determines the length of the standard ruler
BAO scale = rdrag =147.41±0.30Mpc measured from Planck2015 (TT+TE+EE+lensing) (1Mpc = 3.262 million light years = 3.086e22m)
Cosmic Microwave Background Map by Planck satellite How long is the BAO standard ruler? The discovery: 10 years of the detection of BAO
Correlation function ξ(s) Power spectrum P(k)
Eisenstein et al 2005 (SDSS) Cole et al 2005 (2dF) The discovery: 10 years of the detection of BAO
�{f(x)}
Correlation function ξ(s) Power spectrum P(k)
Eisenstein et al 2005 (SDSS) Cole et al 2005 (2dF) The discovery: 10 years of the detection of BAO
�{f(x)}
Correlation function ξ(s) Power spectrum P(k)
Eisenstein et al 2005 (SDSS) Cole et al 2005 (2dF) Reconstructing the linear density field Evolution of the density field Why reconstruction?
• Non-linear evolution makes the BAO peak wider and less detectable, which increases the error bar of the derived distance • It would then be desirable to somehow “reconstruct” the linear density field • The effects of non-linearities can (partially) be un-done using the galaxy positions, which estimate the gravitational potential field. No additional observations needed! courtesy of Daniel Eisenstein courtesy of Daniel Eisenstein Effects of reconstruction
before reconstruction
after reconstruction
from Padmanabhan et al. (2012) SDSS-DR7 Measurement 14 Padmanabhanof DV(z=0.35) et al SDSS-II has been provided by the Alfred P. Sloan Foun- dation, the Participating Institutions, the National Science (3.5%) (2.0%) Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Mon- bukagakusho, and the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, Univer- sity of Basel, University of Cambridge, Case Western Re- σ∼1/√V serve University, The University of Chicago, Drexel Univer- sity, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the from Padmanabhan et al. (2012) Joint Institute for Nuclear Astrophysics, the Kavli Insti- Figure 15. The probability of ↵ before [blue, dashed] and af- tute for Particle Astrophysics and Cosmology, the Korean ter [red, solid] reconstruction. The mean and standard deviations of the two distributions is also listed. The shaded regions show Scientist Group, the Chinese Academy of Sciences (LAM- the 1 [dark shaded] and 2 [light shaded] regions of the recon- OST), Los Alamos National Laboratory, the Max-Planck- structed probability distribution. Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of SDSS LRG data as well as lower redshift data from the Portsmouth, Princeton University, the United States Naval SDSS Main galaxy sample. Their primary distance con- Observatory and the University of Washington. straints are therefore reported at a lower redshift from ours: We thank the LasDamas collaboration for making their DV /rs(z =0.275) = 7.19 0.19, a 2.7% measurement. Com- galaxy mock catalogs public. We thank Cameron McBride ± paring these results with ours requires assuming a model to for assistance in using the LasDamas mocks and comments transform to a higher redshift. This comparison is done in on earlier versions of this work. We thank Martin White for detail in Paper III. We can however scale our results to this useful conversations on reconstruction. NP and AJC are par- redshift (assuming that ↵ does not change significantly with tially supported by NASA grant NNX11AF43G. DJE, XX, redshift) to obtain 7.15 0.13. These results are also con- and KM were supported by NSF grant AST-0707725 and ± sistent with Kazin et al. (2010) who obtain 7.17 0.25. We NASA grant NNX07AH11G. This work was supported in ± note that our error before reconstruction is larger than the part by the facilities and sta↵ of the Yale University Faculty Percival et al. (2010) results; this is however expected given of Arts and Sciences High Performance Computing Center. the somewhat larger volume of that sample. Percival et al. (2010) also split their sample into two redshift slices with their higher redshift slice correspond to our measurements. REFERENCES They obtain DV /rs(z =0.35) = 9.11 0.30, consistent with ± our results before reconstruction. Abazajian K. N. et al., 2009, ApJS, 182, 543 Our results have important implications for current and Angulo R. E., Baugh C. M., Frenk C. S., Lacey C. G., 2008, future surveys. All of these surveys have assumed some level MNRAS, 383, 755 of reconstruction for their projected constraints. This work Balay S. et al., 2011a, PETSc users manual. Tech. Rep. retires a major risk for these surveys, being the first appli- ANL-95/11 - Revision 3.2, Argonne National Laboratory cation to data. Furthermore, the degree of reconstruction Balay S. et al., 2011b, PETSc Web page. assumed (a reduction of the nonlinear smoothing scale by Http://www.mcs.anl.gov/petsc 50%) is consistent with what this work has achieved. Balay S., Gropp W. D., McInnes L. C., Smith B. F., 1997, This work has also limited itself to the angle aver- in Modern Software Tools in Scientific Computing, Arge aged correlation function. One of the promises of the BAO E., Bruaset A. M., Langtangen H. P., eds., Birkh¨auser method is the ability to measure both the angular diame- Press, pp. 163–202 ter distance and the Hubble constant. These measurements Beutler F. et al., 2011, MNRAS, 416, 3017 are complicated by the loss of isotropy in the correlation Blake C., Collister A., Bridle S., Lahav O., 2007, MNRAS, function due to redshift-space distortions. As this paper has 374, 1527 shown, reconstruction has the potential to undo the e↵ects Blake C. et al., 2011a, MNRAS, 415, 2892 of redshift-space distortions and could significantly improve Blake C., Glazebrook K., 2003, ApJ, 594, 665 measurements of the anisotropic BAO signal. We will ex- Blake C. et al., 2011b, ArXiv e-prints plore this in future work. Blake C. et al., 2011c, MNRAS, 1598 This paper has demonstrated that reconstruction is fea- Bond J. R., Efstathiou G., 1984, ApJ, 285, L45 sible on data and that it can significantly improve the dis- Bond J. R., Efstathiou G., 1987, MNRAS, 226, 655 tance constraints. We expect that reconstruction will be- Carroll S. M., Press W. H., Turner E. L., 1992, ARA&A, come a standard method for analyzing the BAO signal from 30, 499 large redshift surveys. Chuang C.-H., Wang Y., 2011, ArXiv e-prints Funding for the Sloan Digital Sky Survey (SDSS) and Cole S. et al., 2005, MNRAS, 362, 505
c 0000 RAS, MNRAS 000,000–000 SDSS-DR7 Measurement 14 Padmanabhanof DV(z=0.35) et al SDSS-II has been provided by the Alfred P. Sloan Foun- dation, the Participating Institutions, the National Science (3.5%) (2.0%) Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Mon- bukagakusho, and the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, Univer- sity of Basel, University of Cambridge, Case Western Re- serve University, The University of Chicago, Drexel Univer- sity, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the from Padmanabhan et al. (2012) Joint Institute for Nuclear Astrophysics, the Kavli Insti- Figure 15. The probability of ↵ before [blue, dashed] and af- tute for Particle Astrophysics and Cosmology, the Korean ter [red, solid] reconstruction. The mean and standard deviations of the two distributions is also listed. The shaded regions show Scientist Group, the Chinese Academy of Sciences (LAM- the 1 [dark shaded] and 2 [light shaded] regions of the recon- OST), Los Alamos National Laboratory, the Max-Planck- structed probability distribution. Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of SDSS LRG data as well as lower redshift data from the Portsmouth, Princeton University, the United States Naval SDSS Main galaxy sample. Their primary distance con- Observatory and the University of Washington. straints are therefore reported at a lower redshift from ours: We thank the LasDamas collaboration for making their DV /rs(z =0.275) = 7.19 0.19, a 2.7% measurement. Com- galaxy mock catalogs public. We thank Cameron McBride ± paring these results with ours requires assuming a model to for assistance in using the LasDamas mocks and comments transform to a higher redshift. This comparison is done in on earlier versions of this work. We thank Martin White for detail in Paper III. We can however scale our results to this useful conversations on reconstruction. NP and AJC are par- redshift (assuming that ↵ does not change significantly with tially supported by NASA grant NNX11AF43G. DJE, XX, redshift) to obtain 7.15 0.13. These results are also con- and KM were supported by NSF grant AST-0707725 and ± sistent with Kazin et al. (2010) who obtain 7.17 0.25. We NASA grant NNX07AH11G. This work was supported in ± note that our error before reconstruction is larger than the part by the facilities and sta↵ of the Yale University Faculty Percival et al. (2010) results; this is however expected given of Arts and Sciences High Performance Computing Center. the somewhat larger volume of that sample. Percival et al. (2010) also split their sample into two redshift slices with their higher redshift slice correspond to our measurements. REFERENCES They obtain DV /rs(z =0.35) = 9.11 0.30, consistent with ± our results before reconstruction. Abazajian K. N. et al., 2009, ApJS, 182, 543 Our results have important implications for current and Angulo R. E., Baugh C. M., Frenk C. S., Lacey C. G., 2008, future surveys. All of these surveys have assumed some level MNRAS, 383, 755 of reconstruction for their projected constraints. This work Balay S. et al., 2011a, PETSc users manual. Tech. Rep. retires a major risk for these surveys, being the first appli- ANL-95/11 - Revision 3.2, Argonne National Laboratory cation to data. Furthermore, the degree of reconstruction Balay S. et al., 2011b, PETSc Web page. assumed (a reduction of the nonlinear smoothing scale by Http://www.mcs.anl.gov/petsc 50%) is consistent with what this work has achieved. Balay S., Gropp W. D., McInnes L. C., Smith B. F., 1997, This work has also limited itself to the angle aver- in Modern Software Tools in Scientific Computing, Arge aged correlation function. One of the promises of the BAO E., Bruaset A. M., Langtangen H. P., eds., Birkh¨auser method is the ability to measure both the angular diame- Press, pp. 163–202 ter distance and the Hubble constant. These measurements Beutler F. et al., 2011, MNRAS, 416, 3017 are complicated by the loss of isotropy in the correlation Blake C., Collister A., Bridle S., Lahav O., 2007, MNRAS, function due to redshift-space distortions. As this paper has 374, 1527 shown, reconstruction has the potential to undo the e↵ects Blake C. et al., 2011a, MNRAS, 415, 2892 of redshift-space distortions and could significantly improve Blake C., Glazebrook K., 2003, ApJ, 594, 665 measurements of the anisotropic BAO signal. We will ex- Blake C. et al., 2011b, ArXiv e-prints plore this in future work. Blake C. et al., 2011c, MNRAS, 1598 This paper has demonstrated that reconstruction is fea- Bond J. R., Efstathiou G., 1984, ApJ, 285, L45 sible on data and that it can significantly improve the dis- Bond J. R., Efstathiou G., 1987, MNRAS, 226, 655 tance constraints. We expect that reconstruction will be- Carroll S. M., Press W. H., Turner E. L., 1992, ARA&A, come a standard method for analyzing the BAO signal from 30, 499 large redshift surveys. Chuang C.-H., Wang Y., 2011, ArXiv e-prints Funding for the Sloan Digital Sky Survey (SDSS) and Cole S. et al., 2005, MNRAS, 362, 505
c 0000 RAS, MNRAS 000,000–000 Anisotropic Clustering: The line-of-sight dependence The line-of-sight dependence If we detect the BAO feature in these two directions, we can measure Transverse both DA(z) and H(z) Alternatively, if we assume a wrong fiducial cosmology to convert
Longitudinal ( ,θ,Φ) into (x,y,z), DA = Angular H = Hubble � diameter distance parameter we will measure an ( = D(z) / (1+z) ) (expansion rate) anisotropic clustering (even though the Universe is isotropic) Two sources of anisotropies Redshift-space distortions Alcock - Paczynski effect
Padmanabhan et al. 2012 Two sources of anisotropies Redshift-space distortions Alcock - Paczynski effect
Padmanabhan et al. 2012 1414 X.X. Xu Xu et et al. al.
FigureFigure 4. 4.AverageAverage monopole monopole (left) (left) and and quadrupole quadrupole (right) (right) of of the the 160 160 mo mockck catalogues catalogues before before reconstruction. reconstruction. The The monopole monopole and and the the quadrupolequadrupole at at large large scales scales are are similar similar to to the the fiducial fiducial templa templatestes (grey (grey dotted dotted lines, lines, identical identical to to the the solid solid lines lines plotted plottedinin Figures Figures 1(b) 1(b) & & 2).2). The The quadrupole quadrupole on on small small scales scales (r (r!!5050hh−−1Mpc),1Mpc), however, however, shows shows substantially substantially di difffferenterent structure structure to to the the fiducial fiducial template. template. The The fit fit to to thethe average average of of the theEffects monopole monopole and and quadrupole quadrupole fromof from the the mocks mocksReconstruction is is overplotted overplotted in in red. red. The The solid solid line line corresponds corresponds to to a a fit fit using using th thefiducialefiducial AA0,02,(2r()(Equation(51))andthedashedlinecorrespondstoafitusinr)(Equation(51))andthedashedlinecorrespondstoafitusinggAA0,02,2(r(r)=0.Weallow)=0.WeallowΣΣ⊥⊥andandΣΣ##toto vary vary in in these these fits fits and and obtain obtain −−1 1 −−11 best-fitbest-fit values values of of 6. 63.h3h MpcMpc and and 10 10.4.h4h MpcMpc respectively respectively using using the the fiducial fiducialAA0,02,2(r(r).). In In the the monopole monopole case, case, the the fit fit using using the the fiducial fiducial 22 AA0,02,(2r()isverysimilartother)isverysimilartotheAA0,02,(2r()=0fit.Inthequadrupole,ther)=0fit.Inthequadrupole,theAA0,02,2(r(r)=0fitismuchworsearoundtheacousticscale.Overall,)=0fitismuchworsearoundtheacousticscale.Overall,χχ decreaseddecreased by by 3333 going going from fromAA0,02,(2r()=0tothefiducialr)=0tothefiducialAA0,02,(2r().r). ∼∼ Monopole Quadrupole
FigureFigure 5. 5.TheThe average average monopole monopole (left) (left) and and quadrupole quadrupole (right) (right) of of the the 16 160mocksbefore(graycrosses)andafter(blackcrosses)reco0mocksbefore(graycrosses)andafter(blackcrosses)recofrom Xu et al. 2012 n-n- struction.struction. One One can can see see that that after after reconstruction, reconstruction, the the acous acoustictic peak peak in in the the monopole monopole has has sharpened sharpened up, up, indicating indicating that that re reconstructionconstruction is is effeffectiveective at at removing removing the the degradation degradation of of the the BAO BAO caused caused by by non non-linear-linear structure structure growth. growth. In In the the quadrupole, quadrupole, the the power power at at la large-scalesrge-scales goesgoes close close to to 0 0 which which implies implies that that reconstruction reconstruction was was eff effectiectiveve at at removing removing the the Kaiser Kaiser eff effect.ect. It It is is not not exactly exactly zero zero due due to to some some small small anisotropyanisotropy introduced introduced by by the the reconstruction reconstruction technique technique its itselfelf (see (see Figure Figure 6). 6). We We note note that that the the quadrupole quadrupole is is multiplied multipliedbybyrr22inin this this figure figure andand hence hence the the magnitude magnitude of of this this anisotropy anisotropy is is exaggerated. exaggerated. areare di difffferenterent from from 0 0 and and from from the the mean mean at at""1-21-2 times times the the er- er- amountamount ( ( √√mm,where,wheremm=2=2,,4or8)ifweconsider4or8)ifweconsider!!toto be be ∼∼ rorror on on the the mean. mean. In In addition, addition, the the post-reconstruction post-reconstruction quan- quan- Gaussian.Gaussian. These These results results are are summarized summarized in in Table Table 1. 1. tilestiles are are asymmetric, asymmetric, implying implying that that the the posterior posterior!!distri-distri- WeWe see see that that there there is is a a persistent persistent bias bias in in!!towardstowards non- non- butionbution deviates deviates from from Gaussian. Gaussian. These These appear appear to to be be in in part part zerozero values values that that is is currently currently below below our our detection detection thresh- thresh- duedue to to the the intrinsic intrinsic noise noise in in the the data data and and in in part part due due to to a a old.old. This This bias bias is is!!11σσsignificantsignificant before before reconstruction reconstruction and and slightslight mismatch mismatch between between the the model model and and the the data. data. To To reduce reduce onlyonly at at the the 1-1 1-1.5.5σσlevellevel after after reconstruction. reconstruction. To To further further test test noise,noise, we we eff effectivelyectively increase increase the the spatial spatial volume volume of of the the data data this,this, we we split split the the mocks mocks into into 2 2 groups groups of of 80 80 which which reduces reduces byby combining combining our our 160 160 mocks mocks into into groups groups of of 2, 2, 4 4 and and 8, 8, and and thethe noise noise in in the the data. data. After After re-performing re-performing the the fits, fits, we we find find re-performre-perform our our fits. fits. In In general, general, we we see see a a better better agreement agreement be- be- !! 00.002.002 both both before before and and after after reconstruction. reconstruction. These These val- val- ##$∼$∼ tweentween the the mean mean and and median median!.Thequantilesremainmildly!.Thequantilesremainmildly uesues agree agree with with the the fit fit results results to to the the average average of of the the 160 160 mocks mocks asymmetricasymmetric in in some some cases cases but but overall overall we we see see improved improved agree- agree- describeddescribed above. above. This This suggests suggests that that the the persistent persistent bias bias in in!!isis ment.ment. The The rms rms scatter scatter decreases decreases by by roughly roughly the the expected expected notnot due due to to noise noise but but is is rather rather a a result result of of some some mismatch mismatch be- be- tweentween the the model model and and the the data. data. In In our our fits fits we we fix fixΣΣ⊥⊥,,ΣΣ##andand Measuring DA and H using BAO 23
Table 4. DR7 fitting results for various models. The model is given in column 1. The measured α values are given in column 2 and the measured " values are given in column 3. The χ2/dof is given in column 4.
Model α"χ2/dof
Redshift Space without Reconstruction
Fiducial [f]1.015 0.044 0.007 0.046 89.60/90 ± ± Fit w/ (Σ , Σ ) (8, 8)h−1Mpc. 1.012 0.045 0.009 0.044 89.77/90 ⊥ " → ± ± −1 Fit w/ Σs 0h Mpc. 1.018 0.040 0.007 0.040 89.60/90 → ± ± Fit w/ A2(r)=poly2. 1.018 0.043 0.013 0.046 91.42/91 ± ± Fit w/ A2(r)=poly4. 1.015 0.044 0.006 0.047 89.58/89 ± ± Fit w/ 30 Fiducial [f]1.012 0.024 0.014 0.036 62.53/90 ± − ± Fit w/ (Σ , Σ ) (2, 4)h−1Mpc. 1.012 0.025 0.014 0.036 62.48/90 ⊥ " → ± − ± −1 Fit w/ Σs 0h Mpc. 1.013 0.021 0.013 0.029 61.83/90 → ± − ± Fit w/ A2(r)=poly2. 1.013 0.025 0.011 0.036 65.61/91 ± − ± Fit w/ A2(r)=poly4. 1.013 0.025 0.011 0.036 61.92/89 ± − ± Fit w/ 30 July 2008 - June 2014 51 participating institutions > 1,000 scientists SDSS Telescope 2.5m dedicated Apache Point, NM (operating since 1998) https://www.sdss3.org/surveys/boss.php The Data Release 10 and 11 of BOSS Data Release 10 6,373 sq.deg. 928,000 galaxies 182,000 quasars Data Release 11 8,976 sq.deg. 1,157,000 galaxies 239,000 quasars ...and what is on DR12 Survey is DONE 1.35M galaxies (1.20M in 0.15 http://blog.sdss3.org BOSS BAO measurements Galaxy BAO Lyman-alpha forest BAO rdrag=147.5±0.6Mpc BAO from the clustering of galaxy pairs BAO from clustering of absorption features pairs Galaxy BAO: CMASS Power spectrum P(k) Anderson et al. 2014 Correlation function �(s) 690,000 galaxies between 0.43 With this we can constrain the angular diameter distance DA(z) and the Hubble parameter H(z) DA(z=0.57)=1421±20Mpc H(z=0.57)=96.8±3.4km/s/Mpc Anderson et al. 2014 Galaxy BAO: LOWZ 314,000 galaxies between 0.15 DV(z=0.32)=1264±25Mpc (a 2% measurement) which is already as good as the SDSS-DR7 LRG result Tojeiro et al. 2014 The Lyman-alpha forest LyaF-LyaF auto-correlation Delubac et al. 2014 137,500 quasars between 2.1 164,000 quasars between 2.0 1% 4% 2% 4% Anderson et al. 2014 Not any arbitrary expansion history can go through these data points! Cosmological constraints on curvature and dark energy The CMASS+LOWZ samples combined with Planck+SN are able to constrain curvature Ωk to 3 parts in 1,000 and the equation of state of dark energy � by 7% Conclusions • BAO is a geometrical technique to probe the distance-redshift relation (i.e. the expansion history of the Universe) with high precision. • The “standard ruler” for BAO is well measured by the CMB. • Reconstruction techniques help reduce the error bar in BAO distances. • The BAO feature has been measured in the clustering of galaxies, as well as in the distribution of neutral gas in the intergalactic medium. • BOSS has measured distances to redshifts z=0.32 (2%), 0.57 (1%), and 2.34 (4%) • The combination of BAO + CMB + SNe places strong constraints on the spatial curvature of the Universe and the equation of state of dark energy. Thanks for your attention