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Baryon Acoustic Oscillations and the Expansion History of the Universe Antonio J

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Baryon Acoustic Oscillations and the Expansion History of the Universe Antonio J 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’sequation (�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’sequation (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’sequation (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’sequation (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 1σ [dark shaded] and 2σ [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.
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