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Baryon Acoustic Oscillations: Baryon Acoustic Oscillations: A Robust and Precise Route to the A Robust and Precise Route to the
Cosmological Distance ScaleCosmological Distance Scale
Daniel EisensteinDaniel Eisenstein(University of Arizona)(University of Arizona)
Michael Blanton, David Hogg, Bob Nichol, Nikhil Michael Blanton, David Hogg, Bob Nichol, Nikhil Padmanabhan, Will Percival, David Schlegel, Padmanabhan, Will Percival, David Schlegel,
Roman Scoccimarro, Ryan Scranton, Hee-Jong Roman Scoccimarro, Ryan Scranton, Hee-Jong Seo, Ed Sirko, David Spergel, Max Tegmark, Seo, Ed Sirko, David Spergel, Max Tegmark,
Martin White, Idit Zehavi, and the SDSS.Martin White, Idit Zehavi, and the SDSS.
OutlineOutline
Baryon acoustic oscillations as a standard ruler.Baryon acoustic oscillations as a standard ruler. Detection of the acoustic signature in the SDSS Detection of the acoustic signature in the SDSS
Luminous Red Galaxy sample at Luminous Red Galaxy sample at zz=0.35.=0.35. Cosmological constraints therefrom.Cosmological constraints therefrom.
Acoustic oscillations in the non-linear Universe.Acoustic oscillations in the non-linear Universe. Large galaxy surveys at higher redshifts.Large galaxy surveys at higher redshifts.
Future surveys can measure H(z) and DFuture surveys can measure H(z) and DAA(z) to better (z) to better than 1% from than 1% from zz=0.3 to =0.3 to zz=3.=3.
Acoustic Oscillations in the CMBAcoustic Oscillations in the CMB
Although there are fluctuations on all scales, Although there are fluctuations on all scales, there is a characteristic angular scale.there is a characteristic angular scale.
Acoustic Oscillations in the CMBAcoustic Oscillations in the CMB
WMAP team (Bennett et al. 2003)WMAP team (Bennett et al. 2003)
Sound Waves in the Early UniverseSound Waves in the Early Universe
Before recombination:Before recombination: Universe is ionized. Universe is ionized. Photons provide enormous Photons provide enormous
pressure and restoring force. pressure and restoring force. Perturbations oscillate as Perturbations oscillate as
acoustic waves.acoustic waves.
After recombination:After recombination: Universe is neutral.Universe is neutral. Photons can travel freely Photons can travel freely
past the baryons.past the baryons. Phase of oscillation at tPhase of oscillation at trecrec
affects late-time amplitude.affects late-time amplitude.
Big
Ban
gTod
ay
Recombinationz ~ 1000
~400,000 yearsIonized Neutral
Time
Sound WavesSound Waves Each initial overdensity (in DM & Each initial overdensity (in DM &
gas) is an overpressure that gas) is an overpressure that launches a spherical sound wave.launches a spherical sound wave.
This wave travels outwards at This wave travels outwards at 57% of the speed of light.57% of the speed of light.
Pressure-providing photons Pressure-providing photons decouple at recombination. CMB decouple at recombination. CMB travels to us from these spheres.travels to us from these spheres.
Sound speed plummets. Wave Sound speed plummets. Wave stalls at a radius of 150 Mpc.stalls at a radius of 150 Mpc.
Overdensity in shell (gas) and in the Overdensity in shell (gas) and in the original center (DM) both seed the original center (DM) both seed the formation of galaxies. Preferred formation of galaxies. Preferred separation of 150 Mpc.separation of 150 Mpc.
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A Statistical SignalA Statistical Signal
The Universe is a super-The Universe is a super-position of these shells.position of these shells.
The shell is weaker than The shell is weaker than displayed.displayed.
Hence, you do not expect Hence, you do not expect to see bullseyes in the to see bullseyes in the galaxy distribution.galaxy distribution.
Instead, we get a 1% Instead, we get a 1% bump in the correlation bump in the correlation function.function.
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Response of a point perturbationResponse of a point perturbation
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Based on CMBfast outputs (Seljak & Based on CMBfast outputs (Seljak & Zaldarriaga). Green’s function view Zaldarriaga). Green’s function view from Bashinsky & Bertschinger 2001.from Bashinsky & Bertschinger 2001.
Remember: This is a tiny ripple on a big background.
Acoustic Oscillations Acoustic Oscillations in Fourier Spacein Fourier Space
A crest launches a planar sound A crest launches a planar sound wave, which at recombination wave, which at recombination may or may not be in phase may or may not be in phase with the next crest. with the next crest.
Get a sequence of constructive Get a sequence of constructive and destructive interferences and destructive interferences as a function of wavenumber.as a function of wavenumber.
Peaks are weak — suppressed Peaks are weak — suppressed by the baryon fraction.by the baryon fraction.
Higher harmonics suffer from Higher harmonics suffer from Silk damping.Silk damping. Linear regime matter Linear regime matter
power spectrumpower spectrum
Acoustic Oscillations, RepriseAcoustic Oscillations, Reprise
Divide by zero-Divide by zero-baryon reference baryon reference model.model.
Acoustic peaks are Acoustic peaks are 10% modulations.10% modulations.
Requires large Requires large surveys to detect!surveys to detect!
Linear regime matter power spectrumLinear regime matter power spectrum
A Standard RulerA Standard Ruler
The acoustic oscillation scale The acoustic oscillation scale depends on the sound speed depends on the sound speed and the propagation time. and the propagation time.
These depend on the matter-to-These depend on the matter-to-radiation ratio (radiation ratio (mmhh22) and the ) and the baryon-to-photon ratio (baryon-to-photon ratio (bbhh22).).
The CMB anisotropies The CMB anisotropies measure these and fix the measure these and fix the oscillation scale.oscillation scale.
In a redshift survey, we can In a redshift survey, we can measure this along and measure this along and across the line of sight.across the line of sight.
Yields Yields HH((zz) and ) and DDAA((zz)!)!
Observer
r = (c/H)zr = DA
Galaxy Redshift SurveysGalaxy Redshift Surveys
Redshift surveys are a popular way to measure the 3-Redshift surveys are a popular way to measure the 3-dimensional clustering of matter.dimensional clustering of matter.
But there are complications from: But there are complications from: Non-linear structure formationNon-linear structure formation Bias (light ≠ mass)Bias (light ≠ mass) Redshift distortionsRedshift distortions
Partially degradePartially degradethe BAO peak, butthe BAO peak, butsystematics are smallsystematics are smallbecause this is abecause this is avery large preferredvery large preferredscale.scale. SDSSSDSS
Virtues of the Acoustic PeaksVirtues of the Acoustic Peaks The acoustic signature is created by physics at z=1000 The acoustic signature is created by physics at z=1000
when the perturbations are 1 in 10when the perturbations are 1 in 1044. Linear perturbation . Linear perturbation theory is excellent.theory is excellent.
Measuring the acoustic peaks across redshift gives a Measuring the acoustic peaks across redshift gives a geometrical measurement of cosmological distance.geometrical measurement of cosmological distance.
The acoustic peaks are a manifestation of a preferred The acoustic peaks are a manifestation of a preferred scale. Still a very large scale today, so non-linear scale. Still a very large scale today, so non-linear effects are mild and dominated by gravitational flows effects are mild and dominated by gravitational flows that we can simulate accurately.that we can simulate accurately.
No known way to create a sharp scale at 150 Mpc with low-No known way to create a sharp scale at 150 Mpc with low-redshift astrophysics.redshift astrophysics.
Measures absolute distance, including that to Measures absolute distance, including that to zz=1000.=1000. Method has intrinsic cross-check between Method has intrinsic cross-check between HH((zz) & ) & DDAA((zz), ),
since since DDAA is an integral of is an integral of HH..
Introduction to SDSS LRGsIntroduction to SDSS LRGs
SDSS uses color to target SDSS uses color to target luminous, early-type luminous, early-type galaxies at 0.2<galaxies at 0.2<zz<0.5.<0.5. Fainter than MAIN Fainter than MAIN
((rr<19.5)<19.5) About 15/sq degAbout 15/sq deg Excellent redshift Excellent redshift
success ratesuccess rate The sample is close to The sample is close to
mass-limited at mass-limited at zz<0.38. <0.38. Number density ~ 10Number density ~ 10-4-4 hh33 MpcMpc-3-3..
Science Goals:Science Goals: Clustering on largest scalesClustering on largest scales Galaxy clusters to z~0.5Galaxy clusters to z~0.5 Evolution of massive galaxiesEvolution of massive galaxies
200 kpc
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Large-scale CorrelationsLarge-scale Correlations
Acoustic series in P(k) becomes a single peak in (r)!
Pure CDM model has no peak.
Warning: Correlated Error Bars
Another ViewAnother View
CDM with baryons is a good fit: 2 = 16.1 with 17 dof.Pure CDM rejected at 2 = 11.7
A Prediction Confirmed!A Prediction Confirmed! Standard inflationary CDM model requires acoustic peaks.Standard inflationary CDM model requires acoustic peaks.
Important confirmation of basic prediction of the model.Important confirmation of basic prediction of the model.
This demonstrates This demonstrates that structure grows that structure grows from z=1000 to z=0 from z=1000 to z=0 by linear theory.by linear theory. Survival of narrow Survival of narrow
feature means no feature means no mode coupling.mode coupling.
Two Scales in ActionTwo Scales in Action
Equality scale depends on (mh2)-1.
Acoustic scale depends on (mh2)-0.25.
mh2 = 0.12
mh2 = 0.13
mh2 = 0.14
Cosmological ConstraintsCosmological Constraints
12
Pure CDM degeneracy
Acoustic scale alone
WMAP 1
A Standard RulerA Standard Ruler
If the LRG sample were If the LRG sample were at at zz=0, then we would =0, then we would measure measure HH00 directly (and directly (and
hence hence mm from from mmhh22).).
Instead, there are small Instead, there are small corrections from corrections from ww and and KK to get to to get to zz=0.35.=0.35.
The uncertainty in The uncertainty in mmhh22
makes it better to makes it better to measure (measure (mmhh22))1/21/2 D.D. This This
is independent of is independent of HH00.. We find We find mm = 0.273 ± 0.025 + 0.123(1+ = 0.273 ± 0.025 + 0.123(1+ww00) + 0.137) + 0.137KK..
Essential ConclusionsEssential Conclusions SDSS LRG correlation function does show a SDSS LRG correlation function does show a
plausible acoustic peak. plausible acoustic peak. Ratio of Ratio of DD((zz=0.35) to =0.35) to DD((zz=1000) measured to 4%.=1000) measured to 4%.
This measurement is insensitive to variations in spectral This measurement is insensitive to variations in spectral tilt and small-scale modeling. We are measuring the tilt and small-scale modeling. We are measuring the same physical feature at low and high redshift.same physical feature at low and high redshift.
mmhh22 from SDSS LRG and from CMB agree. from SDSS LRG and from CMB agree. Roughly 10% precision.Roughly 10% precision. This will improve rapidly from better CMB data and This will improve rapidly from better CMB data and
from better modeling of LRG sample.from better modeling of LRG sample. mm = 0.273 ± 0.025 + 0.123(1+ = 0.273 ± 0.025 + 0.123(1+ww00) + 0.137) + 0.137KK..
Power SpectrumPower Spectrum We have also done We have also done
the analysis in the analysis in Fourier space with Fourier space with a quadratic a quadratic estimator for the estimator for the power spectrum.power spectrum.
Also FKP analysis Also FKP analysis in Percival et al. in Percival et al. (2006, 2007).(2006, 2007).
The results are The results are highly consistent.highly consistent.
mm = 0.25, in part = 0.25, in part due to WMAP-3 vs due to WMAP-3 vs WMAP-1.WMAP-1.
Tegmark et al. (2006)Tegmark et al. (2006)
Power SpectrumPower Spectrum We have also done We have also done
the analysis in the analysis in Fourier space with Fourier space with a quadratic a quadratic estimator for the estimator for the power spectrum.power spectrum.
Also FKP analysis Also FKP analysis in Percival et al. in Percival et al. (2006, 2007).(2006, 2007).
The results are The results are highly consistent.highly consistent.
mm = 0.25, in part = 0.25, in part due to WMAP-3 vs due to WMAP-3 vs WMAP-1.WMAP-1.
Percival et al. (2007)Percival et al. (2007)
Beyond SDSSBeyond SDSS
By performing large spectroscopic surveys at By performing large spectroscopic surveys at higher redshifts, we can measure the acoustic higher redshifts, we can measure the acoustic oscillation standard ruler across cosmic time.oscillation standard ruler across cosmic time.
Higher harmonics are at Higher harmonics are at kk~0.2~0.2hh Mpc Mpc-1-1 ( (=30 Mpc)=30 Mpc) Require several GpcRequire several Gpc33 of survey volume with of survey volume with
number density few x 10number density few x 10-4-4 comoving comoving hh33 Mpc Mpc-3-3, , typically a million or more galaxies! typically a million or more galaxies!
No heroic calibration requirements; just need big No heroic calibration requirements; just need big volume.volume.
Discuss non-linear considerations, then examples.Discuss non-linear considerations, then examples.
Non-linear Structure FormationNon-linear Structure Formation Non-linear gravitational collapse and galaxy formation Non-linear gravitational collapse and galaxy formation
partially erases the acoustic signature. partially erases the acoustic signature. This limits our ability to centroid the peak and could in This limits our ability to centroid the peak and could in
principle shift the peak to bias the answer.principle shift the peak to bias the answer.
Meiksen & White (1997), Meiksen & White (1997), Seo & DJE (2005)Seo & DJE (2005)
Nonlinearities in the BAONonlinearities in the BAO The acoustic signature is carried by pairs of The acoustic signature is carried by pairs of
galaxies separated by 150 Mpc.galaxies separated by 150 Mpc. Nonlinearities push galaxies around by 3-10 Mpc. Nonlinearities push galaxies around by 3-10 Mpc.
Broadens peak, making it hard to measure the Broadens peak, making it hard to measure the scale.scale.
Non-linearities are Non-linearities are increasingly negligible increasingly negligible at z>1. Linear theoryat z>1. Linear theorypeak width dominates.peak width dominates.
Seo & DJE (2005); DJE, Seo, & White (2007)Seo & DJE (2005); DJE, Seo, & White (2007)
Where Does Displacement Where Does Displacement Come From?Come From?
Importantly, most of the Importantly, most of the displacement is due to bulk displacement is due to bulk flows.flows.
Non-linear infall into clusters Non-linear infall into clusters "saturates". Zel'dovich "saturates". Zel'dovich approx. actually overshoots.approx. actually overshoots.
Bulk flows in CDM are Bulk flows in CDM are created on large scales. created on large scales.
Looking at pairwise motion Looking at pairwise motion cuts the very large scales.cuts the very large scales.
The scales generating the The scales generating the displacements are exactly displacements are exactly the ones we're measuring the ones we're measuring for the acoustic oscillations. for the acoustic oscillations.
DJE, Seo, Sirko, & DJE, Seo, Sirko, & Spergel (2007)Spergel (2007)
Fixing the NonlinearitiesFixing the Nonlinearities Because the nonlinear degradation is dominated by bulk Because the nonlinear degradation is dominated by bulk
flows, we can undo the effect.flows, we can undo the effect. Map of galaxies tells us where the mass is that sources Map of galaxies tells us where the mass is that sources
the gravitational forces that create the bulk flows.the gravitational forces that create the bulk flows. Can run this backwards.Can run this backwards. Restore the statistic precision available per unit volume!Restore the statistic precision available per unit volume!
DJE, Seo, Sirko, & Spergel (2007)DJE, Seo, Sirko, & Spergel (2007)
Shifting the Acoustic ScaleShifting the Acoustic Scale Moving the acoustic scale requires net infall on 100 Moving the acoustic scale requires net infall on 100 hh–1–1 Mpc scales. Much smaller than Mpc scales. Much smaller than
random motions on small-scales. Expect infalls are <1%.random motions on small-scales. Expect infalls are <1%. We have used 320We have used 320hh–3–3 Gpc Gpc33
of PM simulations to compute of PM simulations to compute the non-linear shifts.the non-linear shifts.
Find shifts of 0.25% at z=1.5 Find shifts of 0.25% at z=1.5 to 0.5% at z=0.3.to 0.5% at z=0.3.
These shifts are predictableThese shifts are predictableand hence removable! and hence removable! This is just large-scale This is just large-scale gravitational flows.gravitational flows.
Galaxy bias enters throughGalaxy bias enters throughthe relation of galaxies to the relation of galaxies to these flows.these flows.
Seo, Siegel, DJE, & White (2008)Seo, Siegel, DJE, & White (2008)
Measuring the ShiftMeasuring the Shift
Quantifying the shift requires specifying a method for Quantifying the shift requires specifying a method for measuring the acoustic scale, and not all methods are equally measuring the acoustic scale, and not all methods are equally precise or robust.precise or robust.
Measuring the location of the local maximum in the correlation function Measuring the location of the local maximum in the correlation function is far from optimal.is far from optimal.
We have used the linear power spectrum with 8-10 We have used the linear power spectrum with 8-10 broadband marginalization terms.broadband marginalization terms.
P(P(kk) = B() = B(kk) P) Plinearlinear((kk) + A() + A(kk), where B(), where B(kk) and A() and A(kk) are low-order smooth ) are low-order smooth functions. We measure functions. We measure to get acoustic scale. to get acoustic scale.
Fit range of wavenumber using a Gaussian covariance matrix.Fit range of wavenumber using a Gaussian covariance matrix. This removes scale-dependent bias, shot noise, and This removes scale-dependent bias, shot noise, and
smoothing of the acoustic peak.smoothing of the acoustic peak. Results are robust against variations in the form of A(Results are robust against variations in the form of A(kk) and ) and
B(B(kk), as well as errors in the template cosmology. Scatter in ), as well as errors in the template cosmology. Scatter in matches Fisher estimate. matches Fisher estimate.
Demonstrating ReconstructionDemonstrating Reconstruction Applying a very simple reconstruction method to the Applying a very simple reconstruction method to the
simulations does reduce the scatter in the recovered simulations does reduce the scatter in the recovered acoustic scale, as expected.acoustic scale, as expected.
Also decreases the shift in Also decreases the shift in the scale to <0.1%.the scale to <0.1%.
This does not account for This does not account for galaxy bias, but these galaxy bias, but these corrections are small and corrections are small and dominated by large scales.dominated by large scales.We will have large amounts We will have large amounts of information about galaxy of information about galaxy bias from intermediate-bias from intermediate-scale clustering.scale clustering. Seo, Siegel, DJE, & White (2008)Seo, Siegel, DJE, & White (2008)
Cosmic Variance LimitsCosmic Variance Limits
Errors on Errors on DD((zz) in ) in zz=0.1 =0.1 bins. Slices add in bins. Slices add in quadrature.quadrature.
Black: Linear theoryBlack: Linear theory
Blue: Non-linear theoryBlue: Non-linear theory
Red: Reconstruction by Red: Reconstruction by 50% (reasonably easy)50% (reasonably easy)
Seo & DJE, in pressSeo & DJE, in press
Cosmic Variance LimitsCosmic Variance Limits
Errors on Errors on HH((zz) in ) in zz=0.1 =0.1 bins. Slices add in bins. Slices add in quadrature.quadrature.
Black: Linear theoryBlack: Linear theory
Blue: Non-linear theoryBlue: Non-linear theory
Red: Reconstruction by Red: Reconstruction by 50% (reasonably easy)50% (reasonably easy)
Seo & DJE, in pressSeo & DJE, in press
Seeing Sound in the Lyman Seeing Sound in the Lyman Forest Forest
The LyThe Ly forest tracks the large-scale forest tracks the large-scale density field, so a grid of sightlines should show the acoustic peak.density field, so a grid of sightlines should show the acoustic peak.
This may be a cheaper way to measure the acoustic scale at This may be a cheaper way to measure the acoustic scale at zz>2.>2. Require only modest resolution (R=250) and low S/N. Require only modest resolution (R=250) and low S/N.
Bonus: the sampling is better in the radial direction, so favors H(z).Bonus: the sampling is better in the radial direction, so favors H(z).
White (2004); McDonald & DJE (2006)White (2004); McDonald & DJE (2006)
Neutral H absorption observedNeutral H absorption observedin quasar spectrum at z=3.7in quasar spectrum at z=3.7
Neutral H simulation (R. Cen)
Chasing Sound Across RedshiftChasing Sound Across Redshift
Distance Errors versus RedshiftDistance Errors versus Redshift
New Spectroscopic SurveysNew Spectroscopic Surveys
WiggleZ: On-going survey of z~0.8 emission line WiggleZ: On-going survey of z~0.8 emission line galaxies at AAT with new AAOmega upgrade.galaxies at AAT with new AAOmega upgrade.
BOSS: New survey within SDSS-III.BOSS: New survey within SDSS-III. FMOS: FMOS: zz~1.5 Subaru survey with IR spectroscopy ~1.5 Subaru survey with IR spectroscopy
for Hfor H.. HETDeX: LyHETDeX: Ly emission galaxy survey at emission galaxy survey at
1.8<1.8<zz<3.8 with new IFU on HET.<3.8 with new IFU on HET. WFMOS spectrograph for Gemini/Subaru could WFMOS spectrograph for Gemini/Subaru could
do major do major zz~1 and ~1 and zz~2.5 surveys.~2.5 surveys. SKA in certain implementations.SKA in certain implementations. ADEPT and EUCLID.ADEPT and EUCLID.
SDSS-IIISDSS-III SDSS-III will be the next phase of the SDSS project, SDSS-III will be the next phase of the SDSS project,
operating from summer 2008 to summer 2014.operating from summer 2008 to summer 2014. SDSS-III has 4 surveys on 3 major themes.SDSS-III has 4 surveys on 3 major themes.
BOSS: Largest yet redshift survey for large-scale structure.BOSS: Largest yet redshift survey for large-scale structure. SEGUE-2: Optical spectroscopic survey of stars, aimed at SEGUE-2: Optical spectroscopic survey of stars, aimed at
structure and nucleosynthetic enrichment of the outer Milky structure and nucleosynthetic enrichment of the outer Milky Way.Way.
APOGEE: Infrared spectroscopic survey of stars, to study the APOGEE: Infrared spectroscopic survey of stars, to study the enrichment and dynamics of the whole Milky Way.enrichment and dynamics of the whole Milky Way.
MARVELS: Multi-object radial velocity planet search.MARVELS: Multi-object radial velocity planet search. Extensive re-use of existing facility and software.Extensive re-use of existing facility and software. Strong commitment to public data releases.Strong commitment to public data releases. Collaboration is now forming. Collaboration is now forming.
Seeking support from Sloan Foundation, DOE, NSF, and over Seeking support from Sloan Foundation, DOE, NSF, and over 20 member institutions.20 member institutions.
Baryon Oscillation Baryon Oscillation Spectroscopic Survey (BOSS)Spectroscopic Survey (BOSS)
New program for the SDSS telescope for 2008–2014. New program for the SDSS telescope for 2008–2014. Definitive study of the low-redshift acoustic oscillations. Definitive study of the low-redshift acoustic oscillations.
10,000 deg10,000 deg22 of new spectroscopy from SDSS imaging. of new spectroscopy from SDSS imaging. 1.5 million LRGs to 1.5 million LRGs to zz=0.8, including 4x more density at =0.8, including 4x more density at zz<0.5. <0.5. 7-fold improvement on large-scale structure data from entire SDSS 7-fold improvement on large-scale structure data from entire SDSS
survey; measure the distance scale to 1% at survey; measure the distance scale to 1% at zz=0.35 and =0.35 and zz=0.6.=0.6. Easy extension of current program.Easy extension of current program.
Simultaneous project to discover theSimultaneous project to discover theBAO in the Lyman BAO in the Lyman forest. forest.
160,000 quasars. 20% of fibers.160,000 quasars. 20% of fibers. 1.5% measurement of distance to 1.5% measurement of distance to zz=2.3.=2.3. Higher risk but opportunity to open the Higher risk but opportunity to open the
high-redshift distance scale.high-redshift distance scale.
Cosmology with BOSSCosmology with BOSS BOSS measures the cosmic distance scale to BOSS measures the cosmic distance scale to
1.0% at 1.0% at zz = 0.35, 1.1% at = 0.35, 1.1% at zz = 0.6, and 1.5% at = 0.6, and 1.5% at zz = 2.5. Measures = 2.5. Measures HH((zz = 2.5) to 1.5%. = 2.5) to 1.5%.
These distances combined with Planck CMB & These distances combined with Planck CMB & Stage II data gives powerful cosmological Stage II data gives powerful cosmological constraints.constraints.
Dark energy parametersDark energy parameters wwpp to 2.8% and to 2.8% and wwaa to 25%. to 25%. Hubble constant Hubble constant HH00 to 1%. to 1%. Matter densityMatter density mm to 0.01. to 0.01. Curvature of Universe Curvature of Universe kk to 0.2%. to 0.2%. Sum of neutrino masses to 0.13 eV.Sum of neutrino masses to 0.13 eV.
Superb data set for other cosmological tests, Superb data set for other cosmological tests, as well as diverse extragalactic applications.as well as diverse extragalactic applications.
BOSS in ContextBOSS in Context DETF reports states that the BAO method is “less affected DETF reports states that the BAO method is “less affected
by astrophysical uncertainties than other techniques.” by astrophysical uncertainties than other techniques.” Hence, BOSS forecasts are more reliable.Hence, BOSS forecasts are more reliable.
BOSS is nearly cosmic-variance limited (quarter-sky) in its BOSS is nearly cosmic-variance limited (quarter-sky) in its z z < 0.7 BAO measurement.< 0.7 BAO measurement.
Will be the data point that all higher redshift BAO surveys use to Will be the data point that all higher redshift BAO surveys use to connect to low redshift. Cannot be significantly superceded.connect to low redshift. Cannot be significantly superceded.
BOSS will be the first dark energy measurement at BOSS will be the first dark energy measurement at z z > 2.> 2. Moreover, BOSS complements beautifully the new wide-Moreover, BOSS complements beautifully the new wide-
field imaging surveys that focus on weak lensing, SNe, field imaging surveys that focus on weak lensing, SNe, and clusters.and clusters.
BAO adds an absolute distance scale to SNe and extends to BAO adds an absolute distance scale to SNe and extends to z z > 1.> 1. BAO+SNe are a purely BAO+SNe are a purely aa((tt) test, whereas WL and Clusters include ) test, whereas WL and Clusters include
the growth of structure as well. Crucial opportunity to do the growth of structure as well. Crucial opportunity to do consistency checks to test our physical assumptions.consistency checks to test our physical assumptions.
BOSS InstrumentationBOSS Instrumentation
1000 small-core fibers to replace existing1000 small-core fibers to replace existing(more objects, less sky contamination)(more objects, less sky contamination)
LBNL CCDs + new gratings improve throughputLBNL CCDs + new gratings improve throughputUpdate electronics + DAQUpdate electronics + DAQ
• Straightforward upgrades to be Straightforward upgrades to be commissioned in summer 2009commissioned in summer 2009
SDSS telescope + most systems unchangedSDSS telescope + most systems unchanged
What about What about HH00?? Does the CMB+LSS+SNe really measure the Hubble Does the CMB+LSS+SNe really measure the Hubble
constant? What sets the scale in the model?constant? What sets the scale in the model? The energy density of the CMB photons plus the assumed a neutrino The energy density of the CMB photons plus the assumed a neutrino
background gives the radiation density.background gives the radiation density. The redshift of matter-radiation equality then sets the matter density The redshift of matter-radiation equality then sets the matter density
((mmhh22).). Measurements of Measurements of mm (e.g., from distance ratios) then imply (e.g., from distance ratios) then imply HH00..
What if the radiation density were different, i.e. more/fewer What if the radiation density were different, i.e. more/fewer neutrinos or something new?neutrinos or something new?
Sound horizon would shift in scale. LSS inferences of Sound horizon would shift in scale. LSS inferences of mm, , kk, , ww((zz), etc, ), etc, would be correct, but would be correct, but mmhh22 and and HH00 would shift. would shift.
Minor changes in baryon fraction and CMB anisotropic stress.Minor changes in baryon fraction and CMB anisotropic stress.
So comparison of So comparison of HH00 from direct measures to CMB-based from direct measures to CMB-based inferences are a probe of “dark radiation”. inferences are a probe of “dark radiation”.
1 neutrino species is roughly 5% in 1 neutrino species is roughly 5% in HH00. . We could get to ~1%.We could get to ~1%.
DJE & White (2004)DJE & White (2004)
We’ve Only Just BegunWe’ve Only Just Begun
SDSS LRG has only surveyed only 10SDSS LRG has only surveyed only 10–3–3 of of the volume of the Universe out to the volume of the Universe out to zz~5.~5.
Only 10Only 10–4–4 of the modes relevant to the of the modes relevant to the acoustic oscillations.acoustic oscillations.
Fewer than 10Fewer than 10–6–6 of the linear regime of the linear regime modes available.modes available.
There is an immense amount more There is an immense amount more information about the early Universe information about the early Universe available in large-scale structure.available in large-scale structure.
SpergelSpergel
ConclusionsConclusions
Acoustic oscillations provide a robust way to Acoustic oscillations provide a robust way to measure H(z) and Dmeasure H(z) and DAA(z).(z). Clean signature in the galaxy power spectrum.Clean signature in the galaxy power spectrum. Can probe high redshift.Can probe high redshift. Can probe H(z) directly.Can probe H(z) directly. Independent method with good precision. Independent method with good precision.
SDSS LRG sample uses the acoustic signature SDSS LRG sample uses the acoustic signature to measure to measure DDAA((zz=0.35)/=0.35)/DDAA((zz=1000) to 4%.=1000) to 4%.
Larger galaxy surveys are feasible in the coming Larger galaxy surveys are feasible in the coming decade, pushing to 1% and below across a decade, pushing to 1% and below across a range of redshift.range of redshift.
Photometric Redshifts?Photometric Redshifts?
Can we do this without spectroscopy?Can we do this without spectroscopy? Measuring H(z) requires detection Measuring H(z) requires detection
of acoustic oscillation scale alongof acoustic oscillation scale alongthe line of sight.the line of sight.
Need ~10 Mpc accuracy. Need ~10 Mpc accuracy. zz~0.003(1+z).~0.003(1+z).
Measuring Measuring DDAA((zz) from transverse ) from transverse clustering requires only 4% in 1+clustering requires only 4% in 1+zz..
Need 10x more sky than Need 10x more sky than spectroscopy. Less robust, but spectroscopy. Less robust, but likely feasible.likely feasible.
First work by Padmanabhan et al First work by Padmanabhan et al (2006) and Blake et al (2006).(2006) and Blake et al (2006).6% distance to 6% distance to z z = 0.5.= 0.5.
4% photo-z’s don’t smear4% photo-z’s don’t smearthe acoustic oscillations.the acoustic oscillations.
An Optimal Number DensityAn Optimal Number Density Since survey size is at a premium, one wants to design for Since survey size is at a premium, one wants to design for
maximum performance.maximum performance. Statistical errors on large-scale correlations are a Statistical errors on large-scale correlations are a
competition between sample variance and Poisson noise.competition between sample variance and Poisson noise. Sample variance: How many independent samples of a given scale Sample variance: How many independent samples of a given scale
one has.one has. Poisson noise: How many objects per sample one has.Poisson noise: How many objects per sample one has.
Given a fixed number of objects, the optimal choice for Given a fixed number of objects, the optimal choice for measuring the power spectrum is an intermediate density.measuring the power spectrum is an intermediate density.
Number density roughly the inverse of the power spectrum.Number density roughly the inverse of the power spectrum.• 1010-4-4 hh33 Mpc Mpc-3-3 at low redshift; a little higher at high redshift. at low redshift; a little higher at high redshift.
Most flux-limited surveys do not and are therefore inefficient for this Most flux-limited surveys do not and are therefore inefficient for this task.task.
Opening Discovery SpacesOpening Discovery Spaces With CMB and galaxy surveys, we can study dark energy With CMB and galaxy surveys, we can study dark energy
out to z=1000.out to z=1000. SNe should do better at pinning down SNe should do better at pinning down DD((zz) at ) at zz<1. But <1. But
acoustic method gives an absolute scale and opens up acoustic method gives an absolute scale and opens up zz>1 and H(z) to find the unexpected.>1 and H(z) to find the unexpected.
Weak lensing, clusters also Weak lensing, clusters also focus on focus on zz<1. These depend <1. These depend on growth of structure. We on growth of structure. We would like both a growth and would like both a growth and a kinematic probe to look for a kinematic probe to look for changes in gravity.changes in gravity.
Dark Energy Task Force stressed Dark Energy Task Force stressed the combination of methods.the combination of methods.
