dark energy and cosmic sound daniel eisenstein steward observatory eisenstein 2003...

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Dark Energy and Dark Energy and Cosmic Sound Cosmic Sound Daniel Eisenstein Daniel Eisenstein Steward Observatory Steward Observatory Eisenstein 2003 Eisenstein 2003 (astro-ph/0301623) (astro-ph/0301623) Seo & Eisenstein, ApJ, 598, Seo & Eisenstein, ApJ, 598, 720 (2003) 720 (2003) Blake & Glazebrook (2003), Blake & Glazebrook (2003), Hu & Haiman (2003), Linder Hu & Haiman (2003), Linder

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Dark Energy andDark Energy andCosmic SoundCosmic Sound

Daniel EisensteinDaniel EisensteinSteward ObservatorySteward Observatory

Eisenstein 2003 (astro-ph/0301623)Eisenstein 2003 (astro-ph/0301623)Seo & Eisenstein, ApJ, 598, 720 (2003)Seo & Eisenstein, ApJ, 598, 720 (2003)

Blake & Glazebrook (2003), Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003)Hu & Haiman (2003), Linder (2003)

Dark Energy is SubtleDark Energy is Subtle Parameterize by equation of state, Parameterize by equation of state, ww = = pp//, which controls how the energy density evolves , which controls how the energy density evolves

with time.with time. Measuring Measuring ww((zz) requires exquisite precision.) requires exquisite precision.

Varying Varying ww assuming assuming perfect CMB:perfect CMB:

Fixed Fixed mmhh22

DDAA((zz=1000)=1000)

dwdw//dzdz is even harder. is even harder. Need precise, redundant Need precise, redundant

observational probes!observational probes!

Comparing CosmologiesComparing Cosmologies

PunchlinesPunchlines

CMB calibrates baryon acoustic oscillations in CMB calibrates baryon acoustic oscillations in the galaxy power spectrum as a standard ruler.the galaxy power spectrum as a standard ruler.

This can be measured in large (~million galaxy) This can be measured in large (~million galaxy) surveys at high redshift.surveys at high redshift.

Can measure Can measure HH((zz) and ) and DDAA((zz) to few percent from ) to few percent from

zz=0.5 to =0.5 to zz=3.=3. Leverage on dark energy is comparable to future Leverage on dark energy is comparable to future

SNe experiments. Systematics are completely SNe experiments. Systematics are completely different.different.

Acoustic Oscillations in the CMBAcoustic Oscillations in the CMB

WMAP team (Bennett et al. 2003)WMAP team (Bennett et al. 2003)

Sound Waves from the Sound Waves from the Early UniverseEarly 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.

Recombination

TimeAm

plit

ude Maximal Effect

Minimal Effect

Same InitialPhase

Acoustic Oscillations in the Acoustic Oscillations in the Matter Power SpectrumMatter Power Spectrum

Peaks are weak; Peaks are weak; suppressed by a suppressed by a factor of the baryon factor of the baryon fraction.fraction.

Higher harmonics Higher harmonics suffer from Silk suffer from Silk damping.damping.

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 The acoustic oscillation scale depends on the scale depends on the matter-to-radiation ratio matter-to-radiation ratio ((mmhh22) and the baryon-to-) and the baryon-to-photon ratio (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

Large Galaxy Redshift SurveysLarge Galaxy Redshift Surveys

By performing large spectroscopic surveys, we can By performing large spectroscopic surveys, we can measure the acoustic oscillation standard ruler at a range of measure the acoustic oscillation standard ruler at a range of redshifts.redshifts.

Higher harmonics are at Higher harmonics are at kk~0.2h Mpc~0.2h Mpc-1-1 ( (=30 Mpc).=30 Mpc). Measuring 1% bandpowers in the peaks and troughs Measuring 1% bandpowers in the peaks and troughs

requires about 1 Gpcrequires about 1 Gpc33 of survey volume with number of survey volume with number density ~10density ~10-3-3 galaxy Mpc galaxy Mpc-3-3. ~1 million galaxies!. ~1 million galaxies!

SDSS Luminous Red Galaxy Survey provides this at SDSS Luminous Red Galaxy Survey provides this at zz=0.3. =0.3. We have studied possible future surveys at We have studied possible future surveys at zz=1 and =1 and zz=3.=3.

See related works by Blake & Glazebrook (2003), Hu & Haiman See related works by Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003), Amendola et al. (2004).(2003), Linder (2003), Amendola et al. (2004).

A Baseline Survey at A Baseline Survey at zz = 3 = 3

500,000 gal.500,000 gal. ~150 sq. deg.~150 sq. deg. 5x105x1088 hh-3-3 Mpc Mpc33

nn=1/sq. arcmin=1/sq. arcmin

Linear regime Linear regime kk<0.5<0.5hh Mpc Mpc-1-1

4 oscillations4 oscillations

Statistical Errors from the Statistical Errors from the zz=3 Survey=3 Survey

A Baseline Survey at A Baseline Survey at zz = 1 = 1

900,000 gal. 900,000 gal. z z = 0.5 to 1.3 = 0.5 to 1.3 in 4 slices.in 4 slices.

1000 sq. deg.1000 sq. deg. 0.25/sq. arcmin0.25/sq. arcmin

Linear regime Linear regime kk<0.2<0.2hh Mpc Mpc-1-1

2-3 oscillations2-3 oscillations

Statistical Errors from the Statistical Errors from the zz=1 Survey=1 Survey

MethodologyMethodology

Fisher matrix treatment of statistical errors.Fisher matrix treatment of statistical errors. Full three-dimensional modes including redshift and Full three-dimensional modes including redshift and

cosmological distortions.cosmological distortions. Flat-sky and Tegmark (1997) approximations.Flat-sky and Tegmark (1997) approximations. Large CDM parameter space: Large CDM parameter space: mmhh22, , bbhh22, n, T/S, , n, T/S, mm, plus , plus

separate distances, growth functions, separate distances, growth functions, , and anomalous shot , and anomalous shot noises for all redshift slices.noises for all redshift slices.

Planck-level CMB dataPlanck-level CMB data Supernovae: 1% distances in 16 redshift slices, 0.3 to Supernovae: 1% distances in 16 redshift slices, 0.3 to

1.7 plus 0.05, with 5% overall distance scale uncertainty.1.7 plus 0.05, with 5% overall distance scale uncertainty. Combine some or all data; predict statistical errors on Combine some or all data; predict statistical errors on

w(z) = ww(z) = w00 + w + w11z.z.

Baseline PerformanceBaseline Performance

Distance Errors (1-Distance Errors (1-) versus Redshift) versus Redshift

Results for Results for CDMCDM Data sets:Data sets:

CMB (CMB (PlanckPlanck)) SDSS LRG (z=0.3)SDSS LRG (z=0.3) Baseline Baseline zz=1=1 Baseline Baseline zz=3=3 SNe (1% in SNe (1% in zz=0.1 bins =0.1 bins

to to zz=1.7)=1.7)

((mm) = 0.037) = 0.037((ww)= 0.10 at )= 0.10 at zz=0.8=0.8((dwdw//dzdz) = 0.28) = 0.28

SNe+CMB have SNe+CMB have ((dwdw//dzdz) = 0.23) = 0.23

All together has All together has ((dwdw//dzdz) = 0.16) = 0.16

Dark Energy Constraints in Dark Energy Constraints in CDMCDM

Results for w = –2/3Results for w = –2/3

Easier to measure.Easier to measure. ((mm) = 0.025) = 0.025

((ww) = 0.05 at ) = 0.05 at zz=0.8=0.8((dwdw//dzdz) = 0.08) = 0.08

SNe+CMBSNe+CMB((dwdw//dzdz) = 0.12) = 0.12

All data setsAll data sets((dwdw//dzdz) = 0.05!) = 0.05!

Dark Energy Constraints in Dark Energy Constraints in ww=–2/3=–2/3

Nonlinearities & BiasNonlinearities & Bias Non-linear gravitational collapse erases acoustic oscillations on Non-linear gravitational collapse erases acoustic oscillations on

small scales. However, large scale features are preserved.small scales. However, large scale features are preserved. Clustering bias and redshift distortions alter the power Clustering bias and redshift distortions alter the power

spectrum, but they don’t create preferred scales at 100spectrum, but they don’t create preferred scales at 100hh-1-1 Mpc! Mpc! Acoustic peaks expected to survive in the linear regime.Acoustic peaks expected to survive in the linear regime.

Meiksen & White (1997), Seo & DJE (2004)Meiksen & White (1997), Seo & DJE (2004)

z=1

Feasibility?Feasibility? How to survey a million galaxies at How to survey a million galaxies at zz = 1 over 1000 sq. deg? = 1 over 1000 sq. deg?

Or half a million at Or half a million at z z = 3 over 150 sq. deg?= 3 over 150 sq. deg? This is a large step over on-going surveys, but it is a reasonable This is a large step over on-going surveys, but it is a reasonable

goal for the coming decade.goal for the coming decade. KAOS spectrograph concept for Gemini could do these surveys in a KAOS spectrograph concept for Gemini could do these surveys in a

year.year. 4000-5000 fibers, using 4000-5000 fibers, using

Echidna technology, feedingEchidna technology, feedingmultiple bench spectrographs.multiple bench spectrographs.

1.5 degree diameter FOV1.5 degree diameter FOV http://www.noao.edu/kaoshttp://www.noao.edu/kaos Well ranked in Aspen process.Well ranked in Aspen process. Detailed feasibility study in progress.Detailed feasibility study in progress. Also high-res for Galactic studies.Also high-res for Galactic studies. Contact Arjun Dey to get involved.Contact Arjun Dey to get involved.

Photometric Redshifts?Photometric Redshifts?

Can we do this without Can we do this without spectroscopy?spectroscopy?

Measuring H(z) requires Measuring H(z) requires detection of acoustic oscillation detection of acoustic oscillation scale along the line of sight.scale along the line of sight.

Need ~10 Mpc accuracy. Need ~10 Mpc accuracy. zz~0.003(1+z).~0.003(1+z).

But measuring But measuring DDAA((zz) from ) from transverse clustering requires transverse clustering requires only 4% in 1+only 4% in 1+zz..

Need ~half-sky survey to match Need ~half-sky survey to match 1000 sq. deg. of spectra.1000 sq. deg. of spectra.

Less robust, but likely feasible.Less robust, but likely feasible.

4% photo-z’s don’t smear4% photo-z’s don’t smearthe acoustic oscillations.the acoustic oscillations.

Sound in Space?Sound in Space? Ground can do well up to Ground can do well up to zz~1.4 and can pick up again at ~1.4 and can pick up again at

zz~2. Improvements are shrinking this range (but at what ~2. Improvements are shrinking this range (but at what cost in exposure times?).cost in exposure times?).

Space-based spectroscopy may be preferred for 1.5<Space-based spectroscopy may be preferred for 1.5<zz<2.<2. Wide-field IR imaging is important for efficient pre-selection Wide-field IR imaging is important for efficient pre-selection

at 1.3<at 1.3<zz<2.3. <2.3. Not obvious that spatial resolution is crucial for photo-z’s or Not obvious that spatial resolution is crucial for photo-z’s or

spectroscopy.spectroscopy. Don’t need all galaxies; ok to pick the easy ones.Don’t need all galaxies; ok to pick the easy ones.

Only need Only need n n = 10= 10-3 -3 hh33 Mpc Mpc-3-3 comoving. comoving.

1.5<z<2 is likely useful for the study of dark energy. A 1.5<z<2 is likely useful for the study of dark energy. A good place to put constraints on the redshift evolution.good place to put constraints on the redshift evolution.

Pros and ConsPros and Consof the Acoustic Peak Methodof the Acoustic Peak Method

Advantages:Advantages: Geometric measure of Geometric measure of

distance.distance. Robust to systematics.Robust to systematics. Individual measurements Individual measurements

are not hard (but you are not hard (but you need a lot of them!).need a lot of them!).

Can probe Can probe zz>2.>2. Can measure Can measure HH((zz) )

directly (with spectra).directly (with spectra). Is not supernova method.Is not supernova method.

Disadvantages:Disadvantages: Raw statistical precision (of Raw statistical precision (of

surveys of quoted size) surveys of quoted size) lags SNe (SNAP) and lags SNe (SNAP) and lensing/clusters (LSST).lensing/clusters (LSST).

But is this the right But is this the right comparison?comparison?

If dark energy is close to If dark energy is close to , , then then zz<1 is more <1 is more interesting.interesting.

Some model dependence Some model dependence as regards inferences from as regards inferences from CMB.CMB.

ConclusionsConclusions

Acoustic oscillations Acoustic oscillations provide a robust way to provide a robust way to measure measure HH((zz) and ) and DDAA((zz).).

Can probe high redshift.Can probe high redshift. Clean signature in the Clean signature in the

galaxy power spectrum.galaxy power spectrum. Large high-Large high-zz galaxy galaxy

surveys are feasible in surveys are feasible in the coming decade.the coming decade.

Space may be desired to Space may be desired to probe dark energy at probe dark energy at zz~2.~2.

Independent method with Independent method with competitive precision.competitive precision.

Higher Redshifts Perform BetterHigher Redshifts Perform Better

Nonlinear gravitational Nonlinear gravitational clustering erases the clustering erases the acoustic oscillations.acoustic oscillations.

This is less advanced at This is less advanced at higher redshifts.higher redshifts.

Recovering higher Recovering higher harmonics improves the harmonics improves the precision on distances.precision on distances.

Leverage improves from Leverage improves from zz=0 to =0 to zz=1.5, then =1.5, then saturates.saturates.

Errors versus non-linear

cutoff scale

Dark Energy is SubtleDark Energy is Subtle

Measuring Measuring ww((zz) requires exquisite precision.) requires exquisite precision.

Varying Varying ww assuming assuming perfect CMB:perfect CMB: Fixed Fixed mmhh22

DDAA((zz=1000)=1000)

dwdw//dzdz is even is even harder.harder.

ww>–1 is easier.>–1 is easier.Comparing CosmologiesComparing Cosmologies

……but one can measure but one can measure transverse clusteringtransverse clustering

Slices from photometric Slices from photometric redshifts have redshifts have sufficiently uniform Dsufficiently uniform DAA

that the acoustic peaks that the acoustic peaks persist in the angular persist in the angular power spectrum.power spectrum.

Can measure DCan measure DAA(z) from (z) from

large multicolor imaging large multicolor imaging surveys.surveys. 4% photo-z’s don’t smear4% photo-z’s don’t smear

the acoustic oscillations.the acoustic oscillations.

Photo-Photo-zz Surveys Surveys Need much more sky Need much more sky

coverage in order to coverage in order to compensate for the loss of compensate for the loss of modes.modes.

Half-sky survey could give Half-sky survey could give comparable performance on comparable performance on DDAA(z).(z).

Need 4% in (1+z)Need 4% in (1+z) Reasonably shallow:Reasonably shallow:

L* is overkill.L* is overkill. Not measuring H(z) directly.Not measuring H(z) directly.

Performance on w(z) lags.Performance on w(z) lags.

Clustering BiasClustering Bias Small-scale segregation of light and mass does create bias in Small-scale segregation of light and mass does create bias in

clustering on large scales.clustering on large scales. However, on large scales, bias is simple: However, on large scales, bias is simple:

scale-independent form.scale-independent form. Hence, large-scale galaxy clustering is a window into the early Hence, large-scale galaxy clustering is a window into the early

universe!universe!

Distance DerivativesDistance Derivatives

Feasibility?Feasibility? How to survey a million galaxies at How to survey a million galaxies at zz = 1 over = 1 over

1000 sq. deg? Or half a million at 1000 sq. deg? Or half a million at z z = 3 over 150 = 3 over 150 sq. deg?sq. deg?

This is a large step over on-going surveys, but it This is a large step over on-going surveys, but it is a reasonable goal for the coming decade.is a reasonable goal for the coming decade.

KAOS spectrograph concept for Gemini could do KAOS spectrograph concept for Gemini could do these surveys in a year.these surveys in a year. 4000-5000 fibers4000-5000 fibers 1.5 degree diameter FOV1.5 degree diameter FOV See poster by Dey, See poster by Dey,

talk by Glazebrook,talk by Glazebrook,http://www.noao.edu/kaoshttp://www.noao.edu/kaos