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

Dark Energy is Mysterious  Observations suggest that the expansion of the universe is presently accelerating. Normal matter doesn’t do this! Normal matter doesn’t do this! Requires exotic new physics. Requires exotic new physics. Cosmological constant?Cosmological constant? Very low mass field?Very low mass field? Some alteration to gravity?Some alteration to gravity?  We have no compelling theory for this! Need observational measure of the time evolution of the effect. Need observational measure of the time evolution of the effect. Riess et al. (2004)

Dark Energy is Subtle  Parameterize by equation of state, w = p/ , which controls how the energy density evolves with time.  Measuring w(z) requires exquisite precision.  Varying w assuming perfect CMB: Fixed  m h 2 Fixed  m h 2 D A (z=1000) D A (z=1000)  dw/dz is even harder.  Need precise, redundant observational probes! Comparing Cosmologies

Punchlines  CMB calibrates baryon acoustic oscillations in the galaxy power spectrum as a standard ruler.  This can be measured in large (~million galaxy) surveys at high redshift.  Can measure H(z) and D A (z) to few percent from z=0.5 to z=3.  Leverage on dark energy is comparable to future SNe experiments. Systematics are completely different.

Acoustic Oscillations in the CMB WMAP team (Bennett et al. 2003)

Sound Waves from the Early Universe Before recombination: Before recombination: Universe is ionized. Universe is ionized. Photons provide enormous pressure and restoring force. Photons provide enormous pressure and restoring force. Perturbations oscillate as acoustic waves. Perturbations oscillate as acoustic waves. After recombination: After recombination: Universe is neutral. Photons can travel freely past the baryons. Phase of oscillation at t rec affects late-time amplitude.

Acoustic Oscillations in the Matter Power Spectrum  Peaks are weak; suppressed by a factor of the baryon fraction.  Higher harmonics suffer from Silk damping.  Requires large surveys to detect! Linear regime matter power spectrum

A Standard Ruler  The acoustic oscillation scale depends on the matter-to-radiation ratio (  m h 2 ) and the baryon-to- photon ratio (  b h 2 ).  The CMB anisotropies measure these and fix the oscillation scale.  In a redshift survey, we can measure this along and across the line of sight.  Yields H(z) and D A (z)! Observer  r = (c/H)  z  r = D A 

Large Galaxy Redshift Surveys  By performing large spectroscopic surveys, we can measure the acoustic oscillation standard ruler at a range of redshifts.  Higher harmonics are at k~0.2h Mpc -1 ( =30 Mpc).  Measuring 1% bandpowers in the peaks and troughs requires about 1 Gpc 3 of survey volume with number density ~10 -3 galaxy Mpc -3. ~1 million galaxies!  SDSS Luminous Red Galaxy Survey provides this at z=0.3.  We have studied possible future surveys at z=1 and z=3. See related works by Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003), Amendola et al. (2004). See related works by Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003), Amendola et al. (2004).

A Baseline Survey at z = 3  500,000 gal.  ~150 sq. deg.  5x10 8 h -3 Mpc 3  n=1/sq. arcmin  Linear regime k<0.5h Mpc -1  4 oscillations Statistical Errors from the z=3 Survey

A Baseline Survey at z = 1  900,000 gal. z = 0.5 to 1.3 in 4 slices.  1000 sq. deg.  0.25/sq. arcmin  Linear regime k<0.2h Mpc -1  2-3 oscillations Statistical Errors from the z=1 Survey

Methodology  Fisher matrix treatment of statistical errors. Full three-dimensional modes including redshift and cosmological distortions. Full three-dimensional modes including redshift and cosmological distortions. Flat-sky and Tegmark (1997) approximations. Flat-sky and Tegmark (1997) approximations. Large CDM parameter space:  m h 2,  b h 2, n, T/S,  m, plus separate distances, growth functions, , and anomalous shot noises for all redshift slices. Large CDM parameter space:  m h 2,  b h 2, n, T/S,  m, plus separate distances, growth functions, , and anomalous shot noises for all redshift slices.  Planck-level CMB data  Supernovae: 1% distances in 16 redshift slices, 0.3 to 1.7 plus 0.05, with 5% overall distance scale uncertainty.  Combine some or all data; predict statistical errors on w(z) = w 0 + w 1 z.

Baseline Performance Distance Errors (1-  ) versus Redshift

Results for  CDM  Data sets: CMB (Planck) CMB (Planck) SDSS LRG (z=0.3) SDSS LRG (z=0.3) Baseline z=1 Baseline z=1 Baseline z=3 Baseline z=3 SNe (1% in  z=0.1 bins to z=1.7) SNe (1% in  z=0.1 bins to z=1.7)   (  m ) =  (w)= 0.10 at z=0.8  (dw/dz) = 0.28  SNe+CMB have  (dw/dz) = 0.23  All together has  (dw/dz) = 0.16 Dark Energy Constraints in  CDM

Results for w = –2/3  Easier to measure.   (  m ) =  (w) = 0.05 at z=0.8  (dw/dz) = 0.08  SNe+CMB  (dw/dz) = 0.12  All data sets  (dw/dz) = 0.05! Dark Energy Constraints in w=–2/3

Nonlinearities & Bias  Non-linear gravitational collapse erases acoustic oscillations on small scales. However, large scale features are preserved.  Clustering bias and redshift distortions alter the power spectrum, but they don’t create preferred scales at 100h -1 Mpc!  Acoustic peaks expected to survive in the linear regime. Meiksen & White (1997), Seo & DJE (2004) z=1

Feasibility?  How to survey a million galaxies at z = 1 over 1000 sq. deg? Or half a million at z = 3 over 150 sq. deg?  This is a large step over on-going surveys, but it is a reasonable goal for the coming decade.  KAOS spectrograph concept for Gemini could do these surveys in a year fibers, using Echidna technology, feeding multiple bench spectrographs fibers, using Echidna technology, feeding multiple bench spectrographs. 1.5 degree diameter FOV 1.5 degree diameter FOV 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?  Can we do this without spectroscopy?  Measuring H(z) requires detection of acoustic oscillation scale along the line of sight. Need ~10 Mpc accuracy.  z ~0.003(1+z). Need ~10 Mpc accuracy.  z ~0.003(1+z).  But measuring D A (z) from transverse clustering requires only 4% in 1+z.  Need ~half-sky survey to match 1000 sq. deg. of spectra.  Less robust, but likely feasible. 4% photo-z’s don’t smear the acoustic oscillations.

Sound in Space?  Ground can do well up to z~1.4 and can pick up again at z~2. Improvements are shrinking this range (but at what cost in exposure times?). Space-based spectroscopy may be preferred for 1.5<z<2. Space-based spectroscopy may be preferred for 1.5<z<2.  Wide-field IR imaging is important for efficient pre- selection at 1.3<z<2.3.  Not obvious that spatial resolution is crucial for photo-z’s or spectroscopy.  Don’t need all galaxies; ok to pick the easy ones. Only need n = h 3 Mpc -3 comoving. Only need n = h 3 Mpc -3 comoving.  1.5<z<2 is likely useful for the study of dark energy. A good place to put constraints on the redshift evolution.

Pros and Cons of the Acoustic Peak Method Advantages:  Geometric measure of distance.  Robust to systematics.  Individual measurements are not hard (but you need a lot of them!).  Can probe z>2.  Can measure H(z) directly (with spectra).  Is not supernova method. Disadvantages:  Raw statistical precision (of surveys of quoted size) lags SNe (SNAP) and lensing/clusters (LSST). But is this the right comparison?  If dark energy is close to , then z<1 is more interesting.  Some model dependence as regards inferences from CMB.

Conclusions  Acoustic oscillations provide a robust way to measure H(z) and D A (z). Can probe high redshift. Can probe high redshift. Clean signature in the galaxy power spectrum. Clean signature in the galaxy power spectrum.  Large high-z galaxy surveys are feasible in the coming decade.  Space may be desired to probe dark energy at z~2.  Independent method with competitive precision.

Higher Redshifts Perform Better  Nonlinear gravitational clustering erases the acoustic oscillations.  This is less advanced at higher redshifts.  Recovering higher harmonics improves the precision on distances.  Leverage improves from z=0 to z=1.5, then saturates. Errors versus non-linear cutoff scale

Dark Energy is Subtle  Measuring w(z) requires exquisite precision.  Varying w assuming perfect CMB: Fixed  m h 2 Fixed  m h 2 D A (z=1000) D A (z=1000)  dw/dz is even harder.  w>–1 is easier. Comparing Cosmologies

…but one can measure transverse clustering  Slices from photometric redshifts have sufficiently uniform D A that the acoustic peaks persist in the angular power spectrum.  Can measure D A (z) from large multicolor imaging surveys. 4% photo-z’s don’t smear the acoustic oscillations.

Photo-z Surveys  Need much more sky coverage in order to compensate for the loss of modes.  Half-sky survey could give comparable performance on D A (z). Need 4% in (1+z) Need 4% in (1+z) Reasonably shallow: L* is overkill. Reasonably shallow: L* is overkill.  Not measuring H(z) directly. Performance on w(z) lags. Performance on w(z) lags.

Clustering Bias  Small-scale segregation of light and mass does create bias in clustering on large scales.  However, on large scales, bias is simple: scale-independent form.  Hence, large-scale galaxy clustering is a window into the early universe!

Distance Derivatives

Feasibility?  How to survey a million galaxies at z = 1 over 1000 sq. deg? Or half a million at z = 3 over 150 sq. deg?  This is a large step over on-going surveys, but it is a reasonable goal for the coming decade.  KAOS spectrograph concept for Gemini could do these surveys in a year fibers fibers 1.5 degree diameter FOV 1.5 degree diameter FOV See poster by Dey, talk by Glazebrook, See poster by Dey, talk by Glazebrook,