BigBOSS science overview

Uros Seljak LBNL/UC Berkeley

LBNL, Nov 18, 2009

Focus of this talk• Recent progress in large scale structure: weak

lensing, galaxy clustering, cluster abundance, Lyman alpha forest

• A few representative applications: neutrino mass, primordial non-gaussianity, dark energy

• Future directions

Collaborators: P. McDonald, R. Mandelbaum, N. Padmanabhan, C. Hirata, R. Reyes, A. Slosar…

Big questions in cosmology

1) Nature of acceleration of the universe: dark energy

modification of gravitysomething else?

2) Initial conditions for structure in the Universe:

Inflation (of many flavors) or alternatives?3) Nature of matter (dark matter, neutrino

mass…)BigBOSS can test all of these!

How to answer them? 1) Classical tests: dark energy: redshift-distance

relation: BAO and AP2) Growth of structure: dark energy, neutrino

mass etc: need amplitude of perturbations, ie bias: weak lensing, redshift space distortions

3) Scale dependence of clustering: primordial power spectrum, primordial non-gaussianity: need to understand scale dependence of bias

4) Comparing the above tracers, e.g., lensing versus redshift-space distortions: differentiates between dark energy and modified gravity theories

CBI ACBAR

Lyman alpha forest

0≈z 3≈z

1088≈z

Scale dependence of cosmological probes

WMAP

Complementary in scale and redshift

SDSS Galaxy clustering

Weak lensing

Cluster abundance

Sound Waves• Each initial overdensity (in DM &

gas) is an overpressure that launches a spherical sound wave.

• This wave travels outwards at 57% of the speed of light.

• Pressure-providing photons decouple at recombination. CMB travels to us from these spheres.

• Sound speed plummets. Wave stalls at a radius of 150 Mpc.

• Seen in CMB as acoustic peaks• Overdensity in shell (gas) and in

the original center (DM) both seed the formation of galaxies. Preferred separation of 150 Mpc.

QuickTime™ and aGIF decompressor

are needed to see this picture.

A Standard Ruler

• The acoustic oscillation scale depends on the matter-to-radiation ratio (mh2) and the baryon-to-photon ratio (bh2).

• 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 DA(z)!• BigBOSS predictions: see

follow-up talks• Their ratio: Alcock-Paczynski

effect

Observer

r = (c/H)zr = DA

Shape and acoustic oscillations in the Matter

Power Spectrum• Shape determined by

matter and baryon density, primordial slope

• Amplitude not useful (bias)

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

• Higher harmonics suffer from nonlinear damping.

Linear regime matter power spectrumLinear regime matter power spectrum

Weighing neutrinos• Neutrino free streaming

inhibits growth of structure on scales smaller than free streaming distance

• If neutrinos have mass they contribute to the total matter density, but since they are not clumped on small scales dark matter growth is suppressed

• For m=0.1-1eV free-streaming scale is >>10Mpc

• Neutrinos are quasi-relativistic at z=1000: effects on CMB also important (anisotropic stress etc)

• opposite sign, unique signature!

m=0.15x3, 0.3x3, 0.6x3, 0.9x1 eV

Galaxy bias determination

•Galaxies are biased tracers of dark matter; the bias is believed to be scale independent on large scales

(k<0.1/Mpc)•If we can determine the bias we can use galaxy power

spectrum and relate it to the dark matter spectrum• redshift space disortions

•bispectrum•Weak lensing

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kP

kPkb

dm

gg=

Redshift space distortions

• Usual approach: measure power along the radial direction and compare to power along transverse direction to determine beta

• Need linear regime, limited by sampling variance due to finite number of large scale structures, each of which is a random gaussian realization

• Lower bias higher beta: good for BIGBOSS

Hawkins et al. (2003, MNRAS, 346, 78)

a=0 kms-1

=0

a=500 kms-1

=0

a=0 kms-1

=0.4

a=500 kms-1

=0.4

Redshift space Correlation Function

(perpendicular to the l.o.s.)

(a

lon

g t

he

l.o.s

.)

Beta reconstruction of LRGs: quadrupole to monopole ratio (N-body simulations)

Reyes etal 2009

Sources of error in galaxy surveys

• Sampling (cosmic) variance: each structure (mode in Fourier space) is a random variable, error on the power spectrum) is , where N is the number of modes measured. This is a problem for BAO, need large volume

• Shot noise: with a small number of galaxies individual structures (modes) will not be measured precisely; usual assumption: Poisson process where shot noise is where is the number density of galaxies (this can be improved upon)

• Relative contribution: • For BAO we want shot noise error=sampling

error• For RSD one gains as shot noise decreases

How to reduce cosmic variance?

• Two tracers:

• Take the ratio

• Density perturbation drops out, so no cosmic variance• Transverse vs radial allows to determine bias ratio and beta

separately• Full angular dependence: AP geometrical test• What limits the measurement is shot noise and stochasticity:

unclear if BigBOSS can take advantage of this method (number density low, no high bias tracer)

McDonald & US 2008

Velocity divergence power spectrum

Growth of structure to 0.1%

This is potentially better than other probes of growth (weak lensing, cluster abundance)

Can one reduce shot noise? Possibly!

• One can reduce shot noise OR we can achieve the same errors by measuring redshifts of several times fewer galaxies

• Need all of the halos above certain mass• Emission line galaxies in BigBOSS are not

picking out all of the most massive halos

10x reduction in noise relative to signal!US, Hamaus, Desjacques 2009

Uniform weighting

Mass weighting

Scale dependent bias• Current analyses use Q model (Cole etal), no

physical motivation, just a fitting formula• A better model has been developed by P. McDonald

(2008) based on (renormalized) perturbation theory and local bias ansatz

• Seems to work well in simulations (Jeong & Komatsu 2008)

• One result from these analyses: there is a sweet spot where scale dependent bias vanishes at second order, roughly at b=1.7 (but still need to account for shot noise term which is not 1/n)

Weak Gravitational LensingWeak Gravitational Lensing

Distortion of background images by foreground matter

Unlensed Lensed

Galaxy-dark matter correlations: galaxy-galaxy lensing

+ dark matter around galaxies induces tangential distortion of background galaxies+ Specially useful if one has redshifts of foreground galaxies (BigBOSS!): express signal in terms of projected surface density and transverse separation r+: not sensitive to intrinsic alignments (with photozs for source galaxies)

Simulations: dark matter reconstruction

Use simulations with realistic HOD galaxy model to model galaxies

Cross-correlation coefficient r nearly unity

Baldauf, US, Smith (2009)

Dark matter power spectrum reconstruction from galaxy power spectrum and galaxy-shear power spectrum unbiased

Nonlinear

linear

Dark matter clustering reconstruction

Alternative method to determine growth rate with different

systematics than shear-shear correlations and more statistical

power!

BigBOSS can be combined with PanSTARRS, LSST or

something else

This method could blow away shear-shear correlations if the

systematics are not solved (likely for the ground based WL

surveys)

Ly-alpha forest as a Ly-alpha forest as a tracer of dark matter tracer of dark matter and dark energyand dark energy

Basic model: neutral hydrogen (HI) is determined by ionization Basic model: neutral hydrogen (HI) is determined by ionization balance between recombination of e and p and HI ionization from balance between recombination of e and p and HI ionization from UV photons (in denser regions collisional ionization also plays a UV photons (in denser regions collisional ionization also plays a role), this gives role), this gives

Recombination coefficient depends on gas temperatureRecombination coefficient depends on gas temperature

Neutral hydrogen traces overall gas distribution, which traces dark Neutral hydrogen traces overall gas distribution, which traces dark matter on large scales, with additional pressure effects on small matter on large scales, with additional pressure effects on small scales (parametrized with filtering scale kscales (parametrized with filtering scale kFF))

Fully specified within the model, no bias issues

2gasHI ρρ ∝

BAO with Lyman alpha

McDonald and Eisenstein 2007

BigBOSS predictions: TBD (see subsequent

talks)

Non-gaussianity• Local model • Simple single field inflation predicts fnl<<1• Nonlinear corrections give fnl around 1• More complicated inflationary models can give fnl>>1• Ekpyrotic/cyclic models generically give fnl>>1• Other models give different angular dependence of

bispectrum (e.g. equilateral in DBI model, Silverstein…)

• Shows up in galaxy clustering as a scale dependent bias

€

Φ x( ) = ΦG x( ) + fNLΦG2 x( )

Dalal etal 2007

b=3.5

Effect proportional to (bias-1): need high bias tracers

How to improve these limits?

• Effect scales as (b-1), ie no effect for b=1• On large scales limited by cosmic variance: finite number

of large scale patches (modes), which are gaussian random realizations, but we need to measure average power

• Two tracers:

• Take the ratio

• Density perturbation drops out, so no cosmic variance!• This could give error on fnl around unity with BigBOSS if we

have a biased tracer (b>1)!

US 2008

Which method is best? We don’t know!

McDonald & US 2009

Redshift space distortions (including AP, BAO) give larger improvements than

weak lensing or

BAO alone

BAO is a safe bet but other methods could be better (lessons from SDSS: build the most general purpose survey as possible)

Combining the methods

• By combining velocity measurements ( of LRGs with weak lensing measurement of the SAME objects we can eliminate the dependence on the amplitude of fluctuations and bias

Zhang etal 2007

Testing modifications of gravity with EG

Reyes, Mandelbaum, US, Gunn, Baldauf, Lombriser, in prep

SDSS: 6 sigma detection

In agreement with LCDM

Data disagree with TeVeS (aka MOND)

f(R) about 1 sigma below the data: future data should be able to constrain it better

BigBOSS predictions depend on WL data

Conclusions• BigBOSS can answer fundamental questions through a number

of techniques, including galaxy clustering (BAO, RSD, AP, shape and amplitude), weak lensing and their cross-correlations, and Ly-alpha forest

• Best constraints achieved by combining multiple techniques: this is also needed to test robustness of the results against systematics.

• Dark energy, modifications of gravity, primordial spectrum, neutrino mass, non-gaussianity will all be studied with BigBOSS