BigBOSS science overviewUros 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 directionsCollaborators: P. McDonald, R. Mandelbaum, N. Padmanabhan, C. Hirata, R. Reyes, A. Slosar

Big questions in cosmologyNature of acceleration of the universe: dark energymodification 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? Classical tests: dark energy: redshift-distance relation: BAO and APGrowth of structure: dark energy, neutrino mass etc: need amplitude of perturbations, ie bias: weak lensing, redshift space distortionsScale dependence of clustering: primordial power spectrum, primordial non-gaussianity: need to understand scale dependence of biasComparing the above tracers, e.g., lensing versus redshift-space distortions: differentiates between dark energy and modified gravity theories

CBIACBARLyman alpha forestScale dependence of cosmological probesWMAPComplementary in scale and redshiftSDSSGalaxy clusteringWeak lensingCluster abundance

Sound WavesEach 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 peaksOverdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies. Preferred separation of 150 Mpc.

A Standard RulerThe acoustic oscillation scale depends on the matter-to-radiation ratio (Wmh2) and the baryon-to-photon ratio (Wbh2).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 talksTheir ratio: Alcock-Paczynski effect

Shape and acoustic oscillations in the Matter Power SpectrumShape determined by matter and baryon density, primordial slopeAmplitude not useful (bias)Peaks are weak; suppressed by a factor of the baryon fraction.Higher harmonics suffer from nonlinear damping.Linear regime matter power spectrum

Weighing neutrinosNeutrino free streaming inhibits growth of structure on scales smaller than free streaming distanceIf 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 >>10MpcNeutrinos 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

Redshift space distortionsUsual approach: measure power along the radial direction and compare to power along transverse direction to determine betaNeed linear regime, limited by sampling variance due to finite number of large scale structures, each of which is a random gaussian realizationLower bias higher beta: good for BIGBOSS

Redshift space Correlation FunctionHawkins et al. (2003, MNRAS, 346, 78)a=0 kms-1=0a=500 kms-1=0a=0 kms-1 =0.4a=500 kms-1 =0.4 (perpendicular to the l.o.s.) (along the l.o.s.)

Beta reconstruction of LRGs: quadrupole to monopole ratio (N-body simulations)Reyes etal 2009

Sources of error in galaxy surveysSampling (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 volumeShot 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 errorFor RSD one gains as shot noise decreases

How to reduce cosmic variance?Two tracers:

Take the ratio

Density perturbation drops out, so no cosmic varianceTransverse vs radial allows to determine bias ratio and beta separatelyFull angular dependence: AP geometrical testWhat 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 galaxiesNeed all of the halos above certain massEmission line galaxies in BigBOSS are not picking out all of the most massive halos10x reduction in noise relative to signal!US, Hamaus, Desjacques 2009Uniform weightingMass weighting

Scale dependent biasCurrent analyses use Q model (Cole etal), no physical motivation, just a fitting formulaA better model has been developed by P. McDonald (2008) based on (renormalized) perturbation theory and local bias ansatzSeems 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 LensingDistortion of background images by foreground matter UnlensedLensed

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 reconstructionUse simulations with realistic HOD galaxy model to model galaxiesCross-correlation coefficient r nearly unityBaldauf, US, Smith (2009) Dark matter power spectrum reconstruction from galaxy power spectrum and galaxy-shear power spectrum unbiasedNonlinear linear

Dark matter clustering reconstructionAlternative 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 elseThis 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 tracer of dark matter and dark energyBasic model: neutral hydrogen (HI) is determined by ionization balance between recombination of e and p and HI ionization from UV photons (in denser regions collisional ionization also plays a role), this gives

Recombination coefficient depends on gas temperatureNeutral hydrogen traces overall gas distribution, which traces dark matter on large scales, with additional pressure effects on small scales (parametrized with filtering scale kF)Fully specified within the model, no bias issues

BAO with Lyman alphaMcDonald and Eisenstein 2007

BigBOSS predictions: TBD (see subsequent talks)

Warm Dark Matter constraintsSeljak, Makarov, McDonald, & Trac, astro-ph/0602430Flux power spectrum3000+ SDSS spectraHIRES data probes smaller scales2(k) = -1 k P(k) 0.01 s/km ~ 1 h/MpcColors correspond to redshift bins centered at z = 2.2, 2.4, , 4.2 (from bottom to top)

SDSS and high resolution Lya power spectrum analysis McDonald, US etal 2006Combined statistical power is better than 1% in amplitude, comparable to WMAP2

Non-gaussianityLocal model Simple single field inflation predicts fnl1Ekpyrotic/cyclic models generically give fnl>>1Other models give different angular dependence of bispectrum (e.g. equilateral in DBI model, Silverstein)Shows up in galaxy clustering as a scale dependent bias

Dalal etal 2007b=3.5Effect proportional to (bias-1): need high bias tracers

How to improve these limits?Effect scales as (b-1), ie no effect for b=1On large scales limited by cosmic variance: finite number of large scale patches (modes), which are gaussian random realizations, but we need to measure average powerTwo 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 dont know!McDonald & US 2009

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

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

Combining the methodsBy combining velocity measurements (b) 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 EGReyes, Mandelbaum, US, Gunn, Baldauf, Lombriser, in prepSDSS: 6 sigma detectionIn agreement with LCDMData disagree with TeVeS (aka MOND)f(R) about 1 sigma below the data: future data should be able to constrain it betterBigBOSS predictions depend on WL data

ConclusionsBigBOSS 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 forestBest 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

The acoustic oscillations are also quantitatively useful, because they can form a standard ruler.Possible Detection by Miller.

Detection would be a confirmation of gravitational structure formation.It *must* be there.