Constraining Dark Energy and Modified Gravity with the Kinetic SZ effect Eva-Maria Mueller Work in collaboration with Rachel Bean, Francesco De Bernardis, Michael Niemack (arxiv 1408.XXXX, coming out tonight)
Outline 1. Motivation 2. ksz in a nutshell 3. Forecasts for DE and MG 4. Uncertainties and Systematics 5. Concluding thoughts Why should I care? What is it? How well can it do? What are possible problems? What s up next?
Probes of Gravity Galaxies: { BAO and Redshift Space Distortions Weak Lensing Larger scales Why clusters? high mass very sensitive to the gravitational potential Clusters: { Cluster abundance Dynamics of clusters kinetic SZ effect (CMB) S. Bhattacharya, A. Kosowsky, 2007 different systematics different degeneracies
Kinetic SZ effect CMB photon passing though clusters are Doppler shifted due to bulk motion distortion of the CMB spectrum T ksz T CMB = τ vpec c δ + ikv =0 optical depth
Problem: SZ spectrum ksz: weak frequency dependence ksz: Signal is small Hard to observe Solution: Cross-correlate with cluster positions and redshift ned.ipac.caltech.edu Mean pairwise velocity
Method: Mean pairwise statistics First detection : ACT mean pairwise momentum Use cross-correlation with BOSS LRGs: Stack CMB submaps that contain clusters But: need better accuracy How well can we do in the future? Hand et. al 2012
Use mean pairwise velocity to constrain growth of matter 300 250 200 z =0.15 w 0 = 1.0, γ =0.55 w 0 = 0.8, γ =0.55 w 0 = 1.2, γ =0.55 w 0 = 1.0, γ =0.66 w 0 = 1.0, γ =0.44 Growth rate f: f g (a) =Ω m (a) γ Vij [km/s] 150 100 γ GR =0.55 γ GR =0.55 50 0 20 40 60 80 100 120 140 160 180 r [Mpc/h] Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX) v ij (r, a) = 2 3 H(a)a f(a) r ξ halo (r, a) 1+ξ halo (r, a) Sheth et. al 2001
Survey Specifications Survey Stage Survey Parameters II III IV CMB T instr (µkarcmin) 20 7 1 Cluster z min 0.1 0.1 0.1 z max 0.4 0.4 0.6 No. of z bins, N z 3 3 5 M min (10 14 M ) 1 1 0.6 Overlap Area (sq. deg.) 4000 6000 10000 ACTPol AdvancedACT CMB S4 +BOSS +DESI Cross-Correlate cluster position on the sky and redshift with ksz signal use LRGs as tracers of clusters cluster catalog
Potential of ksz surveys Stage III Stage IV +CMB FoM GR 14 61 FoM MG 9 33 γ/γ 0.08 0.05 +DETF FoM GR 156 292 FoM MG 152 273 γ/γ 0.05 0.02 γ 0.62 0.60 0.58 0.56 0.54 Stage IV Stage III Stage II DETF Stage III Current constraints: BOSS: γ =0.71 +0.12 0.11 ksz more powerful for constraining modified gravity than dark energy equation of state 0.52 0.50 + CMB + DETF Stage III 0.48 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 w 0 Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX)
Modified Gravity Parametrization DESI : BAO+RSD Model independent parametrization: Less theoretical prior Comparison to other future probes: f g (z) f g σ 8 f g σ 8 =1.4 1.6% additional constraints from Euclid and WFIRST at higher redshifts Complementary constraints fg/fg γ 0.62 0.10 0.60 0.58 0.08 0.56 0.06 0.54 0.04 0.52 Stage IV + Stage DETF III Stage III + Stage CMBII DETF Stage III Stage IV Stage III Stage II 0.50 0.02 + CMB + DETF Stage III 0.48 1.8 0.1 1.6 0.2 1.4 1.20.3 1.0 0.8 0.4 0.6 0.5 0.4 0.2 zw 0 Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX)
Dependency on the number of clusters 0.45 0.40 0.35 Stage IV Stage III Stage II ksz+cmb priors γ/γ 0.30 0.25 0.20 Higher cluster number densities lead to better constraints! 0.15 0.10 0.05 0.00 10 13 10 14 M min [M ] Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX) Optimistic case: Stage II Stage III Stage IV M min (10 13 M ) 4 4 1 γ/γ 0.07 0.06 0.02
Uncertainty in limiting mass Vij γ/γ [km/s] 0.45 300 0.40 250 0.35 0.30 200 0.25 150 0.20 0.15 100 0.10 50 0.05 Stage IV Stage III Stage II ksz+cmb z =0.15 priors M min =1.0 10 14 M M min =2.0 10 14 M M min =1.0 10 13 M M min =1.2 10 14 M M min =0.8 10 14 M 0.00 010 20 13 40 60 80 100 120 10 14 140 160 180 M min [M ] r [Mpc/h] Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX) Limiting mass changes shape + amplitude Only mild dependency Marginalizing over the minimum mass does not significantly reduce constraints Robust to uncertainties in the mass calibration!
Pairwise momentum T ksz T CMB = τ vpec c τ Pairwise velocity How well do we know the optical depth?
So far: Uncertainty in optical depth Hydro-simulation show a intrinsic dispersion in the optical depth of ~15% averaged over all cluster masses* Use scatter in τ as a proxy for the uncertainty Measurement error is a combination of instrument noise and uncertainty in optical depth σ v = σ 2 instr + σ2 τ C measurement V (r, r )= 2σ2 v N pair δ r,r But: Can we constrain both, optical depth and pairwise velocity? *Private communication with N. Battaglia
1.0 0.8 Stage IV Stage III Stage II ksz+cmb priors Introduce nuisance parameter: Marginalize over the amplitude, i.e. optical depth γ/γ 0.6 0.4 b τ (z) b τ ˆV (z) =b τ (z)v (z) add prior on the τ-bias 0.2 0.0 10 3 10 2 10 1 10 0 10 1 b prior τ Need information on the optical depth Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX) τ 10% leads to interesting constraints
How can we constrain the optical depth? Fitting function from Hydro simulations Robustness? Combine thermal SZ and X-ray observations astro-ph/0504274 Theoretical assumptions and modeling? Polarization signal from scattering astro-ph/9903287 Sensitivity? More work necessary!
Concluding thoughts: ksz surveys have the potential to: Provide a valuable test of the late universe complementary to weak lensing and galaxy redshift space distortions Testing gravity on clusters scales using cluster dynamics as a function of real space separation Future work in progress: Constraining optical depth using simulations! (work by Nick Battaglia) Further consideration of systematic effects Apply to upcoming surveys
Thank you!
Fisher Forecast: Modeling the error F ij = αβ C i,j = F 1 i,j D α Cov 1 D β αβ p i p j mean pairwise velocity Finite Volume errors: Cosmic variance Gaussian shot noise: Velocity measurement error: 1 V s (a) σ2 vel N clusters dk 2 P (k, a)b (1) halo (k)+ 1 n cl (a) 2 use Jenkins mass function uncertainty for individual cluster depends on the minimum observed cluster mass