Constraining Dark Energy and Modified Gravity with the Kinetic SZ effect

Transcription

1 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)

2 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?

3 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

4 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

5 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

6 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

7 Use mean pairwise velocity to constrain growth of matter 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] γ GR =0.55 γ GR = 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

8 Survey Specifications Survey Stage Survey Parameters II III IV CMB T instr (µkarcmin) Cluster z min z max No. of z bins, N z M min (10 14 M ) Overlap Area (sq. deg.) 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

9 Potential of ksz surveys Stage III Stage IV +CMB FoM GR FoM MG 9 33 γ/γ DETF FoM GR FoM MG γ/γ γ Stage IV Stage III Stage II DETF Stage III Current constraints: BOSS: γ = ksz more powerful for constraining modified gravity than dark energy equation of state CMB + DETF Stage III w 0 Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX)

10 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 = % additional constraints from Euclid and WFIRST at higher redshifts Complementary constraints fg/fg γ Stage IV + Stage DETF III Stage III + Stage CMBII DETF Stage III Stage IV Stage III Stage II CMB + DETF Stage III zw 0 Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX)

11 Dependency on the number of clusters Stage IV Stage III Stage II ksz+cmb priors γ/γ Higher cluster number densities lead to better constraints! M min [M ] Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX) Optimistic case: Stage II Stage III Stage IV M min (10 13 M ) γ/γ

12 Uncertainty in limiting mass Vij γ/γ [km/s] Stage IV Stage III Stage II ksz+cmb z =0.15 priors M min = M M min = M M min = M M min = M M min = M 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!

13 Pairwise momentum T ksz T CMB = τ vpec c τ Pairwise velocity How well do we know the optical depth?

14 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

15 Stage IV Stage III Stage II ksz+cmb priors Introduce nuisance parameter: Marginalize over the amplitude, i.e. optical depth γ/γ b τ (z) b τ ˆV (z) =b τ (z)v (z) add prior on the τ-bias b prior τ Need information on the optical depth Mueller, De Bernardis, Bean, Niemack (arxiv 1408.XXXX) τ 10% leads to interesting constraints

16 How can we constrain the optical depth? Fitting function from Hydro simulations Robustness? Combine thermal SZ and X-ray observations astro-ph/ Theoretical assumptions and modeling? Polarization signal from scattering astro-ph/ Sensitivity? More work necessary!

17 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

18 Thank you!

19 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