Constraints on primordial Non-Gaussianity from SDSS quasars

Talk given at various institutions/conferences in 2014-2015, summarizing arXiv:1404.6530 and arXiv:1405.4315

Transcript

1. Constraining primordial non-Gaussianity with photometric quasars Boris Leistedt University College London (UCL) arXiv: 1404.6530 (MNRAS) and 1405.4315 (PRL) In collaboration with Hiranya Peiris & Nina Roth
2. Motivation and key concepts ‣ Early universe physics with galaxy surveys: Primordial Non-Gaussianity (PNG) ‣ Galaxy surveys: many observational systematics Can we fully exploit DES / Euclid / LSST ? ‣ This work: (1) blind mitigation of systematics in quasar clustering (2) robust PNG constraints
3. Road map 1. Primordial non-Gaussianity (PNG) 2. Photometric quasars 3. Power spectra and systematics mitigation 4. Constraints on PNG and quasar bias Interrupt if you’re lost!
5. Thanks, Planck!
6. Post Planck-era Parameters of ΛCDM model fixed at the % level Soon with polarisation!
7. PNG : a window on inflation ‣ Initial conditions ~Gaussian, described by power spectra ‣ Non-Gaussanity: higher order terms ‣ Local PNG: = + fNL[ 2 h 2i] + gNL[ 3 3 h 2i] 3pt: bispectrum 4pt: trispectrum 2pt: power spectrum Skewness + kurtosis from “squeezed” configurations … …
8. PNG in LSS ‣ Planck bispectrum constraints: ‣ # modes LSS >>> # modes CMB ‣ Different scales than CMB, sensitive to other PNG types Dalal, Dore et al (2007) Matarrese & Verde (2008) Slosar et al (2008) … fNL = 2.7 ± 5.8 PNG enhance bias of LSS tracers on large scales Kaiser effect
9. PNG in LSS clustering HSLS white paper (fNL) ⇠ 1 LSST:
10. Constraints on PNG from LSS ‣ Quasars give best PNG constraints ‣ BUT plagued by systematics… Slosar et al (2008) Xia et al (2010) Pullen & Hirata (2012) Leistedt et al (2013) Giannantonio et al (2013) Ho et al (2013) Agarwal et al(2014) … This work: 49 < fNL < 31 (2 ) Giannantonio et al (2013) NVSS +LRG QSO only
11. Why are quasars so good for PNG? ‣ Large volumes + highly biased 㱺 best signal-to-noise ‣ Problem: quasars look like stars! ‣ Option 1: spectroscopic surveys: small, not so deep ‣ Option 2: photometric surveys: large, deep, but plagued by systematics Galaxies Quasars Slosar et al (2008), Xia et al (2010), Pullen & Hirata (2012), Leistedt et al (2013), Giannantonio et al (2013) , Ho et al (2013), Agarwal et al (2014) …
12. Photometric quasars ‣ Star/quasar separation + photometric redshift estimation with a handful of photometric numbers Vanden Berk et al (2001) Leistedt et al (2013)
13. The XDQSOz catalogue ‣ 1.6 million photometric quasars from SDSS DR8 ‣ p(QSO)>0.8 + divided into 4 samples with photo-z cuts Stacked posteriors p(true z | photo-z)
14. Sky coverage stars dust Black: DR8 footprint Blue: analysis mask
15. Optimal Cl estimator ‣ Quadratic maximum likelihood estimator for 10 auto + cross angular power spectra simultaneously ‣ Model of the pixel-pixel covariance matrix: ‣ Why not pseudo spectrum estimator? Because only optimal with flat power spectra and no systematics… Theory spectrum Noise, systematics, ... Covariance matrix between 2 pixels Cij = h xixj i = X ` ✓ 2` + 1 4⇡ ◆ C`P`(cos ✓ij) + Nij
16. Modelling the clustering of quasars ‣ Cosmological parameters (LCDM), shot noise, magnification effects, redshift distributions, RSD Use CAMB_sources (Challinor & Lewis 2011) ‣ Quasar bias model: ‣ PNG bias: ‣ Scaling: ‣ MCMC ‘hammer’: emcee (Foreman-Mackey et al 2013) btot(k, z) = bG(z) + bNG(k, z) bNG(k, z) = f (z)fNL + g(z)gNL ↵(k, z) / k 2 bG(z) = b0 + b0 ✓ 1 + z 2.5 ◆ List of ingredients
17. Clustering of XDQSOz quasars Colours: 50 < fNL < 50
18. Raw power spectra ‣ Evidence for strong systematics in all samples ‣ Mimic PNG signal
19. You said systematics? ‣ Anything that affects point sources or colours e.g. dust extinction, seeing, airmass, zero points, … ‣ Create spatially varying depth & stellar contamination seeing stars dust
21. “If tortured sufficiently, data will confess to almost anything” F. Menger aka confirmation / observer’s bias
22. Treating systematics ‣ Suppose we have maps of systematics ‣ Masking or correcting data is dangerous and insufficient ‣ Need to ignore spatial modes = Bayesian marginalisation = project out weighted data pixels = mode projection ‣ Use “projective” covariance matrix s.t. C 1 = lim ↵i !1 S({C` }) + N + X i ↵i ~ mi ~ mt i ! 1 ~ mi i = 1, . . . , Nsys ~ miC 1 ~ x = 0 8 i signal noise systematics
23. Extended mode projection 1. Collect all possible systematics
    220 templates + pairs 㱺 >20,000 templates 2. Decorrelate set of systematics with SVD
    20,000 templates 㱺 3,700 uncorrelated modes 3. Project out the modes most correlated with data
    3,700 null tests; project out modes with chi2>1 Sacrificing some signal in favour of robustness 㱺 Blind mitigation of systematics
24. Raw spectra vs clean spectra ‣ Project out the templates with reduced chi2 > 1 ‣ Grey band: 50 < fNL < 50
25. Raw spectra vs clean spectra ‣ Project out the templates with reduced chi2 > 1 ‣ Grey band: 50 < fNL < 50
26. Full likelihood
27. Constraints on fNL Fixed cosmology & n(z) Varying all parameters ‣ Competitive with WMAP9 with single LSS tracer ‣ Robust to modelling & priors 16 < fNL < 47 (2 ) 49 < fNL < 31 (2 ) Planck Leistedt, Peiris & Roth (1405.4315)
28. Constraints on the quasar bias bG(z) = b0 + b0 ✓ 1 + z 2.5 ◆
29. Constraints on gNL also gives => degenerate with Roth & Porciani (2012) gNL b / k 2 fNL Hard to constrain from the CMB! 2.7 < gNL/105 < 1.9 4.0 < gNL/105 < 4.9 105 < fNL < 72 (2 ) gNL alone fNL + gNL Leistedt, Peiris & Roth (1405.4315)
30. Constraints on scale-dependent bias Single field inflation with a modified initial state, or models with several light fields. Agullo and Shandera (2012), Dias, Ribeiro and Seery (2013) b(k) / k 2+nfNL 45 e3.7nfNL 34 e3.3nfNL Generalised bias Giannantonio et al (2013) Agarwal et al (2014) Leistedt, Peiris & Roth (2014)
31. What about future surveys? ‣ LSST-like survey: 20 z-bins in 0.5 < z < 3.5 ‣ Fiducial: LCDM, galaxy bias, Fisher matrix forecast: ‣ No systematics: unbiased result, ‣ With a few real systematics: (!) ‣ + mode projection: unbiased result, (fNL) ⇠ 1 (fNL) ⇠ 5 fmeasured NL ⇠ 30 ftruth NL = 0
32. Conclusions ‣ Stringent PNG constraints using quasars only ‣ Extended mode projection: ‘blind’ mitigation of thousands of systematics ‣ Future: Dark Energy Survey, Euclid, LSST… Leistedt & Peiris (1404:6530) Leistedt, Peiris & Roth (1405.4315)
33. Extra Slides
34. Mode projection ‣ Have maps of systematics → can model contamination ‣ Standard approach: fix parameters, correct data / spectra ‣ Extended approach: marginalisation over parameter values Performed analytically in Cl estimator 㱺 mode projection ‣ BUT not suitable for non-linear contamination by many correlated systematics nobserved QSO = ntruth QSO + ↵1 sys1 + ↵2 sys2 + . . . in each pixel
35. Null tests ‣ Cross-spectra of 4 quasar bins x 3,700 systematics ‣ Project out the templates with reduced chi2 > 1
36. Extended mode projection 1. Create set of input systematics
    300 templates + pairs 㱺 >20,000 templates 2. Decorrelate them and remove noisy modes
    20,000 templates 㱺 3,700 uncorrelated modes
37. Full expressions of PNG bias ‣ Total bias: ‣ PNG bias: ‣ fNL term: gNL term: ‣ gNL: fitting functions by Smith et al (2011) ‣ Scaling: btot(k, z) = bG(z) + bNG(k, z) bNG(k, z) = f (z)fNL + g(z)gNL ↵(k, z) / k 2 g = 3 @ log n @fNL ↵(k, z) = 2k2T(k)D(z) 3⌦m H2 0 f = 2 c(bG 1)
38. Extended mode projection 3. Project out the modes the most correlated with data
    Cross correlate modes with QSO samples. Use cross- spectra as null tests. Mode projection based on 2
39. Constraints on the quasar bias b(z) = b0 " 1 + ✓ 1 + z 2.5 ◆ #