Constraining
primordial non-Gaussianity
with photometric quasars
Boris Leistedt
University College London (UCL)
!
arXiv: 1404.6530 and 1405.4315
In collaboration with Hiranya Peiris & Nina Roth
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
Road map
Interrupt if you’re lost!
1. Primordial non-Gaussianity (PNG)
2. Photometric quasars
3. Power spectra and systematics mitigation
4. Constraints on PNG and quasar bias
PNG : a window on inflation
‣
Initial conditions ~Gaussian, described by power spectra
!
‣
2pt: power spectrum
Non-Gaussanity: higher order terms
!
!
…
3pt: bispectrum
!
…
4pt: trispectrum
!
‣
Local PNG:
=
+ fNL [
2
h
2
i] + gNL [
3
3 h
Skewness + kurtosis from “squeezed” configurations
2
i]
PNG in LSS
‣
Planck bispectrum constraints: fNL = 2.7 ± 5.8
‣
# modes LSS >>> # modes CMB
‣
Different scales than CMB, sensitive to other PNG types
PNG enhance bias of LSS
tracers on large scales
Dalal, Dore et al (2007)
Matarrese & Verde (2008)
Slosar et al (2008)
…
HSLS white paper
LSST:
(fNL ) ⇠ 1
Why are quasars so good for PNG?
‣
Large volumes + highly biased
best signal-to-noise
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) …
Quasars
‣
Problem: quasars look
like stars!
‣
Option 1: spectroscopic
surveys: small, not so deep
‣
Option 2: photometric
surveys: large, deep, but
plagued by systematics
Galaxies
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)
Optimal Cl estimator
‣ Quadratic maximum likelihood estimator for 10 auto +
cross angular power spectra simultaneously
dust
Black: DR8 footprint
Blue: analysis mask
stars
Modelling the clustering of quasars
List of ingredients
‣
‣
Cosmological parameters (LCDM), shot noise,
magnification effects, redshift distributions, RSD
Use CAMB_sources (Challinor & Lewis 2011)
✓
◆
1+z
G
Quasar bias model: b (z) = b0 + b0
2.5
tot
G
NG
‣
PNG bias: b
‣
Scaling: b
‣
MCMC ‘hammer’: emcee (Foreman-Mackey et al 2013)
NG
(k, z) = b (z) + b
(k, z) =
(k, z)
f (z)fNL
+ g (z)gNL
/ k
↵(k, z)
2
Raw power spectra
‣ Evidence for strong
systematics in all samples
‣ Mimic PNG signal
You said systematics?
‣ Anything that affects point sources or colours
e.g. dust extinction, seeing, airmass, zero points, …
‣ Create spatially varying depth & stellar contamination
dust
stars
seeing
“If tortured sufficiently,
data will confess to almost anything”
!
F. Menger
!
aka confirmation / observer’s bias
Treating systematics
~i
‣ Suppose we have maps of systematics m
i = 1, . . . , Nsys
‣ Masking or correcting data is dangerous and insufficient
‣ Need to ignore spatial modes = Bayesian marginalisation
= project out weighted data pixels = mode projection
~ iC
‣ Use “projective” covariance matrix s.t. m
!
!
C
1
=
lim
↵i !1
S({C` }) + N +
signal
noise
1
~x = 0 8i
systematics !
X
i
t
↵i m
~ im
~i
1
Extended mode projection
1. Collect all possible systematics
220 templates + pairs
>20,000 templates
2. Decorrelate set of systematics with SVD
20,000 templates
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
Blind mitigation of systematics
Raw spectra vs clean spectra
‣ Project out the templates with reduced chi2 > 1
‣ Grey band:
50 < fNL < 50
Raw spectra vs clean spectra
‣ Project out the templates with reduced chi2 > 1
‣ Grey band:
50 < fNL < 50
Full likelihood
Constraints on fNL
Planck
Fixed cosmology & n(z)
16 < fNL < 47 (2 )
Varying all parameters
49 < fNL < 31 (2 )
‣ Competitive with WMAP9 with single LSS tracer
‣ Robust to modelling & priors
Leistedt, Peiris & Roth (1405.4315)
Constraints on gNL
gNL also gives b / k 2
=> degenerate with fNL
Roth & Porciani (2012)
Hard to constrain
from the CMB!
5
4.0 < gNL /10 < 4.9
gNL alone
105 < fNL < 72 (2 )
2.7 < gNL /10 < 1.9
Leistedt, Peiris & Roth (1405.4315)
5
fNL + gNL
Constraints on scale-dependent bias
34 e3.3nfNL
45 e
3.7nfNL
Generalised bias
b(k) / k 2+nfNL
Giannantonio et al (2013)
Agarwal et al (2014)
Leistedt, Peiris & Roth (2014)
Single field inflation with a modified initial state,
or models with several light fields.
Agullo and Shandera (2012), Dias, Ribeiro and Seery (2013)
What about future surveys?
Leistedt, Peiris & Roth (1405.4315)
‣ LSST-like survey: 20 z-bins in 0.5 < z < 3.5
‣ Fiducial: LCDM, galaxy bias,
truth
fNL
=0
!
Fisher matrix forecast:
‣ No systematics: unbiased result,
‣ With a few real systematics:
(fNL ) ⇠ 1
measured
fNL
‣ + mode projection: unbiased result,
⇠ 30 (!)
(fNL ) ⇠ 5
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)
(extra slides)
Constraints on PNG from LSS
Giannantonio et al (2013)
NVSS +LRG+QSO
This work:
QSO only
49 < fNL < 31 (2 )
‣
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)
…
Photometric quasars
‣
Star/quasar separation + photometric redshift estimation
with a handful of photometric numbers
Vanden Berk et al (2001)
Leistedt et al (2013)
Clustering of XDQSOz quasars
Colours:
50 < fNL < 50
Sky coverage
dust
Black: DR8 footprint
Blue: analysis mask
stars
Optimal Cl estimator
‣ Quadratic maximum likelihood estimator for 10 auto +
cross angular power spectra simultaneously
‣ Model of the pixel-pixel covariance matrix:
✓
◆
X 2` + 1
!
Cij = hxi xj i =
C` P` (cos ✓ij ) + Nij
4⇡
!
`
Covariance matrix
between
2 pixels
!
Theory
spectrum
Noise,
systematics, ...
‣ Why not pseudo spectrum estimator? Because only
optimal with flat power spectra and no systematics…
Mode projection
‣
Have maps of systematics → can model contamination
!
!
observed
nQSO
=
truth
nQSO
+ ↵1 sys1 + ↵2 sys2 + . . .
in each pixel
‣
Standard approach: fix parameters, correct data / spectra
‣
Extended approach: marginalisation over parameter values
Performed analytically in Cl estimator mode projection
‣
BUT not suitable for non-linear contamination by many
correlated systematics
Null tests
‣ Cross-spectra of 4 quasar bins x 3,700 systematics
‣ Project out the templates with reduced chi2 > 1
Extended mode projection
1. Create set of input systematics
300 templates + pairs
>20,000 templates
2. Decorrelate them and remove noisy modes
20,000 templates
3,700 uncorrelated modes
Extended mode projection
3. Project out the modes the most correlated with data
Cross correlate modes with QSO samples. Use cross2
spectra as null tests. Mode projection based on
Constraints on the quasar bias
G
b (z) = b0 + b0
✓
1+z
2.5
◆
Constraints on the quasar bias
"
b(z) = b0 1 +
✓
1+z
2.5
◆ #
Full expressions of PNG bias
‣ Total bias: b
tot
‣ PNG bias:
NG
‣ fNL term:
b
f
G
(k, z) = b (z) + b
(k, z) =
= 2 c (b
G
NG
(k, z)
f (z)fNL
+ g (z)gNL
/ k
↵(k, z)
1)
gNL term:
‣ gNL: fitting functions by Smith et al (2011)
2k 2 T (k)D(z)
‣ Scaling: ↵(k, z) =
3⌦m H02
g
2
@ log n
=3
@fNL
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