Cosmology with photometric redshift surveys: challenges and opportunities David Alonso University of Oxford Geneva, Dec 13 th 2019
Me and Geneva 2009 → CERN summer student
Me and Geneva 2009 → CERN summer student 2012 → PhD
Me and Geneva 2009 → CERN summer student 2012 → PhD 2015 → Postdoc
Me and Geneva 2009 → CERN summer student 2012 → PhD 2015 → Postdoc 2019 → Tenure track
Me and Geneva 2009 → CERN summer student 2012 → PhD 2015 → Postdoc 2019 → Tenure track 2020s → ????
From data to cosmology Parameters Initial conditions Energy components Background evolution
From data to cosmology Parameters Observables Initial conditions Matter fmuctuations Energy components Power spectrum Background evolution
From data to cosmology Parameters (Un)observables Observables Initial conditions Matter fmuctuations a =: Energy components Power spectrum CMB temperature Background evolution CMB polarisation Galaxy density Galaxy shapes Ly a absorption 21cm fmux ...
From data to cosmology Parameters (Un)observables Observables Observations Initial conditions Matter fmuctuations a =: Object catalogues Energy components Power spectrum Intensity maps CMB temperature Background evolution Spectra CMB polarisation Galaxy density Galaxy shapes Ly a absorption 21cm fmux ...
From data to cosmology Parameters (Un)observables Observables Observations Instrumental noise Theoretical Astrophysical Inst. systematics uncertainties uncertainties Selection efgects Initial conditions Matter fmuctuations a =: Object catalogues Energy components Power spectrum Intensity maps CMB temperature Background evolution Spectra CMB polarisation Galaxy density Galaxy shapes Ly a absorption 21cm fmux ...
Photometric surveys Galaxy clustering: ● d g = f[ d M ] ~ b g d M ● Local ● Spin-0 GC Growth Matter GC Scale dependence Small scales GC Galaxies
Photometric surveys Galaxy clustering: ● d g = f[ d M ] ~ b g d M ● Local ● Spin-0 GC Growth WL Weak lensing: ● e i ~ g i ~ d M ● LOS integrated ● Spin-2 GC Scale WL dependence Small scales GC WL
Photometric surveys Galaxy clustering: ● d g = f[ d M ] ~ b g d M ● Local ● Spin-0 GC Growth WL Weak lensing: ● e i ~ g i ~ d M ● LOS integrated ● Spin-2 GC Scale WL dependence Small scales GC WL
Photometric surveys: the LSST Outstanding numbers: ● World's largest imager 8.4 m, 9.6 sq-deg FOV ● Wide: 20K sq-deg ● Deep: r~27 ● Fast: ~100 visits per year ● Big data: ~15 TB per day Dark Energy Science Collaboration: ● Supernovae ● Cluster science ● Strong lensing LSST ● Weak lensing ● Large-scale structure LSST Coll. et al. 0912.0201
Ideal analysis pipeline BORG: Porqueres et al. 1812.05113 Kodi Ramanah et al. 1808.07496 Jasche & Lavaux 1806.11117 Lavaux & Jasche 1509.05040 Jasche & Wandelt 1306.1821 ● Cosmological model ● Structure formation model ● Astrophysical model ● Instrument/noise model
2-point tomographic analysis ● Photo-zs are complicated. ● Bunch galaxies up into photo-z bins and project onto the sphere. DES Y1 data arXiv:1708.01530
2-point tomographic analysis ● Photo-zs are complicated. ● Bunch galaxies up into photo-z bins and project onto the sphere. ● Compute all possible two-point cross- correlations (different bins, different observables). HSC Y1 data arXiv:1809.09148
2-point tomographic analysis -2 log P(d| q ) = (d-t( q )) T C -1 (d-t( q )) + L 0 ● Photo-zs are complicated. ● Bunch galaxies up into photo-z bins and project onto the sphere. ● Compute all possible two-point cross- correlations (different bins, different observables). ● Constrain parameters using a Gaussian likelihood. KV450 data arXiv:1812.06076
2-point tomographic analysis Covariance matrix Gaussian likelihood -2 log P(d| q ) = (d-t( q )) T C -1 (d-t( q )) + L 0 Theory prediction Vector of cross-correlations
Computing two-point functions Covariance matrix Gaussian likelihood -2 log P(d| q ) = (d-t( q )) T C -1 (d-t( q )) + L 0 Theory prediction Vector of cross-correlations
Estimating power spectra A unified pseudo-C l estimator DA, F.J. Sanchez, A. Slosar arXiv:1809.09603
PCL facts ● Why C l ? (as opposed to x ( q )) k-cuts are easy to interpret. No Hankel transform Covariance is a lot more diagonal Good computational scaling (~N 3/2 ) ● PCL vs. QMV PCL == QMV when the covariance matrix is diagonal PCL is precise enough in many common scenarios QMV ~ N 3 , PCL ~ N 3/2 (The trick is being able to estimate mode coupling analytically) Tegmark astro-ph/9611174 Efstathiou astro-ph/0307515 Leistedt et al. arXiv:1306.0005
A unifjed pseudo-C l code Code: https://github.com/LSSTDESC/NaMaster Docs: https://namaster.readthedocs.io/en/latest/index.html
A unifjed pseudo-C l code http://www2.iap.fr/users/hivon/software/PolSpice/ https://gitlab.in2p3.fr/tristram/Xpol What features does it implement? ● Calculate PCL power spectra (including coupling matrix, etc.) ● In curved and flat skies ● Spin-0 (density, CMB T) and spin-2 (shear, CMB Q/U) quantities ● Bells and whistles: Mode deprojection E/B mode purification ● Gaussian covariances Code: https://github.com/LSSTDESC/NaMaster Docs: https://namaster.readthedocs.io/en/latest/index.html
A unifjed pseudo-C l code What features does it implement? ● Calculate PCL power spectra (including coupling matrix, etc.) ● In curved and flat skies ● Spin-0 (density, CMB T) and spin-2 (shear, CMB Q/U) quantities ● Bells and whistles: Garcia-Garcia C., DA, Bellini E. Mode deprojection arXiv:1906.11765 E/B mode purification ● Gaussian covariances Efstathiou astro-ph/0307515 Code: https://github.com/LSSTDESC/NaMaster Docs: https://namaster.readthedocs.io/en/latest/index.html
A unifjed pseudo-C l code What features does it implement? ● Calculate PCL power spectra (including coupling matrix, etc.) ● In curved and flat skies ● Spin-0 (density, CMB T) and spin-2 (shear, CMB Q/U) quantities ● Bells and whistles: Garcia-Garcia C., DA, Bellini E. Mode deprojection arXiv:1906.11765 E/B mode purification ● Gaussian covariances Efstathiou astro-ph/0307515 Code: https://github.com/LSSTDESC/NaMaster Docs: https://namaster.readthedocs.io/en/latest/index.html
Mode deprojection A. Slosar: “The greatest thing since sliced bread” ● Masking: if I have a bad pixel, I make sure it doesn’t get used. ● Mode deprojection is the extension of this idea into an arbitrary linear combination of pixels. Imagine contaminating your data field as True map Observed Contaminant template map (e.g. dust map) A proper analysis would marginalize over a . m d c Leistedt et al. 1306.0005 d cproj Elsner et al. 1609.03577
Mode deprojection A. Slosar: “The greatest thing since sliced bread” ● Masking: if I have a bad pixel, I make sure it doesn’t get used. ● Mode deprojection is the extension of this idea into an arbitrary linear combination of pixels. Imagine contaminating your data field as True map Observed Contaminant template map (e.g. dust map) A proper analysis would marginalize over a . If you do the maths, in PCL this amounts to: ● Finding the best fit value of a. ● Subtracting a contaminant map from the data using this a ● Calculate the PCL and correct for the bias this subtraction has produced ● Multiply by the inverse of the mode-coupling matrix Leistedt et al. 1306.0005 Elsner et al. 1609.03577
NaMaster DES Y1 clustering CMB- k x gals Krolewski et al. CMB B-modes 1909.07412 Dust from HI SO et al. 1808.07445 CMB- k x QSOs Hensley & Clark DES et al. 1807.10163 1909.11673 HSC Y1 clustering tSZ x gals DA et al. 1712.02738 Nicola et al. (in prep) Koukoufilippas et al. 1909.09102 CIB x CMB- k ... Cosmic shear Lenz et al. 1905.00426 Bellini et al. 1903.04957
Example: tomographic analysis Covariance matrix Gaussian likelihood -2 log P(d| q ) = (d-t( q )) T C -1 (d-t( q )) + L 0 Theory prediction Vector of cross-correlations Accuracy of t( q ) >> statistical power. LSST’s statistical power will be awesome. Requirements for LSST: ● Accuracy (errors well below statistical uncertainties) ● Robustness (thorough code validation and comparison) ● Flexibility (many observables, many cosmological models, ability to vary models and absorb systematics) ● Numerical performance (reasonable MCMC-ing time)
Robust theory predictions Core Cosmology Library: precision cosmological predictions for LSST Chisari E., DA, E. Krause +27, arXiv:1812.05995
The Core Cosmology Library Code: https://github.com/LSSTDESC/CCL Docs: https://ccl.readthedocs.io/en/latest/ Latest release: https://github.com/LSSTDESC/CCL/releases/tag/v2.0.1
Code validation Strict code validation requirements ● All calculations are performed with at least one different independent code. ● Agreement must be found within well-motivated/crazy stringent requirements. ● Alternative calculations are kept as benchmarks. ● CCL is automatically compared against benchmarks whenever a new addition is made to the code. ● Unit tested (~95%).
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