1. EGEE-III INFSO-RI-222667 Enabling Grids for E-sciencE www.eu-egee.org EGEE and gLite are registered trademarks Constraints on primordial non-Gaussianity using Planck simulated data Marcos López-Caniego Andrés Curto Enrique Martínez-González Instituto de Física de Cantabria (CSIC-UC)

2. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 2 Introduction After the successful porting of the point source detection code and the SZ clusters detection code to the EGEE GRID, we are in the process of porting and testing a new application. This application is composed of two codes, one to produce Gaussian simulations of Planck and another to look for non-Gaussianity signatures in these maps using spherical wavelets. These applications are part of an ongoing project being carried out by the Observational Cosmology and Instrumentation Group at the Instituto de Física de Cantabria (CSIC-UC) on different analyses of the Cosmic Microwave Background (CMB).

3. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 3 Motivations The Planck mission will provide CMB maps with unprecedented resolution and quality at several frequencies. Therefore, we expect to obtain the very competitive constraints on the primordial non-Gaussianity with this experiment. The study of this kind of non-Gaussianity through the study of the non- linear coupling parameter f nl has become a question of considerable interest as it can be used to discriminate different possible scenarios of the early Universe and also to study other sources of non-Gaussianity non- intrinsic to the CMB. The uncertainties on the f nl,  (f nl ), depend on the cosmological model, the instrumental properties and the available fraction of the sky to be analyzed, e.g., a better estimation on f nl can be achieved with a low instrumental noise and a high sky coverage. The constraints on f nl can be obtained using two methods: simulations analytical equations.

4. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 4 The Analysis with Simulations First, 10,000 of Gaussian CMB maps are simulated and processed through the Planck instrument simulation pipeline for three frequency bands, 100, 143 and 217GHz, producing three maps per simulation. Then, these maps are combined into a single map.

5. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 5

6. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 6 The Analysis with Simulations First, 10,000 of Gaussian CMB maps are simulated and processed through the Planck instrument simulation pipeline for three frequency bands, 100, 143 and 217GHz, producing three maps per simulation. Then, these maps are combined into a single map. Second, for each simulation, the combined map is convolved in harmonic space with a spherical wavelet, in this case the spherical Mexican hat wavelet (SMHW) will be used.

7. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 7 The spherical Mexican hat wavelet (SMHW) Continuous wavelet transform position traslation scale

8. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 8 The wavelet is a filter

9. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 9 The Simulations First, 10,000 of Gaussian CMB maps are simulated and processed through the Planck instrument simulation pipeline for three frequency bands, 100, 143 and 217GHz, producing three maps per simulation. Then, these maps are combined into a single map. Second, for each simulation, the combined map is convolved in harmonic space with a spherical wavelet, in this case the spherical Mexican hat wavelet (SMHW) will be used. The convolved map, the wavelet coefficients map, will contain information about those structures of the initial map with a characteristic size R.

10. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 10 We will repeat this process for several angular scales R between 2.9 arc minutes and about 170 degrees. Finally we use third order statistics (in a similar way as the bispectrum) to constrain the levels of non-Gaussianity of the local type which are expected to be present in Planck data. Index012345678910 RMap2.9’4.5’6.9’10.6’16.3’24.9’38.3’58.7’90.1’138.3’ Index11121314151617181920- R3.5º5.4º8.3º12.8º19.6º30.1º46.2º70.9º108.9º167.1º-

11. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 11 Statistics with the wavelet Select a characteristic set of angular scales R j Compute the wavelet transform map  (b j,R i ) at these scales R j Compute third order statistics by combining different scales Combine in a  2 test all the estimators dataGaussian model f nl model data

12. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 12 Constraints on f nl for an ideal experiment We constrain f nl with a  2 test The variance of f nl through the Fisher matrix  and C are function of the cosmological parameters and the instrumental properties They can be computed with simulations and analytically

13. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 13 Simulation of 10.000 Gaussian maps per frequency Input –Power spectrum of the cosmological model (~1 KB) –Instrumental beams (~1 KB) –Instrumental variance for each pixel (total ~15 MB) Algorithm –Generate Gaussian coefficients in the sphere a lm –Transform the a lm to DT/T maps and add instrumental beam –Add Gaussian noise for each bolometer –Total time and memory per simulation: 5 min, 1GB of RAM Output –10.000 maps/frequency and 10.000 combined maps=40.000 maps –15 MB per map => 0.6 TB –Aprox. 1000 CPU hours per scale => 30.000 CPU hours total

14. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 14 Analysis of the 10.000 simulations Input –Planck Gaussian simulations (15 MB each) Algorithm –Select a set of n angular scales {Ri} –Compute the wavelet transform (5 min and 1 GB RAM each scale) –Evaluate the cubic statistics Output –Cubic statistics: for n scales, (n+2)!/[(n-1)!3!] files (several KB per map) –Aprox. 5000 CPU hours to do the analysis of the 10.000 simulations

15. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 15 Analytic estimation of C and  Input –Cosmological parameters and power spectrum (several KB) –Transfer function generated by gTfast (available on-line by E. Komatsu) ~50 GB Algorithm –Parallelize the estimation of C and  using three indices: l1, l2, l3 from 0 to 3096 each –Number of CPUS: 100-200 –Total time: about 50.000 hours –Total RAM per CPU: 1 GB Output –Each job produces a pair of  (i) and C(i) –Final  and C parameters are the sum

16. Enabling Grids for E-sciencE EGEE-III INFSO-RI-222667 EGEE09, Barcelona, Spain, 24 September 2009 16 First check: Estimate Covariance matrix in 1 scale Evaluate the covariance with 1000 Gaussian simulations C(sims) Evaluate the covariance matrix with the analytical expression C(theo) Check that the analytical value for the covariance agrees with its estimator with 1000 Gaussian simulations and 1 scale The differences are < 6% Future Work: continue with the analysis of the remaining 20 scales Estimate the covariance matrix using 21 scales with sims (~40.000 CPU hours) Estimate the  coefficients using 21 scales analytically (~50.000 CPU hours) Constraint f nl and compare with the bispectrum DONE