![Mapping of clustering from real to redshift spaces
Ps(k,𝝻) = ∫d3x eikx ⟨𝛅𝛅⟩
Ps(k,μ) = ∫d3x eikx ⟨ejv (𝛅+𝝻2ϴ)(𝛅+𝝻2ϴ)⟩
• Higher order polynomials are generated by density and velocity
cross-correlation which generate the infinite tower of correlation
pairs. We take the perturbative approach to cut off higher orders.
= ∫d3x eikx exp{⟨ejv⟩c} [⟨ejv(𝛅+𝝻2ϴ)(𝛅+𝝻2ϴ)⟩c+⟨ejv(𝛅+𝝻2ϴ)⟩c⟨ejv(𝛅+𝝻2ϴ)⟩c]
Ps(k,μ) = [Pgg(k) + 2𝝻2PgΘ(k) + 𝝻4P 𝛉𝛉(k)+ A(k,𝝻) + B(k,𝝻) + T(k,𝝻) + F(k,𝝻)]
exp[-(k𝝻σp)2]
• The FoG effect consists of the one-point contribution and the
correlated velocity pair contribution. The latter is perturbatively
expanded as F term, and the former is parameterised using σp.](https://image.slidesharecdn.com/astanaspherex-170817061123/85/Astana-spherex-30-320.jpg)
![The residual FoG
We subtract out the perturbative higher order polynomials, and the
remaining’s can be considered to be FoG effect. If our formulation is
correct, those all residuals should be consistent in terms of scale,
and fitted to be Gaussian with constant 𝜎p.
exp[-(k𝝻σp)2]](https://image.slidesharecdn.com/astanaspherex-170817061123/85/Astana-spherex-34-320.jpg)
![Test Methodology
Ps(k,μ) = [Pgg(k) + 2𝝻2PgΘ(k) + 𝝻4P 𝛉𝛉(k)+ A(k,𝝻) + B(k,𝝻) + T(k,𝝻) + F(k,𝝻)]
exp[-(k𝝻σp)2]](https://image.slidesharecdn.com/astanaspherex-170817061123/85/Astana-spherex-36-320.jpg)
Astana spherex
- 1. Constraints on initial conditions from the large scale structure formation Yong-Seon Song (Korea Astronomy and Space Science Institute) New Prospective of Cosmology, APCTP February 17th 2017
- 2. New phase to probe initial conditions Although the spectral index clearly indicates that it departs ns=1, we need confirming evidence for inflationary initial condition. But there is no proof of primordial gravitation wave. Demands for alternative evidences
- 3. Future target of astronomy community Most observed wavebands of galaxies have been targeted at optical bands. The remaining targets will be NIR or FIR regions in which star forming and astro-biological informations are available. Optic bands Star Formation ICE Demand for Space Telescope
- 4. Possible collaboration with cosmology 1. Full sky observation is possible at space: horizon size clustering 2. Redshift indicator: quick and rush spectroscopy searches It can be useful for initial condition constraints
- 5. Building 3-D catalogue for initial condition • From our full-sky 97 bands, we extract the spectra of known sources using the full-sky catalogs from PanSTARRS/DES and WISE. ➡ Blending and confusion are easily controlled. • We compare this spectra to a template library (robust for low redshift sources): ➡ For each galaxy, we obtain a redshift but also other properties (stellar mass, dust content…). • We simulated this process extensively using the COSMOS data-set using the same methodology as the one used for Euclid/WFIRST (Capak et al.). • A spectra is obtained for any type of galaxy and not only ELGs: ➡ Ideal for multi-tracer studies (McDonald & Seljak 09). • The power of low-resolution spectroscopy has been demonstrated with PRIMUS (Cool++14), COSMOS (Ilbert+ +09), NMBS (van Dokkum++09). • The 1.6 μm bump is a well known universal photometric redshift indicator (e.g., Simpson & Eisenhardt 99)
- 6. All sky galaxy density • Full source extraction and redshit measurement pipeline (Capak & Masters). • Detect 1.4 billions sources: ➡ 301M of which with 10% z accuracy, 120M with 3% and 9.8M 0.3%. • Spectra of all types of galaxies, i.e., not only emission line galaxies: ➡ Ideally suited for multi-tracer studies. • The high σ(z) sample drives the power-spectrum fNL constraints while the lower σ(z) sample drive the bispectrum and other cosmological parameter constraints. σ(z)/(1+z)
- 7. Primordial Non-Gaussianity affects galaxy clustering • The effect of primordial non-Gaussianity on galaxy clustering is most important on large scales ➡ Full sky survey, low spectral resolution sample. • E.g., SDSS QSOs : −49 < fNL loc < 31 (95% C.L., Leistedt & Peiris 13)
- 8. Probing the effective non-Gaussianity Definition of scale dependent bias Observable non-Gaussianity current bound: fNL < 5.8
- 9. Primordial Non-Gaussianity affects dark matter clustering
- 10. All sky galaxy density • Full source extraction and redshit measurement pipeline (Capak & Masters). • Detect 1.4 billions sources: ➡ 301M of which with 10% z accuracy, 120M with 3% and 9.8M 0.3%. • Spectra of all types of galaxies, i.e., not only emission line galaxies: ➡ Ideally suited for multi-tracer studies. • The high σ(z) sample drives the power-spectrum fNL constraints while the lower σ(z) sample drive the bispectrum and other cosmological parameter constraints. σ(z)/(1+z) Power Spectrum Bispectrum
- 11. Current status of projects JPL and KASI submitted the SPHEREx project to NASA SMEX program (2016) 1. The submitted proposal was unsuccessful 2. There are demands for surveys with bigger telescopes, which exceeds the limit of SMEX program 3. NASA recommends the program to be upgraded to be submitted for middle class space telescope call JPL will lead middle class space telescope call, and CosKASI stays in collaborating in data analysis (2017 on going)
- 12. Probing a large effective volume Veff = Vsurvey s Pgal Pgal + 1 ngal
- 13. Why Studying primordial non-Gaussianity? Testing Inflation with Large Scale Structure: Connecting Hopes with Reality (conveners: O.Dore, D. Green, Alvarez et al., arXiv:1412.4671)
- 14. New phase to probe the initial condition We plan to launch the full sky survey to access the horizon mode structure formation to probe fNL using both power and bi spectra. Thermal shields Spacecraft boresight Instrument boresight Instrument boresight is canted so NCP/SCP can be viewed even when spacecraft tilts for Sun- avoidance
- 15. Instrument structure OBA S/C Top Deck RING WE=FW+SW CE BAFFLE FPA Radiators “Warm” Harness (WH) COVER COLDRADIATOR FPA = Focal Plane Assembly OBA = Optical Bench Assembly WE = Warm Electronics CE = Cold Electronics (SIDECARs) C&DH TELECOM Solar Shield Assembly Thermal Structural Assembly Electronics System Optical System
- 16. Parameter for spacecraft SPHEREx We define the spacecraft SPHEREx parameters for measuring galaxy spectroscopy to determine redshift. Parameter Required Value Capability Value Telescope aperture 20 cm Focal ratio 3 Band 1 0.75 – 1.25 um; λ/Δλ = 40; H2RG-2.5 um Band 2 1.25 – 2.10 um; λ/Δλ = 40; H2RG-2.5 um Band 3 2.10 – 3.50 um; λ/Δλ = 40; H2RG-5 um Band 4 2.60 – 5.00 um; λ/Δλ = 150; H2RG-5 um Total FOV 3.5 deg x 7 deg Pixel size 6 x 6 Optics temperature 80 K 5um array temperature 50 K Total efficiency 30 % 50 % Pointing jitter (1σ, 200 s) 3 1.5 Large (70º) slew time 150 s 90 s Small (10′) slew time 20 s 10 s Read noise CDS 18/15 e- 10.5 e-
- 17. Spectroscopy pipeline 7ºx3.5° 6pixels B4: 2.6 - 5.0 µm T R = 150 In Transmission B2: 1.25 - 2.1 µm R = 40 In Reflection B1: 0.75 - 1.25 µm R = 40 In Reflection λ !λ ! 2048 x 2048 2048 x 2048 Full coverage requires 20 steps across each detector (100 for Band 4) Teledyne H2RG arrays - H1RGs flown on HST (1.7um), OCO (2.5um), WISE (5um) (TRL 9) - H2RGs and SIDECAR for JWST (TRL 6) - H2RGs wide use in ground-based astronomy LVFs in space applications - HST as order sorters - ISO as CVFs - OSIRIS-Rex for spectral imaging - Ralph/New Horizons for spectral imaging FOV: B3: 2.1 - 3.5 µm T R = 40 In Transmission
- 18. Bispectrum Configuration Configuration in redshift space k1 k2 k3 𝛍1 𝛍2 B(k1,k2,k3,𝛍1,𝛍2) We choose this specific configuration because it is easy to include FoG effect and to handle AP projection. We include all possible configuration as each parameter is extractable at specific configuration.
- 19. Full covariance approach F 𝝰𝝱 = 𝝨k 𝝨k1k2k3 (𝞉S/𝞉p 𝝰) C-1 (𝞉S/𝞉p 𝝱) S = P(k,𝛍) ( C-1 = M -MCPBCBB-1 -CBB-1CBB-1M CBB-1+CBB-1CBpMCPBCBB-1 Fisher matrix is given by where the vector field S is given by The full covariance matrix is given by, This full covariance calculation is performed for DESI forecast. B(k1,k2,k3,𝛍1,𝛍2)) ( )
- 20. Cosmological Parameters Constraints Using the power spectrum only and assuming Planck prior (GC)
- 21. Constraints on initial conditions σ(fNL loc) ~ 0.8 (3-D Power-spectrum) σ(fNL loc) ~ 0.2 (3-D Bispectrum)
- 22. Challenges to be faced We have never applied 1.6 micro bump as redshift indicators before. We will need the pathfinder 1. KASI launches the 40cm class space telescope NISS in 2017 2. It provides the full SED covered by the future telescope with lower sensitivity In order to constraints on non-Gaussianity of bispectrum, we need to understand the bispectrum higher order polynomials 1. The squeezed higher order connected terms are known to be non- negligible in power spectrum case 2. The lowest order contributions of the squeezed higher order terms are not next order in bispectrum
- 23. The Simulated Field The FoV of NISS is correspondent to 4 sq. degrees, so we cut the same size of SDSS field.
- 24. Theoretical SED model using SDSS data We use MAGPHYS to fit SED over NISS range of 0.9𝛍m to 3.5𝛍m SDSS SDSS We will have approximately 10,000 galaxies
- 25. Selection of targeted fields We pay attention to GAMA DR2 galaxies with 21 band photometry 1. Using full band GAMA galaxies, we run MAGPHYS and estimate SED 2. We select galaxy samples which have spectroscopy follow up 3. We locate bump peak assuming narrow bandwidth & low magnitude 4. We select a group galaxy having consistent bump peak and true z 5. We vary threshold selection z resolution limit from 10-3 to 10-4
- 26. Simulating NISS data We apply S/N to mock data points on fitted SED using NISS limit
- 27. Simulating NISS data There will be 28 data points on NISS simulated SED 1. Generating simulated data from 0.9𝛍m to 3.5 𝛍m for selected galaxy 2. We apply NISS magnitude limit over 28 bins 3. We run SED code to determine z after fully marginalising others 4. We compare it with true z which is given by GAMA spectroscopy
- 28. Challenges to be faced We have never applied 1.6 micro bump as redshift indicators before. We will need the pathfinder 1. KASI launches the 40cm class space telescope NISS in 2017 2. It provides the full SED covered by the future telescope with lower sensitivity In order to constraints on non-Gaussianity of bispectrum, we need to understand the bispectrum higher order polynomials 1. The squeezed higher order connected terms are known to be non- negligible in power spectrum case 2. The lowest order contributions of the squeezed higher order terms are not next order in bispectrum
- 29. Bispectrum seen at redshift space First order (equivalent to Kaiser term) Second order FoG term 𝝙 = 𝛅+𝝻2ϴ
- 30. Mapping of clustering from real to redshift spaces Ps(k,𝝻) = ∫d3x eikx ⟨𝛅𝛅⟩ Ps(k,μ) = ∫d3x eikx ⟨ejv (𝛅+𝝻2ϴ)(𝛅+𝝻2ϴ)⟩ • Higher order polynomials are generated by density and velocity cross-correlation which generate the infinite tower of correlation pairs. We take the perturbative approach to cut off higher orders. = ∫d3x eikx exp{⟨ejv⟩c} [⟨ejv(𝛅+𝝻2ϴ)(𝛅+𝝻2ϴ)⟩c+⟨ejv(𝛅+𝝻2ϴ)⟩c⟨ejv(𝛅+𝝻2ϴ)⟩c] Ps(k,μ) = [Pgg(k) + 2𝝻2PgΘ(k) + 𝝻4P 𝛉𝛉(k)+ A(k,𝝻) + B(k,𝝻) + T(k,𝝻) + F(k,𝝻)] exp[-(k𝝻σp)2] • The FoG effect consists of the one-point contribution and the correlated velocity pair contribution. The latter is perturbatively expanded as F term, and the former is parameterised using σp.
- 33. Direct measurement of higher order polynomials A(k,𝝻) B(k,𝝻) T(k,𝝻) F(k,𝝻) Yi, YSS 2016
- 34. The residual FoG We subtract out the perturbative higher order polynomials, and the remaining’s can be considered to be FoG effect. If our formulation is correct, those all residuals should be consistent in terms of scale, and fitted to be Gaussian with constant 𝜎p. exp[-(k𝝻σp)2]
- 35. Challenge to the precision cosmology
- 36. Test Methodology Ps(k,μ) = [Pgg(k) + 2𝝻2PgΘ(k) + 𝝻4P 𝛉𝛉(k)+ A(k,𝝻) + B(k,𝝻) + T(k,𝝻) + F(k,𝝻)] exp[-(k𝝻σp)2]
- 37. The effect from the squeezed trispectrum The reconstructed linear spectrum of density and velocity spectra With the squeezed trispectrum Without the squeezed trispectrum
- 38. Bispectrum seen at redshift space First order (equivalent to Kaiser term) Second order FoG term 𝝙 = 𝛅+𝝻2ϴ
- 39. Conclusion • We measure coherent motion of the universe with BOSS catalogue using RSD perturbative theory, which provides us with trustable measurements. • The full perturbative approaches allow us to prove the exotic cosmic acceleration model such as modified gravity of f(R) gravity. • We probe the non-trivial neutrino mass about 0.2eV, and the measured Hubble constant gets to be even smaller about 65. • The future experiment opens new precision cosmology era, and we are ready for the challenge. Our new RSD theoretical model is promising to probe coherent motion in a percentage precision. • The combination of power and bi spectra is essential to probe the coherent motion tightly. We make lots of efforts for it.