On relativistic effects and large scale cosmology In collaboration with Enea Di Dio (INAF, Trieste) Matteo Viel (SISSA, Trieste) Carlo Baccigalupi (SISSA, Trieste) Ruth Durrer (Université de Genève) Eleonora Villa (SISSA, Trieste) Francesca Lepori Cosmology at large and small scales Universitá di Cagliari (7 marzo 2017)
Introduction 1 Analysis of CMB anisotropies started the era of PRECISION COSMOLOGY Credit: ESA and the Planck Collaboration. ◮ CMB offers a 2D map of the universe − → LSS will provide 3D map of the distribution of galaxies: potentially richer information Francesca Lepori | @Casteddu
Power spectrum in Fourier space 2 NOT DIRECTLY OBSERVABLE Credit: A. Challinor, A. Lewis (2011) → Assume a cosmology to convert observed redshift and angles into length scales. → Theoretical predictions are gauge-dependent. Francesca Lepori | @Casteddu
Observable in Galaxy Surveys 3 Which coordinates do we observe? ◮ Redshift z ◮ Direction of incoming photons n = ( θ, φ ) d Ω Credit: M. Blanton and the Sloan dz Digital Sky Survey. Francesca Lepori | @Casteddu
Galaxy Number Count 4 ∆ obs ( n , z ) = N ( n , z ) − ¯ N ( z ) ¯ N ( z ) ◮ Relate the observable to the local density of galaxies ¯ ρ ( z ) · ¯ N ( n , z ) = ρ ( n , z ) · V ( n , z ) , N ( z ) = ¯ V ( z ) ρ ( z ) ≈ ¯ ¯ ρ (¯ z ) + ∂ z ¯ ρ · δz ◮ In the linear regime 1 + z δz ( n , z ) + δV ( n , z ) 3 ∆ obs ( n , z ) = δ g − ¯ V C. Bonvin, R. Durrer - What galaxy surveys really measure (2011) A. Challinor, A. Lewis - Linear power spectrum of observed source number counts (2011) Francesca Lepori | @Casteddu
Physical interpretation of δz 5 The distance we measure between us and the bin depends on the motion of the galaxies inside the bin d Ω d Ω dz dz − → If in a redshift bin the galaxies are moving towards us with the same velocities, it will appear closer Francesca Lepori | @Casteddu
Physical interpretation of δV 6 The direction of the incoming light is perturbed by the presence of intervening matter: fluctuation in the observed solid angle δθ d Ω d Ω dz dz Francesca Lepori | @Casteddu
Relation with velocity and metric perturbation 7 1 ∆ obs ( n , z ) = ∆ g + H ( z ) ∂ r ( V · n ) Standard terms � r ( z ) r ( z ) − r s ( m ∗ , z ) +(5 − 2) 2 r ( z ) r ∆ Ω (Φ + Ψ) dr 0 Magnification bias! � � H 2 + 2 − 5 s ( m ∗ , z ) H ′ + 5 s ( m ∗ , z ) + ( V · n ) − 3 H V r H � r ( z ) +(5 s − 2)Φ + (1 + 5 s )Ψ + 1 H Φ ′ + 2 − 5 s dr (Φ + Ψ)+ r ( z ) 0 � r ( z ) � �� � H ′ H 2 + 2 − 5 s dr (Φ ′ + Ψ ′ ) + r ( z ) H + 5 s Ψ + 0 � 2 � ∼ H H Hierarchy − → ∼ ∆ g k ∆ g ∼ D k Francesca Lepori | @Casteddu
Do we care about relativistic effects? 8 1. Neglecting relativistic corrections correction may bias the analysis Credit: Cardona et al. (2016) Francesca Lepori | @Casteddu
A model independent method for the Alcock Paczyński test In collaboration with Enea Di Dio, Matteo Viel, Carlo Baccigalupi, Ruth Durrer Based on arxiv:1606.03114 - Published in JCAP
Introduction - The Alcock Paczyński test 9 Purely geometric test of cosmic expansion C. Alcock, B. Paczyński - An evolution free test for non-zero cosmological constant (1979) z mean L θ = (1+ z ) D A ( z ) θ OBS ∆ z = L H ( z ) ∆ z The BAO feature in the galaxy correlation function can provide the scale L ! Francesca Lepori | @Casteddu
Baryon Acoustic Oscillations 10 In the early universe baryons are coupled to photons: single photon-baryon fluid GRAVITY PHOTON PRESSURE Credit: Wayne Hu. Credit: Wayne Hu. Sound waves which propagates until recombination imprint a feature in the correlation function at the sound horizon: ≈ 150 Mpc Francesca Lepori | @Casteddu
BAO feature in the correlation function 11 Evolution of an overdense region at a single point: dark matter , baryons, photons. ◮ The coupled fluid of photons and baryons move away from the dark matter at the centre (top panels) ◮ After recombination, photons continue propagating, baryons stay were they are (middle panels) ◮ Baryons fall into the gravitational potential generated by Dark Matter and viceversa. They share the same distribution (bottom panels) D., Eisenstein, H. Seo, M. White - On the Robustness of the Acoustic Scale in the Low-Redshift Clustering of Matter (2007) Francesca Lepori | @Casteddu
Current and future BAO measurements 12 Sound horizon at the drag epoch is measured by Planck at the 0 . 3 % level − → Use BAO scale as a standard ruler to test distance-redshift relation and map the expansion history BAOs are one of the main target of future generation of galaxy surveys BOSS DESI & Euclid Next generation of surveys ◮ Euclid Spacecraft, launch planned for 2020 Current measurements ◮ DESI (Dark Energy Spectroscopic ◮ From BOSS (the Baryon Instrument), starting in 2018 Oscillation Spectroscopic Survey) 0 . 1% precision 1% precision Francesca Lepori | @Casteddu
Overview & Notation 13 OVERVIEW 1. Test a model independent method for the AP test (Montanari and Durrer, 2012) 2. Systematic effects due to lensing and galaxy bias 3. Window function shift 4. Statistical uncertainties (shot-noise and cosmic variance) NOTATION ∆ obs ( n , z ) = ∆ g + ∆ RSD + ∆ κ + ✟✟ ❍❍ ∆ rel , ◮ Redshift space distortion � � H ′ 1 H 2 + 2 ∆ RSD ( n , z ) = H ( z ) ∂ r ( V · n ) + ( V · n ) − 3 H V r H ◮ Lensing Convergence � r ( z ) r ( z ) − r ∆ κ = (5 [ s ( m ∗ , z ) − 2) 2 r ( z ) r ∆ Ω (Φ + Ψ) dr 0 =0 Francesca Lepori | @Casteddu
Methodology 14 1. Compute the angular power spectrum ◮ Run class gal for our fiducial cosmology (Planck + external data) E. Di Dio, F. Montanari, J. Lesgourgues, R. Durrer (2013) 2. Compute the correlation function in both radial and transverse direction from the redshift dependent angular power spectra 3. Use a phenomenological model for the correlation function N ξ ( x ) = A · e − ( x − x FIT ) 2 / 2 σ 2 + � K n · x n , n =0 4. Estimate the peak position ∆ z F IT and θ FIT 5. Compare F AP = ∆ z FIT /θ FIT to its expected value F AP = (1 + z ) H ( z ) D A ( z ) Francesca Lepori | @Casteddu
Results: RSD & Lensing 15 z = 0 . 7 Transverse Radial r [ Mpc/h ] r [ Mpc/h ] 70 80 90 100 110 120 130 70 80 90 100 110 120 130 0 . 008 DENSITY CLASSgal DENSITY CLASSgal 0 . 007 DENSITY + RSD FIT DENSITY + RSD FIT 0 . 002 DENSITY + RSD + LENS FIT - GAUSSIAN DENSITY + RSD + LENS FIT - GAUSSIAN 0 . 006 0 . 000 0 . 005 ξ (∆ z ) ξ ( θ ) 0 . 004 − 0 . 002 0 . 003 0 . 002 − 0 . 004 0 . 001 − 0 . 006 0 . 000 2 . 5 3 . 0 3 . 5 4 . 0 0 . 035 0 . 040 0 . 045 0 . 050 0 . 055 0 . 060 0 . 065 θ [ deg ] ∆ z Francesca Lepori | @Casteddu
RSD & Lensing 16 z = 1 Transverse Radial r [ Mpc/h ] r [ Mpc/h ] 70 80 90 100 110 120 130 70 80 90 100 110 120 130 DENSITY CLASSgal DENSITY CLASSgal 0 . 006 DENSITY + RSD FIT DENSITY + RSD FIT 0 . 002 DENSITY + RSD + LENS FIT - GAUSSIAN DENSITY + RSD + LENS FIT - GAUSSIAN 0 . 005 0 . 004 0 . 000 ξ (∆ z ) ξ ( θ ) 0 . 003 − 0 . 002 0 . 002 0 . 001 − 0 . 004 0 . 000 − 0 . 006 1 . 8 2 . 0 2 . 2 2 . 4 2 . 6 2 . 8 3 . 0 3 . 2 0 . 045 0 . 050 0 . 055 0 . 060 0 . 065 0 . 070 0 . 075 0 . 080 θ [ deg ] ∆ z Francesca Lepori | @Casteddu
RSD & Lensing 17 z = 1 . 5 Transverse Radial r [ Mpc/h ] r [ Mpc/h ] 70 80 90 100 110 120 130 70 80 90 100 110 120 130 0 . 002 DENSITY CLASSgal DENSITY CLASSgal 0 . 004 DENSITY + RSD FIT DENSITY + RSD FIT 0 . 001 DENSITY + RSD + LENS FIT - GAUSSIAN DENSITY + RSD + LENS FIT - GAUSSIAN 0 . 003 0 . 000 ξ (∆ z ) − 0 . 001 ξ ( θ ) 0 . 002 − 0 . 002 0 . 001 − 0 . 003 0 . 000 − 0 . 004 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 2 . 4 0 . 06 0 . 07 0 . 08 0 . 09 0 . 10 θ [ deg ] ∆ z Francesca Lepori | @Casteddu
RSD & Lensing 18 z = 2 . 0 Transverse Radial r [ Mpc/h ] r [ Mpc/h ] 70 80 90 100 110 120 130 70 80 90 100 110 120 130 DENSITY CLASSgal DENSITY CLASSgal 0 . 0035 0 . 001 DENSITY + RSD FIT DENSITY + RSD FIT DENSITY + RSD + LENS FIT - GAUSSIAN DENSITY + RSD + LENS FIT - GAUSSIAN 0 . 0030 0 . 0025 0 . 000 0 . 0020 ξ (∆ z ) ξ ( θ ) 0 . 0015 − 0 . 001 0 . 0010 − 0 . 002 0 . 0005 0 . 0000 − 0 . 003 − 0 . 0005 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 0 . 07 0 . 08 0 . 09 0 . 10 0 . 11 0 . 12 0 . 13 θ [ deg ] ∆ z ONLY DENSITY: shift in the estimated peak position ≈ 0 . 5% in both directions plus LENSING: change in the amplitude of radial correlations, but the peak positions is not affected in both directions Francesca Lepori | @Casteddu
Consistency Test 19 0.03 DENSITY DENSITY + RSD DENSITY + RSD + LENSING 0.02 When ONLY DENSITY: F AP ( z ) /F ( z ) − 1 0.01 ∼ 1% offset between the expected and 0.00 computed value of F AP 0.01 LENSING does not affect the AP test 0.02 0.5 1.0 1.5 2.0 z mean The shaded region shows the errors computed from the resolution in ∆ z and θ Francesca Lepori | @Casteddu
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