The impact of relativistic effects on cosmological parameter estimation

Transcription

1 The impact of relativistic effects on cosmological parameter estimation arxiv: (PRD) with David Alonso and Pedro Ferreira Christiane S. Lorenz University of Oxford Rencontres de Moriond, La Thuile, 22 nd of March 2018

2 Relativistic effects in large scale structure Key quantity is the fluctuation in the number density of galaxies at a particular solid angle and at a particular redshift (Challinor and Lewis, 2011; Bonvin and Durrer, 2011; Di Dio et al., 2016) The terms correspond to N D + RSD + L + GR D: density perturbations RSD: redshift space distortions L: lensing magnification GR: general-relativistic corrections (e.g. the Shapiro time delay or the ISW effect) Christiane S. Lorenz University of Oxford 2 / 23

3 Relativistic effects in large scale structure Alonso et al., 2015 Christiane S. Lorenz University of Oxford 3 / 23

4 How important are the lensing and GR terms? 1. Information Content: How much are constraints on cosmological parameters improved when lensing magnification/gr terms are included? 2. Bias: How much are cosmological parameters biased when lensing magnification/gr terms are neglected? Christiane S. Lorenz University of Oxford 4 / 23

5 Fisher matrix forecasting algorithm The Fisher matrix gives us lower limits for the standard deviations of the parameters for a given experiment. Christiane S. Lorenz University of Oxford 5 / 23

6 Fisher information 1. Data vector is given by perturbations in the number density of galaxies N D + RSD + L + GR 2. Data vector feeds into power spectra C l 3. Fisher matrix F αβ = l max l=2 f sky 2l [ Tr ( α C l )C 1 l 4. Standard deviations of parameters θ are given by σ(θ α ) = (F 1 ) αα ] ( β C l )C 1 l Christiane S. Lorenz University of Oxford 6 / 23

7 Fisher bias Bias on each cosmological parameter θ α is given by where the entries of v are v α = and C l = C obs l l max l=2 C th l. θ α = (F 1 v) α, 2l + 1 [ f sky Tr 2 ( α C l )C 1 l ] C l C 1, l Christiane S. Lorenz University of Oxford 7 / 23

8 Fisher bias Bias on each cosmological parameter θ α is given by where the entries of v are v α = and C l = C obs l l max l=2 C th l. θ α = (F 1 v) α, 2l + 1 [ f sky Tr 2 ( α C l )C 1 l ] C l C 1, Example: Bias from neglecting lensing magnification C obs C th l : l : power spectrum computed accounting for lensing power spectrum computed neglecting lensing l Christiane S. Lorenz University of Oxford 8 / 23

9 Surveys 1. Large Synoptic Survey Telescope (LSST) galaxy clustering, galaxy shear, type Ia supernovae, strong lensing... considered here: galaxy clustering and galaxy shear 2. CMB Stage 4 Followed multi-tracer approach (Seljak, 2008; Alonso, 2015) Two combinations of tracers: galaxy clustering only galaxy clustering, galaxy shear, CMB and CMB lensing Christiane S. Lorenz University of Oxford 9 / 23

10 Dark energy and neutrino masses Why should we look at dark energy and neutrinos? Lensing magnification is relevant for constraining neutrino and dark energy parameters (Duncan et al., 2014 and Cardona et al., 2016) Degeneracies between neutrinos and dark energy (Allison et al., 2015) Model chosen for this analysis: Simple parameterization of the dark energy equation of state parameter (Chevallier and Polarski, 2001) w(a) = w 0 + (1 a)w a Included massive neutrinos in terms of m ν Christiane S. Lorenz University of Oxford 10 / 23

11 Dark energy and neutrino masses wa w Σ m ν (mev) all tracers, w.o. mag. all tracers, w. mag. clustering, w.o. mag. clustering, w. mag. all tracers, bias clustering, bias fiducial value w a CSL, Alonso and Ferreira, 2017 Christiane S. Lorenz University of Oxford 11 / 23

12 Does lensing magnification contain information about deviations from general relativity? Christiane S. Lorenz University of Oxford 12 / 23

13 Horndeski scalar-tensor theories Suggested by Horndeski, 1974 and Deffayet et al., 2009 Parameterization chosen here (Bellini and Sawicki, 2014): α X (z) = c X Ω DE (z) Ω DE (z = 0) α M α K α T α B time variation of Newton s constant form of the scalar kinetic term speed of propagation of tensor modes mixing between the scalar field and the scalar perturbations Here we consider only c M, c B and c T. Christiane S. Lorenz University of Oxford 13 / 23

14 Horndeski scalar-tensor theories ct cb c M all tracers, w.o. mag. all tracers, w. mag. clustering, w.o. mag. clustering, w. mag. all tracers, bias clustering, bias fiducial value c T CL, Alonso and Ferreira, 2017 Christiane S. Lorenz University of Oxford 14 / 23

15 To what extent must the magnification bias be known? Magnification bias depends on the slope of the physical number density of sources, N (η, L > L ), as a function of conformal time η and cumulative luminosity L, as (Hui et al., 2007): s 5 ln N. 2 ln L Blanton et al., 2005 (ApJ) Parameters Max. error on s(z) wcdm mν 9.8% w a 5.6% w 0 4.2% Horndeski c M 22% c B 11% c T 23% CSL, Alonso and Ferreira, 2017 Christiane S. Lorenz University of Oxford 15 / 23

16 What is the impact of general-relativistic corrections? all tracers LSST galaxy clustering Parameters improvement bias from improvement bias from on σ from GR effects on σ from GR effects GR effects GR effects wcdm mν < 1% 3% < 1% 3% w a < 1% < 1% < 1% -2% w 0 < 1% -3% < 1% 6% Horndeski c M < 1% -7% < 1% < 1% c B < 1% 1% < 1% -5% c T < 1% 8% < 1% < 1% CSL, Alonso and Ferreira, 2017 Christiane S. Lorenz University of Oxford 16 / 23

17 Primordial non-gaussianity Non-Gaussian density perturbations are created in many inflation scenarios Local primordial non-gaussianity (Komatsu and Spergel, 2001): Φ(x) = Φ G (x) + f NL (Φ 2 G(x) Φ 2 G ), Constraint from the Planck satellite: f NL = 2.5 ± 5.7 (Planck Coll., 2015) Large Scale Structure (LSS) observations will help to improve current constraints on f NL (Dalal et al., 2008 and Matarrese and Verde, 2008) Christiane S. Lorenz University of Oxford 17 / 23

18 Primordial non-gaussianity all tracers clustering clustering (red) clustering (blue) bias (all tracers) p(fnl) f NL CSL, Alonso and Ferreira, 2017 Bias on f NL from neglecting GR terms: f NL = 0.45σ fnl Christiane S. Lorenz University of Oxford 18 / 23

19 Conclusion Lensing magnification improves parameter constraints marginally, but only in the case when galaxy clustering is the only tracer. Lensing magnification biases significantly parameter constraints (of the order of a few standard deviations). The magnification bias s(z) needs to be known to approximately 5% for constraining the dark energy equation of state and the total neutrino mass, and to approximately 10% for constraining Horndeski parameters. General-relativistic corrections are negligible in most cases. General-relativistic corrections are significant for constraining primordial non-gaussianity, the bias on f NL from neglecting GR terms is of the order of half a standard deviation. Christiane S. Lorenz University of Oxford 19 / 23