Testing the Copernican principle with radio-astronomy observations

Julien Larena

Department of Mathematics and Applied Mathematics University of Cape Town South Africa Outline

The

Test of with radio data

Test of the Copernican Principle with radio data

Conclusion Cosmological Principle

In standard : Geometry = Isotropy around us + Copernican principle

• Foundation of model.

• Precision Cosmo: It needs to be tested as accurately as possible. Cosmological Principle

In standard cosmology: Geometry = Isotropy around us + Copernican principle

• Isotropy:

• Well tested (CMB)

[Saadeh et al. (2016)] Cosmological Principle

In standard cosmology: Geometry = Isotropy around us + Copernican principle

Our Worldline A distant Observer • Copernican Principle: We are a typical observer.

• All other observers see an isotropic ⇒

Homogeneity ⇒ FLRW ??? background. Test of CP with CMB kSZ Looking into our PLC • Extra kSZ: bulk motion wrt CMB.

[Zibin and Moss (2011); Bull et al.

(2012)]

• (Mostly) ruled out From [Clifton et al. (2012)] models for DE. Scatterings give us access to inside • But: CMB rest-frame subtle our PLC. in LTB [Clarkson and Regis (2011)] Test of Isotropy: Dipole in LSS

• wrt CMB rest frame ⇒ Kinetic dipole:

  −3 T˜ ~n˜ = T (~n) (1 + ~v0 · ~n) , v0 ∼ 10

• In Standard Cosmo: LSS rest-frame = CMB rest-frame

• LSS dipole should be aligned with CMB one.

• Observed in:

  N˜ z,˜ ~n˜ = N (z, ~n) (1 + 3~vLSS · ~n) Dipole in LSS

• Strategy: Measure N in opposite patches of the sky. • Integrate : 2D angular correlations. • ⇒ Radio-continuum. • Forecast on LSS dipole direction: 5o for SKA 1; 1o for SKA 2.

[Schwarz et al. (2015)] Testing the Copernican Principle

Suppose isotropy around us: ΛLTB. Metric:

ds2 = −A(w, v)dw2 + 2dwdv + D2(w, v)dΩ2

• Dust: ρ(w, v), uµ(w, v) + Λ.

• Observational Cosmology

program [Ellis et al. (1985)]

• Can we get A(w, v) and D(w, v)? Copernicus

With L. Bester and N. Bishop: [Bester et al. (2014), Bester et al. (2015); Bester et al. (2017): arxiv:170500994]

• Code available at https://github.com/landmanbester/Copernicus. • Smoothes data on current PLC using Gaussian Processes. • Integrates to reconstruct geometry inside our PLC. Copernicus

Initial data:

• Distances D(z) • GR Eqs act as constraints on PLC: • Expansion Hk(z): 2D00(v) Z z dz∗ ρ (w , v) = − v(z) = 0 2 ∗ 2 ∗ κ(1 + z(v)) D(v) 0 (1 + z ) Hk (z ) • Propagate to next PLC using:

a ∇aT b = 0

• Iterate Current (Optical) data

• D(z): Union 2.1

[Suzuki et al. (2012)]

• Hk(z): Cosmic chronometers

[Moresco (2015)] Future radio data

0.8 σA /A σfσ /fσ8 8 0.04 0.6

0.4 0.02 • D(z) H (z) 0.2 and k from IM.

0.0 0.00 σ /D σ /H 0.06 DA A H DETF IV 0.06 Facility • Larger redshift, better error Stage II 0.04 Stage I 0.04

0.02 0.02 bars.

0.00 0.00 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 z • Very optimistic: Facility.

From [Bull et al. (2015)] Future radio data

5 5 x10 x10 2 8 ec t n u co ce r u o S Absorber count 1.5 6 Source count 1 4

0.5 2 Absorber count 0.5 1 1.5 2 2.5 ΛCDM 0.5 Matter only, Ω M = 0.27

0.4 Matter only, Ω M = 1.0 ) 1 − 0.3 Fore c ast yr 1

− 0.2

0.1 ( cm s v 0

-0.1 -0.2 • ∆z Acceleration-0.3 ˙ Redshift drift: ∆w -0.4 -0.5 • Helps to constrain Λ. 0 0.5 1 1.5 2 2.5 3 R ed s h i f t z • Can be done with SKA: From [Yu et al. (2014)] [Klöckner et al. (2015)] Smoothing the data

• Full posterior distributions in function space. • Can draw IC.

2.0 250 ] 1

1.5 − c

p 200 ] c M p 1 − G 1.0 [ s / ΛCDM Simulated 150 m D k LTB1 0 [ 0.5 D / LTB2 2 D H 100 Real 0.0

0.3 12 0.2 10 0.1 ]

8 1 0.0 − r y c

ρ 6 0.1 ρ G [

/ 0.2 z w δ

4 δ 0.3 2 0.4

0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 z z A measure of deviation from CP

• σ2(w, v): Shear of matter flow. σ2(w, v) = 0 in FLRW. Measuring Λ

1.4

1.2 On central worldline:

1.0 Λ Ω = 0 0.8 Λ0 2 Λ 3H (w , 0)

Ω 0 0.6 8πGρ (w0, 0) Ωm0 = 2 0.4 3H (w0, 0) Flat

0.2 D0 D1 D2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Ωm0 • Independent of geometry.

• Accurate at ∼ 20% Conclusion

• Testing the Cosmological Principle is important.

• But very hard, even with optimistic ideas on future data.

• A way to mesure Λ without assuming FLRW.

• Other methods? THANK YOU.