SKA tests of the Copernican Principle

Bruce Bassett

SAAO and UCT

Clarkson, BB, Hui-Ching Lu, Phys.Rev.Lett., 2008

Important Breakthrough

114 citations

Tempting to not talk to other people…

• Scientists vs Engineers

• Theorists vs observers/experimentalists

• Classical vs quantum

• Analytical vs numerical

• Bayesians vs frequentists

• Radio vs optical

The Copernican Principle

“We don’t live in a special space/time in the cosmos”

• This could either mean the universe is the same everywhere (standard FLRW cosmology) or…

• Everywhere is different so none is special

Proving or disproving this is perhaps the most important task left in cosmology and the one that will have the biggest social impact.

What do we know?

• The CMB and galaxy distribution are highly isotropic

Bright NVSS radio sources (1.4GHz) distributed on the sky

so …

Either the cosmos is FLRW

or We live near the centre of a spherically symmetric universe…

Why Bother?

• The standard accelerating cosmos with dark energy has two fundamental problems:

1. We need to invoke energy with repulsive new properties to drive the acceleration

2. We need to live at a special time (which therefore violates the Copernican Principle in time)

No dark energy?

• Instead, if you are willing to live near the centre of the cosmos you don’t need any dark energy to explain the dimming of the SNIa! (Mustapha, BB, Hellaby, Ellis, 1998)

• It is currently a matter of taste as to which you prefer…

• But it should be an issue of science…

Why haven’t we proven the CP yet?

If we do not assume FLRW, the Einstein equations are nonlinear coupled PDEs with free functions of space

• Makes analysis difficult and • Hard to draw interesting conclusions due to the extra

freedom (infinite number of model parameters)

Until last year there was no generic test of the CP (now we have three…)

Curvature to the Rescue• FLRW models can have 3 possible curvatures: Closed (positive) k = +1 Flat k = 0 Hyperbolic (open) k = -1

• In the flat case, light travels on straight lines; otherwise the null geodesics are curved.

Curvature parameter

• Usual to quantify curvature via

Radius of curvature (scale factor)

20

2Ha

kk

The FLRW luminosity distance

• This is valid for all curvatures since

sinh(ix) = i sin(x)

kNow, Find

It took 80 years to rearrange this to give….

Where D = dL/(1+z)

• There is our test of the Copernican Principle!

The basic strategy: measure the RHS at

different redshifts and look for inconsistencies

The Curvature TODAY(a constant)

In general, the RHS is a function of z. Only in FLRWdoes it conspire to be a constant, independent of redshift

Not so easy…

• We need H(z), dA(z) or dL (z) and the derivative of the distance wrt redshift.

• All measured at the same redshift in at least two different bins…

• Current constraints are very weak…

SKA and friends…

• SKA BAO – 109 galaxy redshifts at z < 1 will give ~ 1% accuracy on H(z) and dA(z) in several redshift bins (see Renee’s talk)

COSMOS

SKA lensing – high resolution images would provide excellent distances (<1%) through cross-correlation tomography

LSST/JDEM will get ~1%

measurements of dL(z) in many bins at z < 1 from SNIa

The importance of curvature - I

• General tests of the Copernican Principle can now be done by testing a simple FLRW curvature consistency relation

• It does not assume General Relativity, so is valid even if GR is incorrect

• We have also developed another test of the CP using the Alcock-Paczynski test and BAO (but it is more esoteric)

The importance of curvature - II

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