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SKA tests of the Copernican Principle
Bruce Bassett
SAAO and UCT
Clarkson, BB, Hui-Ching Lu, Phys.Rev.Lett., 2008
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Important Breakthrough
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114 citations
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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
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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.
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What do we know?
• The CMB and galaxy distribution are highly isotropic
Bright NVSS radio sources (1.4GHz) distributed on the sky
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so …
Either the cosmos is FLRW
or We live near the centre of a spherically symmetric universe…
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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)
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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…
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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…)
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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.
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Curvature parameter
• Usual to quantify curvature via
Radius of curvature (scale factor)
20
2Ha
kk
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The FLRW luminosity distance
• This is valid for all curvatures since
sinh(ix) = i sin(x)
kNow, Find
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It took 80 years to rearrange this to give….
Where D = dL/(1+z)
• There is our test of the Copernican Principle!
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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
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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…
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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
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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)
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The importance of curvature - II
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