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"The Hubble Constant"

Neal Jackson

	Abstract
1	Introduction
	1.1	A brief history
	1.2	A little cosmology
2	One-Step Distance Methods
	2.1	Megamaser cosmology
	2.2	Gravitational lenses
	2.3	The Sunyaev–Zel’dovich effect
	2.4	Gamma-ray propagation
3	Local Distance Ladder
	3.1	Preliminary remarks
	3.2	Basic principle
	3.3	Problems and comments
4	The CMB and Cosmological Estimates of the Distance Scale
	4.1	The physics of the anisotropy spectrum and its implications
	4.2	Degeneracies and implications for H₀
5	Conclusion
	Acknowledgements
	References
	Footnotes
	Updates
	Figures
	Tables

As discussed extensively in [113 *, 117 ], this is not a global degeneracy, but arises because the lensed images tell you about the mass distribution in the annulus centred on the galaxy and with inner and outer radii defined by the inner and outer images. Kochanek [113 ] derives detailed expressions for the time delay in terms of the central underlying and controlling parameter, the surface density in this annulus [76 *].