Slides of 5 lectures at XV Brazilian School on Cosmology and ...

Cosmic “rest frame”P<strong>at</strong>ch together CIFs for observers who see an isotropicCMB by taking surfaces <strong>of</strong> uniform volume expansion1〈l r (τ)dl r (τ)〉 = 1 dτ 3 〈θ〉 1 = 1 3 〈θ〉 2 = · · · = ¯H(τ)Average over regions in which (i) sp<strong>at</strong>ial curv<strong>at</strong>ure iszero or neg<strong>at</strong>ive; (ii) space is expanding <strong>at</strong> theboundaries, <strong>at</strong> least marginally.Solves the Sandage–de Vaucouleurs paradox implicitly.Voids appear to expand faster; but canonical r<strong>at</strong>e τ vfaster, locally measured expansion can still be uniform.Global average H av on large scales with respect to anyone set <strong>of</strong> clocks may differ from ¯H15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.50/143