From “Do recent accurate measurements of H0 really rule out void models as alternatives to dark energy?” --Antonio Enea Romano --10, May, 2011

### What is done before

Void Model

ΛCDM Model

Pro: Explain most of data with two variables, simple

Con: Origin of cosmological constant remains unknown

- Pro: No new physics introduced
- Con: Too many possibilities, violate Copernican principle

Expressed by LTB metric, which is a generalization of FRW metric to inhomogeneous universe.

M in FRW is the same as mass, so for simplicity and compatibility we should set it proportional to r3, to wit ρ0 is constant (FLRW gauge)

Variable Transformation to FRW-like form

E acts like the spatial curvature

Change to conformal timeη=∫dt/a(t,r)+tb(r) , the integration constant tb is called bang function

From now on we set tb=0

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