Table 2
Evolution of the best-fitting LTB models for varying radial size L in Gpc.
| L | h | Ωm | a 1 | a 2 | a 3 | H LS | log (ℒ) |
|
|
|||||||
| 3 | 0.39 | 1.10 | 0.07 | 0.27 | 0.45 | 56.01 | –320.14 |
| 4.5 | 0.39 | 1.18 | 0.01 | 0.12 | 0.17 | 60.13 | –299.95 |
| 7.5 | 0.39 | 1.37 | 0.01 | 0.12 | 0.44 | 62.52 | –293.26 |
Notes. h and Ωm denote the dimensionless Hubble parameter and the matter density parameter of the background FLRW model, respectively. The matter density profiles were parametrised by cubic spline interpolation schemes with three equidistant nodes at the radial coordinates ri = (i − 1) × L/ 3. The coefficients ai denote the matter densities at these nodes normalised with respect to the background density today, viz. ai = ρ(t0,ri) /ρbg(t0). HLS is the effective Hubble rate measured at the origin. The last column shows the log likelihood values. The LTB models were fitted to observational data of the local Hubble rate, supernovae, and the CMB.
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