Homogeneity and the causal boundary


الملخص بالإنكليزية

A Universe with finite age also has a finite causal scale $chi_S$, so the metric can not be homogeneous for $chi>chi_S$, as it is usually assumed. To account for this, we propose a new causal boundary condition, that can be fulfil by fixing the cosmological constant $Lambda$ (a free parameter for gravity). The resulting Universe is inhomogeneous, with possible variation of cosmological parameters on scales $chi simeq chi_S$. The size of $chi_S$ depends on the details of inflation, but regardless of its size, the boundary condition forces $Lambda/8pi G $ to cancel the contribution of a constant vacuum energy $rho_{vac}$ to the measured $rho_Lambda equiv Lambda/8pi G + rho_{vac}$. To reproduce the observed $rho_{Lambda} simeq 2 rho_m$ today with $chi_S rightarrow infty$ we then need a universe filled with evolving dark energy (DE) with pressure $p_{DE}> - rho_{DE}$ and a fine tuned value of $rho_{DE} simeq 2 rho_m$ today. This seems very odd, but there is another solution to this puzzle. We can have a finite value of $chi_S simeq 3 c/H_0$ without the need of DE. This scale corresponds to half the sky at $z sim 1$ and 60deg at $z sim 1000$, which is consistent with the anomalous lack of correlations observed in the CMB.

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