Homogeneity and the causal boundary
  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/8\pi G $ to cancel the contribution of a constant
vacuum energy $\rho_{vac}$ to the measured $\rho_\Lambda \equiv \Lambda/8\pi G
+ \rho_{vac}$. 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.
