Homogeneity and the causal boundary

Enrique Gaztañaga

A Universe with finite age also has a finite causal scale χ_§ , so the metric can not be homogeneous for χ>χ_§ , as it is usually assumed. To account for this, we propose a new causal boundary condition, that can be fulfill by fixing the cosmological constant Λ (a free parameter for gravity). The resulting Universe is inhomogeneous, with possible variation of cosmological parameters on scales χ≃χ_§ . The size of χ_§ depends on the details of inflation, but regardless of its size, the boundary condition forces Λ/8πG to cancel the contribution of a constant vacuum energy ρ vac to the measured ρ_Λ ≡ Λ/8πG + ρ_vac. To reproduce the observed ρ_Λ ≃2ρ_m today we then need a Universe with χ_§ → ∞ filled with evolving dark energy (DE) with preassure p_DE > −ρ_DE and a fine tuned value of ρ_DE≃2ρ_m today. This seems very odd, but there is another solution to this puzzle. We can have a finite value of χ_§≃3c/H₀ without need of DE. This scale corresponds to half the sky at z∼1 and 60deg at z∼1000, which is consistent with the anomalous lack of correlations observed above 60 deg in the CMB.

Proceedings of the Polish Astronomical Society, vol. 10, 293-302 (2020)

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