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arXiv · 1911.13199

Homogeneity and the causal boundary

Enrique Gaztanaga
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Abstract

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 fulfil by fixing the cosmological constant $Λ$ (a free parameter for gravity). The resulting Universe is inhomogeneous, with possible variation of cosmological parameters on scales $χ\simeq χ_§$. 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 $ρ_Λ\equiv Λ/8πG + ρ_{vac}$. To reproduce the observed $ρ_Λ \simeq 2 ρ_m$ today with $χ_§\rightarrow \infty$ we then need a universe filled with evolving dark energy (DE) with pressure $p_{DE}> - ρ_{DE}$ and a fine tuned value of $ρ_{DE} \simeq 2 ρ_m$ today. This seems very odd, but there is another solution to this puzzle. We can have a finite value of $χ_§\simeq 3 c/H_0$ 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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Enrique Gaztanaga. 2019-11-26. Homogeneity and the causal boundary. https://arxiv.org/abs/1911.13199

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