Homogeneity and the causal boundary

TL;DR

This paper proposes a new causal boundary condition in cosmology that links the finite causal scale to the cosmological constant, leading to inhomogeneous universes and offering explanations for dark energy and CMB anomalies.

Contribution

It introduces a causal boundary condition that constrains the cosmological constant and explains inhomogeneity and observed cosmic anomalies without requiring dark energy.

Findings

A finite causal scale can explain the observed dark energy density.

The model accounts for the CMB anomalies with a finite causal boundary.

The cosmological constant is constrained by the causal boundary condition.

Abstract

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.