宇宙学常数能被一个以上可观测的光滑大尺度不均匀性所模拟吗？
Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?
摘要：
作为暗能量的另一种说法，有人认为我们可能处于爱因斯坦场方程的勒梅特-托尔曼-邦迪（LTB）解所描述的非均匀各向同性宇宙的中心。为了检验这样一个假设，我们计算的低红移膨胀的光度距离$D_L(z)$和红移球壳质量密度$mn(z)$的中心观察者在LTB空间没有宇宙学常数，并显示他们如何不能拟合的观测隐含的$ΛCDM $模型，如果施加的条件，以避免一个弱的中心奇点，即如果物质分布是光滑的。我们的结论是有效的任何值的宇宙学常数，而不仅仅是$Ω_Λ>1/3$所暗示的$q^{app}_0$必须是积极的，在一个光滑的LTB空间的基础上，只考虑光度距离。光滑LTB物质主导模型的观测特征与$ΛCDM $模型的观测特征有着根本的不同，这不仅是因为它不可能再现负的表观中心减速$q^{app}_0$，而且是因为它们的时空几何结构存在更深的差异，这使得当考虑多个观测时不可能出现反演问题，并且出现在任何红移，而不仅仅是$z=0$。
英文摘要：
As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test such an hypothesis we calculate the low redshift expansion of the luminosity distance $D_L(z)$ and the redshift spherical shell mass density $mn(z)$ for a central observer in a LTB space without cosmological constant and show how they cannot fit the observations implied by a $ΛCDM $ model if the conditions to avoid a weak central singularity are imposed, i.e. if the matter distribution is smooth everywhere. Our conclusions are valid for any value of the cosmological constant, not only for $Ω_Λ>1/3$ as implied by previous proofs that $q^{app}_0$ has to be positive in a smooth LTB space, based on considering only the luminosity distance. The observational signatures of smooth LTB matter dominated models are fundamentally different from the ones of $ΛCDM $ models not only because it is not possible to reproduce a negative apparent central deceleration $q^{app}_0$, but because of deeper differences in their space-time geometry which make impossible the inversion problem when more than one observable is considered, and emerge at any redshift, not only for $z=0$.
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