We study cosmographic expansions of the luminosity distance for a variety of Lemaître–Tolman–Bondi (LTB) models which we specify inspired by local large-scale structures of the Universe. We consider cosmographic expansions valid for general spacetimes and compare to the Friedmann–Lemaître–Robertson–Walker (FLRW) limit of the expansions as well as to its naive isotropic extrapolation to an inhomogeneous Universe. The FLRW expansions are often poor near the observer but become better at higher redshifts, where the light rays have reached the FLRW background. In line with this we find that the effective Hubble, deceleration and jerk parameters of the general cosmographic expansion are often very different from the global ΛCDM values, with deviations up to several orders of magnitude. By comparing with the naive isotropic extrapolation of the FLRW expansion, we assess that these large deviations are mainly due to gradients of the shear. Very close to the observer, the general cosmographic expansion is always best and becomes more precise when more expansion terms are included. However, we find that the convergence radius of the general cosmographic expansion is small for all studied models and observers and the general cosmographic expansion becomes poor for most of the studied observers already before a single LTB structure has been traversed. The small radius of convergence of the general cosmographic expansion has also been indicated by earlier work and may need careful attention before we can safely apply the general cosmographic expansion to real data.

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关于 Lemaître-Tolman-Bondi 模型中宇宙学膨胀的收敛


我们研究了各种 Lemaître-Tolman-Bondi （LTB） 模型的光度距离的宇宙学扩展，我们指定这些模型的灵感来自宇宙的局部大尺度结构。我们认为宇宙学膨胀对一般时空有效，并与膨胀的弗里德曼-勒梅特-罗伯逊-沃克 （FLRW） 极限以及它对非均匀宇宙的朴素各向同性外推进行比较。FLRW 膨胀在观察者附近通常很差，但在光线到达 FLRW 背景的较高红移时会变得更好。与此一致，我们发现一般宇宙学膨胀的有效哈勃、减速和加加速度参数通常与全局 ΛCDM 值有很大不同，偏差高达几个数量级。通过与 FLRW 膨胀的朴素各向同性外推进行比较，我们评估这些大的偏差主要是由于剪切的梯度。非常接近观察者，一般的宇宙膨胀总是最好的，当包含更多的膨胀项时，它会变得更加精确。然而，我们发现，对于所有研究的模型和观测者来说，一般宇宙学膨胀的收敛半径都很小，并且对于大多数研究的观测者来说，在穿越单个 LTB 结构之前，一般宇宙学膨胀就已经变得很差。早期的工作也指出了一般宇宙学膨胀的小收敛半径，在我们安全地将一般宇宙学膨胀应用于真实数据之前，可能需要仔细注意。