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arXiv 0710.0022gr-qcastro-phhep-phphysics.space-ph
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修正引力的某些长程模型的天文学约束

Astronomical constraints on some long-range models of modified gravity

Lorenzo Iorio

备注：
Latex, 13 pages, no figures, 1 table. Other references added. Minor stylistic changes. To appear in AHEP (Advances in High Energy Physics). Typo corrected in eq. 6: thanks to G.E. Melki
发表信息：
Adv.High Energy Phys.2009:90731,2009
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摘要：

在本文中，我们使用了对太阳系内行星近日点通常的牛顿-爱因斯坦长期岁差的修正，俄罗斯天文学家E. V. Pitjeva通过将近一个世纪的数据与EPM 2004星历拟合，为了约束最近提出的一些修正引力的长程模型，以解决暗能量和暗物质问题。这里研究的模型是四维的，除了一些曲率不变量的逆幂和对数，和Dvali，Gabadadze和Porrati（DGP）的多维braneworld模型。在计算出这些模型的牛顿势修正引起的长期近日点进动的解析表达式后，我们将它们与对不同行星对的近日点速率的估计修正进行了比较，而不是像文献中那样，一次对每个行星分别使用一个近日点。因此，即使将Pitjeva估计的行星轨道参数的误差按10倍重新缩放，也排除了基于曲率不变量的模型。DGP模型的情况就不那么整齐了。只有广义相对论的透镜-瑟林效应，不包括在内，因为其他外来的模型考虑在这里，由Pitjeva在动力学模型中使用的估计过程中，通过这样的测试。通过使用其他天文学家团队独立估计的近日点岁差校正来重复当前的分析是很重要的，但是，目前还没有这样的速率。

英文摘要：

In this paper we use the corrections to the usual Newton-Einstein secular precessions of the perihelia of the inner planets of the Solar System, phenomenologically estimated as solve-for parameters by the Russian astronomer E.V. Pitjeva by fitting almost one century of data with the EPM2004 ephemerides, in order to constrain some long-range models of modified gravity recently put forth to address the dark energy and dark matter problems. The models examined here are the four-dimensional ones obtained with the addition of inverse powers and logarithm of some curvature invariants, and the multidimensional braneworld model by Dvali, Gabadadze and Porrati (DGP). After working out the analytical expressions of the secular perihelion precessions induced by the corrections to the Newtonian potential of such models, we compare them to the estimated corrections to the rates of perihelia by taking their ratio for different pairs of planets instead of using one perihelion at a time for each planet separately, as done so far in literature. As a result, the curvature invariants-based models are ruled out, even by re-scaling by a factor 10 the errors in the planetary orbital parameters estimated by Pitjeva. Less neat is the situation for the DGP model. Only the general relativistic Lense-Thirring effect, not included, as the other exotic models considered here, by Pitjeva in the dynamical force models used in the estimation process, passes such a test. It would be important to repeat the present analysis by using corrections to the precessions of perihelia independently estimated by other teams of astronomers as well, but, at present, such rates are not yet available.

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