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arXiv 0901.1639astro-ph.COgr-qcmath.AP
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在宇宙学标准模型中引入反常加速度的Einstein方程的单参数膨胀波解族

A One Parameter Family of Expanding Wave Solutions of the Einstein Equations That Induces an Anomalous Acceleration Into the Standard Model of Cosmology

Joel Smoller, Blake Temple

摘要:

我们推导出一组新的方程,它描述了爱因斯坦方程的一个连续的单参数膨胀波解族,使得与宇宙学的标准模型的纯辐射相有关的弗里德曼宇宙作为一个单点嵌入到这个族中。所有与这个族相关的时空度规都满足状态方程$p=ρc^2/3$,修正了大爆炸标准模型中暴胀后的纯辐射相。通过将中心的解扩展到哈勃长度的首阶,这个族简化为一个单参数的扩展时空族,它代表了标准模型的微扰。然后,我们推导出一个共同移动的坐标系,在这个坐标系中,扰动的时空可以与标准模型进行比较。在这个坐标系中,我们计算了对哈勃常数的修正,以及对位于扩展FRW时空中心的观测者的红移与光度关系的精确的首阶二次修正。对红移与光度关系的首阶修正需要一个可调的自由参数,它引入了反常加速度。我们的结论是,任何修正后观察到的辐射阶段的大爆炸的红移与光度的关系可以占,在领先的二次阶水平,通过调整这个自由参数。由于确切的非相互作用的膨胀波代表可能的时间渐近波模式的守恒定律,我们建议进一步调查的可能性,这些修正的标准模型可能占异常加速的星系,没有引进的宇宙学常数。

英文摘要:

We derive a new set of equations which describe a continuous one parameter family of expanding wave solutions of the Einstein equations such that the Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology, is embedded as a single point in this family. All of the spacetime metrics associated with this family satisfy the equation of state $p=ρc^2/3$, correct for the pure radiation phase after inflation in the Standard Model of the Big Bang. By expanding solutions about the center to leading order in the Hubble length, the family reduces to a one-parameter family of expanding spacetimes that represent a perturbation of the Standard Model. We then derive a co-moving coordinate system in which the perturbed spacetimes can be compared with the Standard Model. In this coordinate system we calculate the correction to the Hubble constant, as well as the exact leading order quadratic correction to the redshift vs luminosity relation for an observer at the center of the expanding FRW spacetime. The leading order correction to the redshift vs luminosity relation entails an adjustable free parameter that introduces an anomalous acceleration. We conclude that any correction to the redshift vs luminosity relation observed after the radiation phase of the Big Bang can be accounted for, at the leading order quadratic level, by adjustment of this free parameter. Since exact non-interacting expanding waves represent possible time-asymptotic wave patterns for conservation laws, we propose to further investigate the possibility that these corrections to the Standard Model might account for the anomalous acceleration of the galaxies, without the introduction of the cosmological constant.

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