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arXiv 0911.0178gr-qc
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具有动力学时间的引力理论

Gravitational Theory with a Dynamical Time

E. I. Guendelman

摘要:

研究了一个包含矢量场$χ^μ$的引力理论,该矢量场的零分量具有动力学时间的性质。作用量相对于$χ^μ$的变化给出了能量动量张量$ T^{μν}_{(χ)}$的协变守恒。在有killing矢量和killing张量的背景下研究该理论,我们发现了场$χ^μ$的适当的移位对称性,这些移位对称性导致守恒律。作为重力$ T^{μν}_{(G)}$的来源的能量动量与$ T^{μν}_{(χ)}$不同但相关,并且$ T^{μν}_{(G)}$的协变守恒一般决定了矢量场$χ^μ$。当选择$ T^{μν}_{(χ)}$与度规成比例时,该理论与双测度理论相一致,该理论之前已经在宇宙学常数问题中进行了研究。当物质模型由点粒子或弦组成时,$ T^{μν}_{(G)}$的形式,$χ^μ$的解决方案被发现。对于弦气体宇宙学的情况下,我们发现米尔恩宇宙可以是一个解决方案,其中弦气体不弯曲时空,因为虽然$ T^{μν}_{(χ)} \neq 0$,$ T^{μν}_{(G)}= 0$,作为早期宇宙的模型,这个解决方案也是免费的视界问题。它也可以应用于量子宇宙学的“时间问题”。

英文摘要:

A gravitational theory involving a vector field $χ^μ$, whose zero component has the properties of a dynamical time, is studied. The variation of the action with respect to $χ^μ$ gives the covariant conservation of an energy momentum tensor $ T^{μν}_{(χ)}$. Studying the theory in a background which has killing vectors and killing tensors we find appropriate shift symmetries of the field $χ^μ$ which lead to conservation laws. The energy momentum that is the source of gravity $ T^{μν}_{(G)}$ is different but related to $ T^{μν}_{(χ)}$ and the covariant conservation of $ T^{μν}_{(G)}$ determines in general the vector field $χ^μ$. When $ T^{μν}_{(χ)}$ is chosen to be proportional to the metric, the theory coincides with the Two Measures Theory, which has been studied before in relation to the Cosmological Constant Problem. When the matter model consists of point particles, or strings, the form of $ T^{μν}_{(G)}$, solutions for $χ^μ$ are found. For the case of a string gas cosmology, we find that the Milne Universe can be a solution, where the gas of strings does not curve the spacetime since although $ T^{μν}_{(χ)} \neq 0$, $ T^{μν}_{(G)}= 0$, as a model for the early universe, this solution is also free of the horizon problem. There may be also an application to the "time problem" of quantum cosmology.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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