Generally covariant model of a scalar field with high frequency dispersion and the cosmological horizon problem
Generally covariant model of a scalar field with high frequency dispersion and the cosmological horizon problem
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DOI：
10.1103/physrevd.63.041502
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发表时间：
2000-09
影响因子：
5
通讯作者：
T. Jacobson;D. Mattingly
中科院分区：
文献类型：
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作者：
T. Jacobson;D. Mattingly
时空的短程结构可能以高频色散的形式出现。虽然这样的色散不是局部洛伦兹不变的，我们在标量场模型中展示了它如何仍然可以被纳入到一个一般的协变度量引力理论提供的局部首选帧是动态的。我们评估由此产生的能量动量张量，并计算其期望值的量子场在热态。状态方程在高温下与通常的状态方程不同，但不足以影响热大爆炸宇宙学的问题。我们表明，超光速色散关系可以通过超光速平衡来解决视界问题，但是它不能这样做，同时保持在普朗克制度之外，除非色散关系被人为地选择为对波矢有相当陡峭的依赖。
Short distance structure of spacetime may show up in the form of high freqency dispersion. Although such dispersion is not locally Lorentz invariant, we show in a scalar field model how it can nevertheless be incorporated into a generally covariant metric theory of gravity provided the locally preferred frame is dynamical. We evaluate the resulting energy-momentum tensor and compute its expectation value for a quantum field in a thermal state. The equation of state differs at high temperatures from the usual one, but not by enough to impact the problems of a hot big bang cosmology. We show that a superluminal dispersion relation can solve the horizon problem via superluminal equilibration, however it cannot do so while remaining outside the Planck regime unless the dispersion relation is artificially chosen to have a rather steep dependence on wavevector.