德拜熵引力修正的Friedmann方程
Modified Friedmann Equations From Debye Entropic Gravity
摘要：
最近，Verlinde提出了一个关于引力起源的新观点，他声称引力定律不再是基本的，而是作为熵力自然出现的。在Verlinde推导中，全息屏上的能量均分定律起着至关重要的作用。然而，能量均分定律在很低的温度下失效。因此，在全息屏温度很低的情况下，熵力的形式应加以修正。在考虑德拜熵引力的情况下，遵循Verlinde的策略，导出了修正的牛顿引力定律和相应的Friedmann方程，它们在所有温度范围内都是有效的。在强引力场的极限，即与德拜温度相比的高温，$T\gg T_D$，人们恢复了标准牛顿定律和弗里德曼方程。我们还将我们的研究推广到熵修正面积定律，并导出了适用于所有温度范围的动力学宇宙学方程。对所得结果的一些局限性也进行了研究。
英文摘要：
A remarkable new idea on the origin of gravity was recently proposed by Verlinde who claimed that the laws of gravitation are no longer fundamental, but rather emerge naturally as an entropic force. In Verlinde derivation, the equipartition law of energy on the holographic screen plays a crucial role. However, the equipartition law of energy fails at the very low temperature. Therefore, the formalism of the entropic force should be modified while the temperature of the holographic screen is very low. Considering the Debye entropic gravity and following the strategy of Verlinde, we derive the modified Newton's law of gravitation and the corresponding Friedmann equations which are valid in all range of temperature. In the limit of strong gravitational field, i.e. high temperature compared to Debye temperature, $T\gg T_D$, one recovers the standard Newton's law and Friedmann equations. We also generalize our study to the entropy corrected area law and derive the dynamical cosmological equations for all range of temperature. Some limits of the obtained results are also studied.
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