用高精度原子钟进行宇宙重力测量
Cosmological Gravimetry Using High-Precision Atomic Clocks
摘要：
本文提出并证实了宇宙引力势可以用高精度原子钟测量的假设。的考虑是使用准经典描述的引力转移，在于非度量引力理论的框架。假设宇宙学势是由宇宙的所有物质（包括暗物质和暗能量）形成的，并且在行星尺度上是空间均匀的。很明显，宇宙学势$Φ_\text{CP}$比地球引力势$φ_\text{E}$（地球表面的$|φ_\text{E}/c^2|\sim 10^{-9}$）大几个数量级。在我们的方法中，相同的原子钟的滴答率在两个不同的引力势点，即在不同的高度进行比较。在这种情况下，关于$Φ_\text{CP}$的信息包含在宇宙学校正$α\neq 0$中，在测量点处的频率$Δω/ω$（以原子钟计）的相对变化和重力势差$Δφ$之间的关系$Δω/ω=(1+α)Δφ/c^2$中。我们估计了宇宙学修正的下限$α>10^{-6}$。它表明，使用现代原子钟的光学范围内，它是可能的，以测量值的$α$在地球上的实验，如果$|α|>10^{-5}$。在实验证实的情况下，所获得的结果将为宇宙的研究和各种宇宙学模型的测试开辟新的独特机会。这些结果也将提高相对论大地测量、精密重力测量、全球导航系统和全球原子钟网络的测量精度。
英文摘要：
In this paper, a hypothesis that the cosmological gravitational potential can be measured with the use of high-precision atomic clocks is proposed and substantiated. The consideration is made with the use of a quasi-classical description of the gravitational shift that lies in the frame of nonmetric theories of gravity. It is assumed that the cosmological potential is formed by all matter of the Universe (including dark matter and dark energy) and that it is spatially uniform on planet scales. It is obvious that the cosmological potential, $Φ_\text{CP}$, is several orders of magnitude greater than Earth's gravitational potential $φ_\text{E}$ (where $|φ_\text{E}/c^2|\sim 10^{-9}$ on Earth's surface). In our method, the tick rates of identical atomic clocks are compared at two points with different gravitational potentials, i.e. at different heights. In this case, the information on $Φ_\text{CP}$ is contained in the cosmological correction $α\neq 0$ in the relationship $Δω/ω=(1+α)Δφ/c^2$ between the relative change of the frequencies $Δω/ω$ (in atomic clocks) and the difference of the gravitational potential $Δφ$ at the measurement points. We have estimated the low limit of cosmological correction, $α>10^{-6}$. It is shown that using a modern atomic clock of the optical range it is possible to measure the value of $α$ in earth-based experiments if $|α|>10^{-5}$. The obtained results, in the case of their experimental confirmation, will open up new unique opportunities for the study of the Universe and the testing of various cosmological models. These results will also increase the measurement accuracy in relativistic geodesy, chronometric gravimetry, global navigation systems, and global networks of atomic clocks.
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