We use two models in order to deal with a rotating universe. The first one is a thin rotating spherical shell. When we introduce in this shell an Hydrogen atom we found that the gravitomagnetic field of this universe can split the energy levels of the atom in a way analogous to the Zeeman effect.
The second model is the Gödel universe. There we use the solution of the Dirac equation on an arbitrary spacetime to find the shifts on energy levels of Hydrogen atoms caused by the rotation of the universe.
In both cases the interaction energy is very small, so we have to study the effect of cosmic rotation on Hydrogen atoms in a rotating expanding universe.
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Cortés-Huerto, R., Tejeiro, J. (2007). Effect of the Rotation of the Universe on the Energy Levels of Hydrogen Atoms. In: Aschenbach, B., Burwitz, V., Hasinger, G., Leibundgut, B. (eds) Relativistic Astrophysics Legacy and Cosmology – Einstein’s. ESO Astrophysics Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74713-0_2
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