2025/08/03 by Mannheim, Philip D., Norman, Daniel A., Liu, Tianye · 1 citation
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2508.02756
In the cosmological Robertson-Walker geometry required of the cosmological principle both the Weyl tensor Cμλνκ and the Bach tensor Wμν=[2∇κ∇λ-Rλκ]Cμλνκ vanish. In general, in perturbations around the cosmological background neither of the fluctuating δCμλνκ or δWμν would vanish. However, it is possible for δWμν to vanish even as δCμλνκ does not. In this paper we construct an explicit model in which this is the case. The model consists of a 3-tensor gravitational wave fluctuating around a background with a constant negative 3-curvature. The model is exactly solvable and consists purely of geometric quantities with no matter fields at all (i.e., Gμν=0, δGμν=0, Wμν=0, δWμν=0, where Gμν is the Einstein tensor). The model can thus be created out of nothing, with creating a universe from nothing thus being an alternative principle to the cosmological principle. The fluctuating gravitational wave contributes to the temperature anisotropy in the cosmic microwave background and its B mode polarization in a calculable manner, one for which we provide a simple analytic way of treating spatial modes that is based on the use of a spatial mode addition theorem. In addition, we provide a treatment of the anisotropy that is based on properties of bandwidth limited functions. Classically by ``nothing" we mean that there are no Tμν or δTμν matter field terms. Quantum-mechanically by ``nothing" we mean that all fields other than the gravitational field are in a negative energy mode vacuum state, with the only occupied positive energy modes being graviton modes. As well as use the Bach tensor as a diagnostic, we consider dynamics based on it.