The Lambda-CDM model, based on Friedmann solution, is the simplest model that provides a reasonably good description of the observed universe’s accelerated expansion. However, this model don’t solve some problems, like “dark energy” and the coincidence problem. Thus, there are alternative approaches. One of the possibilities here is to consider inhomogeneous cosmological models such as the “Stephani solution”.
It allows building of the model of the universe with accelerated expansion within general relativity with no modifications or suggestions of the exotic types of matter. This is a non-static solution for expanding perfect fluid with zero shear and rotation, which contains the known Friedmann solution as a particular case. Initially, it has no symmetries, but the spatial sections of the Stephani space–time in the case of spherical symmetry have the same geometry as corresponding subspaces of the Friedmann solution. Therefore, these models have an intuitively clear interpretation. The spatial curvature in the Stephani solution depends on time that allows the attainment of the accelerated expansion of the universe.
Recently, Elena Kopteva and colleagues investigated the inhomogeneous spherically symmetric stephani universe filled with a perfect fluid with uniform energy density and non-uniform pressure, as a possible model of the acceleration of universe expansion. These models are characterized by the spatial curvature, depending on time. It has been shown that, despite possible singularities, the model can describe the current stage of the universe’s evolution.
Now, they investigated the geodesic structure of this model to verify if the singularities of the model can affect the light and test particle motion within the observable area. Their study recently appeared in the Journal Symmetry.
They showed that, in the case of purely radial motion, the radial velocity slightly decreases with time and radial distance, due to the universe expansion. They also showed that, both particles and photons spiral out of the center when the radial coordinate is constant.
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In addition, one interesting thing has been found in this model is that, in the case of the test particle motion with arbitrary initial velocity, the observable radial distance increases even under negative observable radial velocity, which is caused by the fact that radial distance depends on both time (T) and singularity (χ), so it can grow even when χ decreases.
“The singularities are indistinguishable for observations and do not influence the test particles and photons motion up to the current age of the universe as well as in the far enough future.”
Finally, their analysis of the geodesic structure with respect to the singularity behavior showed that the closer the exponent k to −1, the slower the solution χ(T) tends towards singularity.
Reference: Bormotova, I.; Kopteva, E.; Stuchlík, Z. Geodesic Structure of the Accelerated Stephani Universe. Symmetry 2021, 13, 1001. https://doi.org/10.3390/sym13061001
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