An Attractor-Repeller model of the Local Universe : The Λ-Szekeres spacetime and Perturbation Theory
Abstract
The standard linearly perturbed Friedmann-Lemaître-Robertson-Walker (FLRW) framework provides an accurate description of the Universe on large scales but cannot fully capture the non-linear inhomogeneities that characterize the local Universe. In this work, we investigate whether an exact inhomogeneous solution of the Einstein field equations can provide a more realistic description of the nearby cosmic environment. To this end, we employ the quasi-spherical Szekeres class I solution with Λ and focus on its axisymmetric subclass, motivated by recent observations indicating an axisymmetric expansion rate of the local Universe. We determine light propagation by numerically integrating the Sachs optical equations, thereby obtaining the luminosity distance and its evolution with redshift. We further compute the multipoles of the covariant cosmographic parameters and apply the formalism to an attractor-repeller configuration representative of the local matter distribution. We find that the resulting covariant cosmographic parameters are consistent with current observational constraints. Finally, we derive the gravitational potential and peculiar velocity field generated by the Szekeres density distribution, establishing the connection between the exact relativistic solution and its Newtonian counterparts.
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BibTeX
@misc{sarma2026attractorrepeller,
title = {{An Attractor-Repeller model of the Local Universe : The $Λ$-Szekeres spacetime and Perturbation Theory}},
author = {Maharshi Sarma and Christian Marinoni and Basheer Kalbouneh},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04375},
eprint = {2609.04375},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05749324v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Attractor-Repeller model of the Local Universe : The Λ-Szekeres spacetime and Perturbation Theory
AU - Maharshi Sarma
AU - Christian Marinoni
AU - Basheer Kalbouneh
PY - 2026
DA - 2026/09/03
PB - HAL
DO - 10.48550/arxiv.2609.04375
UR - https://hal.science/hal-05749324v1
AB - The standard linearly perturbed Friedmann-Lemaître-Robertson-Walker (FLRW) framework provides an accurate description of the Universe on large scales but cannot fully capture the non-linear inhomogeneities that characterize the local Universe. In this work, we investigate whether an exact inhomogeneous solution of the Einstein field equations can provide a more realistic description of the nearby cosmic environment. To this end, we employ the quasi-spherical Szekeres class I solution with Λ and focus on its axisymmetric subclass, motivated by recent observations indicating an axisymmetric expansion rate of the local Universe. We determine light propagation by numerically integrating the Sachs optical equations, thereby obtaining the luminosity distance and its evolution with redshift. We further compute the multipoles of the covariant cosmographic parameters and apply the formalism to an attractor-repeller configuration representative of the local matter distribution. We find that the resulting covariant cosmographic parameters are consistent with current observational constraints. Finally, we derive the gravitational potential and peculiar velocity field generated by the Szekeres density distribution, establishing the connection between the exact relativistic solution and its Newtonian counterparts.
ER -