Cosmic topology. Part Ic. Limits on lens spaces from circle searches
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| Autores principales: | , , , , , , , , , , , , , |
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2024
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| author | Saha, Samanta Copi, Craig J. Starkman, Glenn D. Anselmi, Stefano Duque, Javier Carrón Barandiaran, Mikel Martin Akrami, Yashar Cornet-Gomez, Fernando Jaffe, Andrew H. Kosowsky, Arthur Mihaylov, Deyan P. Pereira, Thiago S. Samandar, Amirhossein Tamosiunas, Andrius |
| author_facet | Saha, Samanta Copi, Craig J. Starkman, Glenn D. Anselmi, Stefano Duque, Javier Carrón Barandiaran, Mikel Martin Akrami, Yashar Cornet-Gomez, Fernando Jaffe, Andrew H. Kosowsky, Arthur Mihaylov, Deyan P. Pereira, Thiago S. Samandar, Amirhossein Tamosiunas, Andrius |
| contents | Cosmic microwave background (CMB) temperature and polarization observations indicate that in the best-fit $Λ$ Cold Dark Matter model of the Universe, the local geometry is consistent with at most a small amount of positive or negative curvature, i.e., $\vertΩ_K\vert\ll1$. However, whether the geometry is flat ($E^3$), positively curved ($S^3$) or negatively curved ($H^3$), there are many possible topologies. Among the topologies of $S^3$ geometry, the lens spaces $L(p,q)$, where $p$ and $q$ ($p>1$ and $0<q<p$) are positive integers, are quotients of the covering space of $S^3$ (the three-sphere) by ${\mathbb{Z}}_p$, the cyclic group of order $p$. We use the absence of any pair of circles on the CMB sky with matching patterns of temperature fluctuations to establish constraints on $p$ and $q$ as a function of the curvature scale that are considerably stronger than those previously asserted for most values of $p$ and $q$. The smaller the value of $\vertΩ_K\vert$, i.e., the larger the curvature radius, the larger the maximum allowed value of $p$. For example, if $\vertΩ_K\vert\simeq 0.05$ then $p\leq 9 $, while if $\vertΩ_K\vert\simeq 0.02$, $p$ can be as high as 24. Future work will extend these constraints to a wider set of $S^{3}$ topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cosmic topology. Part Ic. Limits on lens spaces from circle searches Saha, Samanta Copi, Craig J. Starkman, Glenn D. Anselmi, Stefano Duque, Javier Carrón Barandiaran, Mikel Martin Akrami, Yashar Cornet-Gomez, Fernando Jaffe, Andrew H. Kosowsky, Arthur Mihaylov, Deyan P. Pereira, Thiago S. Samandar, Amirhossein Tamosiunas, Andrius Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory Cosmic microwave background (CMB) temperature and polarization observations indicate that in the best-fit $Λ$ Cold Dark Matter model of the Universe, the local geometry is consistent with at most a small amount of positive or negative curvature, i.e., $\vertΩ_K\vert\ll1$. However, whether the geometry is flat ($E^3$), positively curved ($S^3$) or negatively curved ($H^3$), there are many possible topologies. Among the topologies of $S^3$ geometry, the lens spaces $L(p,q)$, where $p$ and $q$ ($p>1$ and $0<q<p$) are positive integers, are quotients of the covering space of $S^3$ (the three-sphere) by ${\mathbb{Z}}_p$, the cyclic group of order $p$. We use the absence of any pair of circles on the CMB sky with matching patterns of temperature fluctuations to establish constraints on $p$ and $q$ as a function of the curvature scale that are considerably stronger than those previously asserted for most values of $p$ and $q$. The smaller the value of $\vertΩ_K\vert$, i.e., the larger the curvature radius, the larger the maximum allowed value of $p$. For example, if $\vertΩ_K\vert\simeq 0.05$ then $p\leq 9 $, while if $\vertΩ_K\vert\simeq 0.02$, $p$ can be as high as 24. Future work will extend these constraints to a wider set of $S^{3}$ topologies. |
| title | Cosmic topology. Part Ic. Limits on lens spaces from circle searches |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.02226 |