Generalized α-Attractor Models from Elementary Hyperbolic Surfaces
We consider generalized α-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincaré disk D, such surfaces include the hyperbolic punctured disk D⁎ and the hyperbolic annuli A(R) of modulus μ=2logR>0. For...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/7323090 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832555068450144256 |
|---|---|
| author | Elena Mirela Babalic Calin Iuliu Lazaroiu |
| author_facet | Elena Mirela Babalic Calin Iuliu Lazaroiu |
| author_sort | Elena Mirela Babalic |
| collection | DOAJ |
| description | We consider generalized α-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincaré disk D, such surfaces include the hyperbolic punctured disk D⁎ and the hyperbolic annuli A(R) of modulus μ=2logR>0. For each elementary surface, we discuss its decomposition into canonical end regions and give an explicit construction of the embedding into the Kerekjarto-Stoilow compactification (which in all three cases is the unit sphere), showing how this embedding allows for a universal treatment of globally well-behaved scalar potentials upon expanding their extension in real spherical harmonics. For certain simple but natural choices of extended potentials, we compute scalar field trajectories by projecting numerical solutions of the lifted equations of motion from the Poincaré half plane through the uniformization map, thus illustrating the rich cosmological dynamics of such models. |
| format | Article |
| id | doaj-art-b9ae5e57265d45d389de175b2c4e79b5 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-b9ae5e57265d45d389de175b2c4e79b52025-02-03T05:49:46ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/73230907323090Generalized α-Attractor Models from Elementary Hyperbolic SurfacesElena Mirela Babalic0Calin Iuliu Lazaroiu1Center for Geometry and Physics, Institute for Basic Science, Pohang 37673, Republic of KoreaCenter for Geometry and Physics, Institute for Basic Science, Pohang 37673, Republic of KoreaWe consider generalized α-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincaré disk D, such surfaces include the hyperbolic punctured disk D⁎ and the hyperbolic annuli A(R) of modulus μ=2logR>0. For each elementary surface, we discuss its decomposition into canonical end regions and give an explicit construction of the embedding into the Kerekjarto-Stoilow compactification (which in all three cases is the unit sphere), showing how this embedding allows for a universal treatment of globally well-behaved scalar potentials upon expanding their extension in real spherical harmonics. For certain simple but natural choices of extended potentials, we compute scalar field trajectories by projecting numerical solutions of the lifted equations of motion from the Poincaré half plane through the uniformization map, thus illustrating the rich cosmological dynamics of such models.http://dx.doi.org/10.1155/2018/7323090 |
| spellingShingle | Elena Mirela Babalic Calin Iuliu Lazaroiu Generalized α-Attractor Models from Elementary Hyperbolic Surfaces Advances in Mathematical Physics |
| title | Generalized α-Attractor Models from Elementary Hyperbolic Surfaces |
| title_full | Generalized α-Attractor Models from Elementary Hyperbolic Surfaces |
| title_fullStr | Generalized α-Attractor Models from Elementary Hyperbolic Surfaces |
| title_full_unstemmed | Generalized α-Attractor Models from Elementary Hyperbolic Surfaces |
| title_short | Generalized α-Attractor Models from Elementary Hyperbolic Surfaces |
| title_sort | generalized α attractor models from elementary hyperbolic surfaces |
| url | http://dx.doi.org/10.1155/2018/7323090 |
| work_keys_str_mv | AT elenamirelababalic generalizedaattractormodelsfromelementaryhyperbolicsurfaces AT caliniuliulazaroiu generalizedaattractormodelsfromelementaryhyperbolicsurfaces |