Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation
This paper presents a noncommutative (NC) version of an extended Sáez–Ballester (SB) theory. Concretely, considering the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and, applying the Hamiltonian forma...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/3/165 |
| _version_ | 1797441306562134016 |
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| author | S. M. M. Rasouli |
| author_facet | S. M. M. Rasouli |
| author_sort | S. M. M. Rasouli |
| collection | DOAJ |
| description | This paper presents a noncommutative (NC) version of an extended Sáez–Ballester (SB) theory. Concretely, considering the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and, applying the Hamiltonian formalism, obtain deformed equations of motion. In our model, the NC parameter appears linearly in the deformed Poisson bracket and the equations of the NC SB cosmology. When it goes to zero, we get the corresponding commutative counterparts. Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; (ii) for the late times, there is a zero acceleration epoch. By establishing an appropriate dynamical framework, we show that the results (i) and (ii) can be obtained for many sets of the initial conditions and the parameters of the model. Finally, we indicate that, at the level of the field equations, one may find a close resemblance between our NC model and the Starobinsky inflationary model. |
| first_indexed | 2024-03-09T12:21:08Z |
| format | Article |
| id | doaj.art-bc91d119b6664a04a083768227d0acd3 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T12:21:08Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-bc91d119b6664a04a083768227d0acd32023-11-30T22:40:42ZengMDPI AGUniverse2218-19972022-03-018316510.3390/universe8030165Noncommutativity, Sáez–Ballester Theory and Kinetic InflationS. M. M. Rasouli0Departamento de Física, Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200-001 Covilhã, PortugalThis paper presents a noncommutative (NC) version of an extended Sáez–Ballester (SB) theory. Concretely, considering the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and, applying the Hamiltonian formalism, obtain deformed equations of motion. In our model, the NC parameter appears linearly in the deformed Poisson bracket and the equations of the NC SB cosmology. When it goes to zero, we get the corresponding commutative counterparts. Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; (ii) for the late times, there is a zero acceleration epoch. By establishing an appropriate dynamical framework, we show that the results (i) and (ii) can be obtained for many sets of the initial conditions and the parameters of the model. Finally, we indicate that, at the level of the field equations, one may find a close resemblance between our NC model and the Starobinsky inflationary model.https://www.mdpi.com/2218-1997/8/3/165kinetic inflationdeformed phase spacenoncommutativityscalar tensor theoriesSáez–Ballester theorydynamical analysis |
| spellingShingle | S. M. M. Rasouli Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation Universe kinetic inflation deformed phase space noncommutativity scalar tensor theories Sáez–Ballester theory dynamical analysis |
| title | Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation |
| title_full | Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation |
| title_fullStr | Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation |
| title_full_unstemmed | Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation |
| title_short | Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation |
| title_sort | noncommutativity saez ballester theory and kinetic inflation |
| topic | kinetic inflation deformed phase space noncommutativity scalar tensor theories Sáez–Ballester theory dynamical analysis |
| url | https://www.mdpi.com/2218-1997/8/3/165 |
| work_keys_str_mv | AT smmrasouli noncommutativitysaezballestertheoryandkineticinflation |