Revisiting dynamics of interacting quintessence
Abstract We apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field $$\phi $$ ϕ . For a coupling function $$Q = -(\alpha d\rho _m/dt + \beta d\rho _\phi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-12-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-021-09857-4 |
| _version_ | 1818406209169915904 |
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| author | Patrocinio Pérez Ulises Nucamendi Roberto De Arcia |
| author_facet | Patrocinio Pérez Ulises Nucamendi Roberto De Arcia |
| author_sort | Patrocinio Pérez |
| collection | DOAJ |
| description | Abstract We apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field $$\phi $$ ϕ . For a coupling function $$Q = -(\alpha d\rho _m/dt + \beta d\rho _\phi /dt )$$ Q = - ( α d ρ m / d t + β d ρ ϕ / d t ) , where t is the cosmic time, we have found that it can be rewritten in the form $$Q = 3H (\alpha \rho _m + \beta (d\phi /dt)^2 )/(1-\alpha +\beta )$$ Q = 3 H ( α ρ m + β ( d ϕ / d t ) 2 ) / ( 1 - α + β ) , so that its dependence on the dark matter density and on the kinetic term of the scalar field is linear and proportional to the Hubble parameter. We analyze the scenarios $$\alpha =0$$ α = 0 , $$\alpha = \beta $$ α = β and $$\alpha = -\beta $$ α = - β , separately and in order to describe the cosmological evolution we have calculated various observables. A notable result of this work is that, unlike for the noninteracting scalar field with exponential potential where five critical points appear, in the case studied here, with the exception of the matter dominated solution, the remaining singular points are transformed into scaling solutions enriching the phase space. It is shown that for $$\alpha \ne 0$$ α ≠ 0 , a separatrix arises modifying prominently the structure of the phase space. This represents a novel feature no mentioned before in the literature. |
| first_indexed | 2024-12-14T09:08:18Z |
| format | Article |
| id | doaj.art-bc8071d3f2714c33bf79cd5858b6df5c |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-14T09:08:18Z |
| publishDate | 2021-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-bc8071d3f2714c33bf79cd5858b6df5c2022-12-21T23:08:39ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522021-12-01811211610.1140/epjc/s10052-021-09857-4Revisiting dynamics of interacting quintessencePatrocinio Pérez0Ulises Nucamendi1Roberto De Arcia2Instituto de Física y Matemáticas Universidad Michoacana de San Nicolás de HidalgoInstituto de Física y Matemáticas Universidad Michoacana de San Nicolás de HidalgoDpto. Ingeniería Civil, División de Ingeniería, Universidad de GuanajuatoAbstract We apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field $$\phi $$ ϕ . For a coupling function $$Q = -(\alpha d\rho _m/dt + \beta d\rho _\phi /dt )$$ Q = - ( α d ρ m / d t + β d ρ ϕ / d t ) , where t is the cosmic time, we have found that it can be rewritten in the form $$Q = 3H (\alpha \rho _m + \beta (d\phi /dt)^2 )/(1-\alpha +\beta )$$ Q = 3 H ( α ρ m + β ( d ϕ / d t ) 2 ) / ( 1 - α + β ) , so that its dependence on the dark matter density and on the kinetic term of the scalar field is linear and proportional to the Hubble parameter. We analyze the scenarios $$\alpha =0$$ α = 0 , $$\alpha = \beta $$ α = β and $$\alpha = -\beta $$ α = - β , separately and in order to describe the cosmological evolution we have calculated various observables. A notable result of this work is that, unlike for the noninteracting scalar field with exponential potential where five critical points appear, in the case studied here, with the exception of the matter dominated solution, the remaining singular points are transformed into scaling solutions enriching the phase space. It is shown that for $$\alpha \ne 0$$ α ≠ 0 , a separatrix arises modifying prominently the structure of the phase space. This represents a novel feature no mentioned before in the literature.https://doi.org/10.1140/epjc/s10052-021-09857-4 |
| spellingShingle | Patrocinio Pérez Ulises Nucamendi Roberto De Arcia Revisiting dynamics of interacting quintessence European Physical Journal C: Particles and Fields |
| title | Revisiting dynamics of interacting quintessence |
| title_full | Revisiting dynamics of interacting quintessence |
| title_fullStr | Revisiting dynamics of interacting quintessence |
| title_full_unstemmed | Revisiting dynamics of interacting quintessence |
| title_short | Revisiting dynamics of interacting quintessence |
| title_sort | revisiting dynamics of interacting quintessence |
| url | https://doi.org/10.1140/epjc/s10052-021-09857-4 |
| work_keys_str_mv | AT patrocinioperez revisitingdynamicsofinteractingquintessence AT ulisesnucamendi revisitingdynamicsofinteractingquintessence AT robertodearcia revisitingdynamicsofinteractingquintessence |