Interactions between cosmic fluids may appear in many cosmological scenarios that go far beyond t... more Interactions between cosmic fluids may appear in many cosmological scenarios that go far beyond the usually studied energy exchange in the dark sector. They may arise in situations that go from the electron-positron annihilation after neutrino decoupling to the evaporation of a population of primordial black holes and to gravitational collapse itself. In the absence of known microscopic interaction mechanisms, phenomenological ansatzes are usually proposed in order to describe such models. The aim of the present paper is to investigate some formal aspects of two of the most used of such ansatzes. In this sense, it should not, in principle, be taken as a paper specifically about interactions between dark energy and dark matter. Presently, however, possible energy exchanges in the dark sector remain as the main motivation for studying cosmic interactions and, as such, they will be frequently mentioned as examples of applications of the formalism developed here. In particular, we will derive a generalization of the ansatz based on the initial proposal of Shapiro, Sol`a, Espan ̃a-Bonet and Ruiz-Lapuente, who described a time-dependent cosmological “constant” whose variation arises from quantum e↵ects near the Planck scale [I. L. Shapiro, J. Sol`a, C. Espan ̃a- Bonet, and P. Ruiz-Lapuente, Phys. Lett. B 574, 149 (2003) (arXiv:astro-ph/0303306)]. This physically motivated model was based on a single free parameter ⌫, and was subsequently studied by Wang and Meng [P.Wang and X. Meng, Class. Quantum Grav. 22, 283 (2005), (arXiv:astro-ph 0408495)] under the pure phenomenological reasoning that the vacuum decay would slightly modify the exponent describing how the energy density of matter decreases with the scale factor. This modification is described by a single parameter "(= 3⌫ of the former paper). For short, we shall call these proposals (and their extensions, developed by several authors, in order to include interactions between other forms of dark energy and dark matter) the “Shapiro and Sol`a ansatz” (hereafter the SS ansatz). The generalization derived in the present article requires two free parameters ("1, "2) and shall be denominated the “generalized Shapiro and Sol`a ansatz” (henceforth the GSS ansatz). We will show that, dynamically, this extension (and, consequently, also the restricted SS ansatz) is, in fact, contained in the ansatz proposed by Barrow and Clifton [J. D. Barrow and T. Clifton, Phys. Rev. D 73, 103520 (2006) (arXiv:gr-qc/0604063)] (from now on the BC ansatz) which deals with the transfer of energy between any two fluids (not necessarily in the dark sector) using a two-parameter scheme (↵1, ↵2) and that has the advantage of exhibiting, explicitly, the form of the interaction factor appearing in the continuity equation of each fluid (the Q interaction factor), besides being linear in both densities. By considering a scenario with two interacting linear barotropic fluids with constant, but otherwise arbitrary, equation of state parameters !1 and !2, we will find the explicit relations between (↵1, ↵2) and ("1, "2). Depending on the type of problem that one has to face, either the GSS or the BC ansatz may be more convenient from a mathematical point of view. Therefore, the demonstration of their relationship may be useful to simplify the calculations in several cases. Moreover, as !1 and !2 will not be restricted to any particular values, our treatment may be used to analyze interactions in many di↵erent cosmological frameworks, related to any cosmic epoch, such as the very early universe or the present epoch of accelerated expansion. We will review the thermodynamics of this two-fluid model and shall investigate how the thermodynamic quantities depend on the factor describing the interaction (the Q factor of the BC scheme). As an example, the general formalism will then be applied to study the dynamics and the thermodynamics of vacuum decay. We will show that most, but not all, of the expressions proposed in the literature for the time dependence of the cosmological “constant” ⇤ are compatible with particular cases (one parameter set to zero) of the BC ansatz (equivalently, the SS approach). Only one of them is compatible with the general BC two-parameter case (or the GSS ansatz). The analysis performed here - under the point of view of an interaction process between the vacuum and the second fluid - shows explicitly how the vacuum decay depends on the equation of state parameter of the second fluid. We will also derive an exact solution for the scale factor in the vacuum decay scenario corresponding to the two-parameter GSS scheme. Under convenient conditions imposed on the signs of the quantities involved, this solution may lead to non-singular cosmologies and to universe expansions that exhibit transitions from a non-accelerated to an accelerated era or vice-versa. In fact, the interaction process can modify the dynamics in such a way that, for certain values of the parameters, “unusual” cosmic histories may result, even if the relevant fluids are not “exotic”. Another interesting feature of our generalization of the SS ansatz (in the context of vacuum decay) is the possibility of having a zero initial condition for the energy density of the second fluid. Our analysis is entirely made at the background level. PACS numbers: 98.80.Es, 95.36.+x, 98.80.-k, 95.30.Tg
In this paper, we reanalysis the cosmological scenery with vacuum decay in dark matter proposed b... more In this paper, we reanalysis the cosmological scenery with vacuum decay in dark matter proposed by Wand and Meng. Here, the baryonic matter is also considered as a fluid gravitationally coupled with dark matter. It is made a careful analysis to constrain this model with the observational data of growth rate of cosmic structures. The theoretical growth rate is followed since the primordial recombination and the main physical processes on the baryonic component are considered. As a complementary constraint, this model is compared with the observed CMB-BAO ratio as well with the gas mass fraction of cluster of galaxies. We found the best fit values for dark matter $\Omega_{d0} = 0.269 ^{+0.023}_{-0.023}$ and for the decay parameter $\epsilon = 0.02 ^{+0.04}_{-0.05}$.
Interactions between cosmic fluids may appear in many cosmological scenarios that go far beyond t... more Interactions between cosmic fluids may appear in many cosmological scenarios that go far beyond the usually studied energy exchange in the dark sector. They may arise in situations that go from the electron-positron annihilation after neutrino decoupling to the evaporation of a population of primordial black holes and to gravitational collapse itself. In the absence of known microscopic interaction mechanisms, phenomenological ansatzes are usually proposed in order to describe such models. The aim of the present paper is to investigate some formal aspects of two of the most used of such ansatzes. In this sense, it should not, in principle, be taken as a paper specifically about interactions between dark energy and dark matter. Presently, however, possible energy exchanges in the dark sector remain as the main motivation for studying cosmic interactions and, as such, they will be frequently mentioned as examples of applications of the formalism developed here. In particular, we will derive a generalization of the ansatz based on the initial proposal of Shapiro, Sol`a, Espan ̃a-Bonet and Ruiz-Lapuente, who described a time-dependent cosmological “constant” whose variation arises from quantum e↵ects near the Planck scale [I. L. Shapiro, J. Sol`a, C. Espan ̃a- Bonet, and P. Ruiz-Lapuente, Phys. Lett. B 574, 149 (2003) (arXiv:astro-ph/0303306)]. This physically motivated model was based on a single free parameter ⌫, and was subsequently studied by Wang and Meng [P.Wang and X. Meng, Class. Quantum Grav. 22, 283 (2005), (arXiv:astro-ph 0408495)] under the pure phenomenological reasoning that the vacuum decay would slightly modify the exponent describing how the energy density of matter decreases with the scale factor. This modification is described by a single parameter "(= 3⌫ of the former paper). For short, we shall call these proposals (and their extensions, developed by several authors, in order to include interactions between other forms of dark energy and dark matter) the “Shapiro and Sol`a ansatz” (hereafter the SS ansatz). The generalization derived in the present article requires two free parameters ("1, "2) and shall be denominated the “generalized Shapiro and Sol`a ansatz” (henceforth the GSS ansatz). We will show that, dynamically, this extension (and, consequently, also the restricted SS ansatz) is, in fact, contained in the ansatz proposed by Barrow and Clifton [J. D. Barrow and T. Clifton, Phys. Rev. D 73, 103520 (2006) (arXiv:gr-qc/0604063)] (from now on the BC ansatz) which deals with the transfer of energy between any two fluids (not necessarily in the dark sector) using a two-parameter scheme (↵1, ↵2) and that has the advantage of exhibiting, explicitly, the form of the interaction factor appearing in the continuity equation of each fluid (the Q interaction factor), besides being linear in both densities. By considering a scenario with two interacting linear barotropic fluids with constant, but otherwise arbitrary, equation of state parameters !1 and !2, we will find the explicit relations between (↵1, ↵2) and ("1, "2). Depending on the type of problem that one has to face, either the GSS or the BC ansatz may be more convenient from a mathematical point of view. Therefore, the demonstration of their relationship may be useful to simplify the calculations in several cases. Moreover, as !1 and !2 will not be restricted to any particular values, our treatment may be used to analyze interactions in many di↵erent cosmological frameworks, related to any cosmic epoch, such as the very early universe or the present epoch of accelerated expansion. We will review the thermodynamics of this two-fluid model and shall investigate how the thermodynamic quantities depend on the factor describing the interaction (the Q factor of the BC scheme). As an example, the general formalism will then be applied to study the dynamics and the thermodynamics of vacuum decay. We will show that most, but not all, of the expressions proposed in the literature for the time dependence of the cosmological “constant” ⇤ are compatible with particular cases (one parameter set to zero) of the BC ansatz (equivalently, the SS approach). Only one of them is compatible with the general BC two-parameter case (or the GSS ansatz). The analysis performed here - under the point of view of an interaction process between the vacuum and the second fluid - shows explicitly how the vacuum decay depends on the equation of state parameter of the second fluid. We will also derive an exact solution for the scale factor in the vacuum decay scenario corresponding to the two-parameter GSS scheme. Under convenient conditions imposed on the signs of the quantities involved, this solution may lead to non-singular cosmologies and to universe expansions that exhibit transitions from a non-accelerated to an accelerated era or vice-versa. In fact, the interaction process can modify the dynamics in such a way that, for certain values of the parameters, “unusual” cosmic histories may result, even if the relevant fluids are not “exotic”. Another interesting feature of our generalization of the SS ansatz (in the context of vacuum decay) is the possibility of having a zero initial condition for the energy density of the second fluid. Our analysis is entirely made at the background level. PACS numbers: 98.80.Es, 95.36.+x, 98.80.-k, 95.30.Tg
In this paper, we reanalysis the cosmological scenery with vacuum decay in dark matter proposed b... more In this paper, we reanalysis the cosmological scenery with vacuum decay in dark matter proposed by Wand and Meng. Here, the baryonic matter is also considered as a fluid gravitationally coupled with dark matter. It is made a careful analysis to constrain this model with the observational data of growth rate of cosmic structures. The theoretical growth rate is followed since the primordial recombination and the main physical processes on the baryonic component are considered. As a complementary constraint, this model is compared with the observed CMB-BAO ratio as well with the gas mass fraction of cluster of galaxies. We found the best fit values for dark matter $\Omega_{d0} = 0.269 ^{+0.023}_{-0.023}$ and for the decay parameter $\epsilon = 0.02 ^{+0.04}_{-0.05}$.
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Drafts by H. S. Gimenes
PACS numbers: 98.80.Es, 95.36.+x, 98.80.-k, 95.30.Tg
Papers by H. S. Gimenes
PACS numbers: 98.80.Es, 95.36.+x, 98.80.-k, 95.30.Tg