scholarly journals Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open Friedmann–Lemaître–Robertson–Walker models

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Genly Leon ◽  
Esteban González ◽  
Samuel Lepe ◽  
Claudio Michea ◽  
Alfredo D. Millano

AbstractScalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $$\gamma $$ γ for locally rotationally symmetric (LRS) Bianchi III metric and open Friedmann–Lemaître–Robertson–Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic index $$\gamma $$ γ late-time attractors of physical interests for LRS Bianchi III metric are Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de Sitter, quintessence or zero acceleration solutions) and matter-curvature scaling solution. For open FLRW metric late-time attractors are a matter dominated FLRW universe and Milne solution. With this approach, oscillations entering nonlinear system through Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble factor H – acting as a time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behaviour.

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Genly Leon ◽  
Sebastián Cuéllar ◽  
Esteban González ◽  
Samuel Lepe ◽  
Claudio Michea ◽  
...  

AbstractScalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic equation of state (EoS) with barotropic index $$\gamma $$ γ for the locally rotationally symmetric (LRS) Bianchi I and flat Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $$\gamma $$ γ , the late-time attractors of physical interests are flat quintessence dominated FLRW universe and Einstein-de Sitter solution. With this approach, the oscillations entering the system through the Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble parameter H – acting as time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behavior.


2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Genly Leon ◽  
Esteban González ◽  
Samuel Lepe ◽  
Claudio Michea ◽  
Alfredo D. Millano

AbstractScalar-field cosmologies with a generalized harmonic potential and matter with energy density $$\rho _m$$ ρ m , pressure $$p_m$$ p m , and barotropic equation of state (EoS) $$p_m=(\gamma -1)\rho _m, \; \gamma \in [0,2]$$ p m = ( γ - 1 ) ρ m , γ ∈ [ 0 , 2 ] in Kantowski–Sachs (KS) and closed Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. We use methods from non-linear dynamical systems theory and averaging theory considering a time-dependent perturbation function D. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late-time attractors of full and time-averaged systems are two anisotropic contracting solutions, which are non-flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for $$0\le \gamma \le 2$$ 0 ≤ γ ≤ 2 , and flat FLRW matter-dominated universe if $$0\le \gamma \le \frac{2}{3}$$ 0 ≤ γ ≤ 2 3 . For closed FLRW metric late-time attractors of full and averaged systems are a flat matter-dominated FLRW universe for $$0\le \gamma \le \frac{2}{3}$$ 0 ≤ γ ≤ 2 3 as in KS and Einstein–de Sitter solution for $$0\le \gamma <1$$ 0 ≤ γ < 1 . Therefore, a time-averaged system determines future asymptotics of the full system. Also, oscillations entering the system through Klein–Gordon (KG) equation can be controlled and smoothed out when D goes monotonically to zero, and incidentally for the whole D-range for KS and closed FLRW (if $$0\le \gamma < 1$$ 0 ≤ γ < 1 ) too. However, for $$\gamma \ge 1$$ γ ≥ 1 closed FLRW solutions of the full system depart from the solutions of the averaged system as D is large. Our results are supported by numerical simulations.


2018 ◽  
Vol 33 (34) ◽  
pp. 1850199 ◽  
Author(s):  
A. I. Keskin

In this study, we examine two models of the scalar field, that is, a normal scalar field and a tachyon scalar field in [Formula: see text] gravity to describe cosmic acceleration of the universe, where [Formula: see text], [Formula: see text] and [Formula: see text] are Ricci curvature scalar, trace of energy–momentum tensor and kinetic energy of scalar field [Formula: see text], respectively. Using the minimal-coupling Lagrangian [Formula: see text], for both the scalar models we obtain a viable cosmological system, where [Formula: see text] and [Formula: see text] are real constants. While a normal scalar field gives a system describing expansion from the deceleration to the late-time acceleration, tachyon field together with [Formula: see text] in the system produces a quintessential expansion which is very close to de Sitter point, where we find a new condition [Formula: see text] for inflation.


2016 ◽  
Vol 25 (02) ◽  
pp. 1650025 ◽  
Author(s):  
Giovanni Otalora

Although equivalent to general relativity, teleparallel gravity (TG) is conceptually speaking a completely different theory. In this theory, the gravitational field is described by torsion, not by curvature. By working in this context, a new model is proposed in which the four-derivative of a canonical scalar field representing dark energy is nonminimally coupled to the “vector torsion”. This type of coupling is motivated by the fact that a scalar field couples to torsion through its four-derivative, which is consistent with local spacetime kinematics regulated by the de Sitter group [Formula: see text]. It is found that the current state of accelerated expansion of the universe corresponds to a late-time attractor that can be (i) a dark energy-dominated de Sitter solution ([Formula: see text]), (ii) a quintessence-type solution with [Formula: see text], or (iii) a phantom-type [Formula: see text] dark energy.


2019 ◽  
Vol 28 (12) ◽  
pp. 1950161 ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Supriya Pan ◽  
Weiqiang Yang

We investigate the cosmological dynamics of interacting dark energy models in which the interaction function is nonlinear in terms of the energy densities. Considering explicitly the interaction between a pressureless dark matter and a scalar field, minimally coupled to Einstein gravity, we explore the dynamics of the spatially flat FLRW universe for the exponential potential of the scalar field. We perform the stability analysis for three nonlinear interaction models of our consideration through the analysis of critical points and we investigate the cosmological parameters and discuss the physical behavior at the critical points. From the analysis of the critical points we find a number of possibilities that include the stable late-time accelerated solution, [Formula: see text]CDM-like solution, radiation-like solution and moreover the unstable inflationary solution.


2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
F. F. Santos ◽  
R. M. P. Neves ◽  
F. A. Brito

We investigate a cosmological scenario by finding solutions using first-order formalism in the Horndeski gravity that constrains the superpotential and implies that no free choice of scalar potential is allowed. Despite this, we show that a de Sitter phase at late-time cosmology can be realized, where the dark energy sector can be identified. The scalar field equation of state tends to the cosmological scenario at present time and allows us to conclude that it can simulate the dark energy in the Horndeski gravity.


2012 ◽  
Vol 21 (06) ◽  
pp. 1250055 ◽  
Author(s):  
MUHAMMAD SHARIF ◽  
SAIRA WAHEED

We explore locally rotationally symmetric Bianchi I universe in Brans–Dicke gravity with self-interacting potential by using charged viscous cosmological string fluid. We use a relationship between the shear and expansion scalars and also take the power law for scalar field as well as self-interacting potential. It is found that the resulting universe model maintains its anisotropic nature at all times due to the proportionality relationship between expansion and shear scalars. The physical implications of this model are discussed by using different parameters and their graphs. We conclude that this model corresponds to an accelerated expanding universe for particular values of the parameters.


2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Saikat Chakraborty ◽  
Esteban González ◽  
Genly Leon ◽  
Bin Wang

AbstractIn this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $$\phi _1$$ ϕ 1 and $$\phi _2$$ ϕ 2 interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless time variable, the resulting dynamical system is studied. The main difficulties arising in the standard dynamical systems approach, where expansion normalized dynamical variables are usually adopted, are due to the oscillations entering the nonlinear system through the Klein–Gordon (KG) equations. This motivates the analysis of the oscillations using methods from the theory of averaging nonlinear dynamical systems. We prove that time-dependent systems, and their corresponding time-averaged versions, have the same late-time dynamics. Then, we study the time-averaged system using standard techniques of dynamical systems. We present numerical simulations as evidence of such behavior.


2006 ◽  
Vol 84 (6-7) ◽  
pp. 583-589
Author(s):  
V Faraoni

The accelerating Universe may end in eternal de Sitter expansion, in a Big Rip, or in super-exponential expansion. We discuss a gauge-independent stability analysis of de Sitter space in scalar–tensor and in modified gravity, the late-time dynamics of a phantom Universe with general potential, and the recent proposal of evading the Big Rip through wormhole tunneling.PACS Nos.: 98.80.–k, 04.50.+h, 04.20.–q


Sign in / Sign up

Export Citation Format

Share Document