Some late-time cosmological aspects of a Gauss–Bonnet gravity with nonminimal coupling à la Brans–Dicke: solutions and perspectives

2013 ◽  
Vol 91 (4) ◽  
pp. 300-321 ◽  
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
Scalar Field ◽  
String Theory ◽  
Modified Gravity ◽  
Cosmological Models ◽  
Gravity Theory ◽  
Accelerating Universe ◽  
Late Time ◽  
Nonminimal Coupling ◽  
Bonnet Gravity ◽  
Time Dynamics

In this paper, we study modified homogeneous and isotropic cosmological models based on the Gauss–Bonnet invariant term as models of an accelerating universe. We discuss and criticize the late-time dynamics of six independent cosmological models: in the first model, we discuss the case of the modified gravity f(R) ∝ R1+δ for δ = −1/2 and 1 augmented by the Gauss–Bonnet invariant term; in the second model, we discuss the general case of f(R) ∝ R1+δ accompanied by a nonminimal coupling between the scalar field and the Ricci curvature as well as the Gauss–Bonnet invariant; in the third model, we discuss a generalized modified gravity model that includes the Einstein–Hilbert action, a dynamical cosmological constant, and an effective gravitational coupling constant; in the fourth model, we discuss a more generalized modified scalar–tensor cosmology that includes in addition to the Gauss–Bonnet invariant term, stringy corrections motivated from string and heterotic superstring arguments; in the fifth model, we discuss the cosmological dynamics of a nonminimal scalar Gauss–Bonnet gravity theory motivated from string theory; and finally in the sixth model, we discuss the possibility of having an extension of the generalized modified gravity theory, free from nonminimal coupling with δ = 0, with a Hubble expansion rate and an equation of state parameter that depend on the Gauss–Bonnet invariant term. In the first five models, we conjecture that the Hubble parameter is related to the scalar field by the relation [Formula: see text], which is applied merely to the late time epoch. This ansatz is in fact motivated by some recent advances in scalar–tensor theory and string theory. All of the six models reveal interesting consequences, which are discussed in some detail. Our main objective in this work is to analyze, criticize, and differentiate between viable realistic models and those that are not. Many critical points are discussed in some detail.

Possible fates for the accelerating Universe

2006 ◽  
Vol 84 (6-7) ◽  
pp. 583-589
Author(s):  
V Faraoni
Keyword(s):  
Stability Analysis ◽  
Modified Gravity ◽  
Accelerating Universe ◽  
Late Time ◽  
De Sitter ◽  
Recent Proposal ◽  
Time Dynamics ◽  
Big Rip ◽  
Exponential Expansion ◽  
General Potential

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

scholarly journals RECONSTRUCTING A STRING-INSPIRED NONMINIMALLY COUPLED QUINTOM MODEL

2009 ◽  
Vol 18 (08) ◽  
pp. 1291-1301 ◽  
Author(s):  
M. R. SETARE ◽  
J. SADEGHI ◽  
A. R. AMANI
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
String Theory ◽  
Scalar Curvature ◽  
Recent Work ◽  
Nonminimal Coupling ◽  
Tachyon Field ◽  
Dynamical Dark Energy

Motivated by the recent work of Zhang and Chen,1we generalize their work to the nonminimally coupled case. We consider a quintom model of dark energy with a single scalar field T given by a Lagrangian inspired by a tachyonic Lagrangian in string theory. We consider nonminimal coupling of the tachyon field to the scalar curvature, and then we reconstruct this model in the light of three forms of parametrization for dynamical dark energy.

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

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Genly Leon ◽  
Sebastián Cuéllar ◽  
Esteban González ◽  
Samuel Lepe ◽  
Claudio Michea ◽  
...  
Keyword(s):  
Scalar Field ◽  
Nonlinear Dynamical Systems ◽  
Perturbation Parameter ◽  
Time Dependent ◽  
Late Time ◽  
De Sitter ◽  
Time Dynamics ◽  
Locally Rotationally Symmetric ◽  
Bianchi I ◽  
Rotationally Symmetric

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.

scholarly journals Anisotropic cosmological reconstruction in f(R, T) gravity

2018 ◽  
Vol 33 (29) ◽  
pp. 1850170 ◽  
Author(s):  
B. Mishra ◽  
Sankarsan Tarai ◽  
S. K. Tripathy
Keyword(s):  
Simple Approach ◽  
Cosmological Models ◽  
Gravity Theory ◽  
Cosmic Acceleration ◽  
Late Time ◽  
Coupling Constant ◽  
Anisotropic Cosmological Models

Anisotropic cosmological models are constructed in f(R, T) gravity theory to investigate the dynamics of universe concerning the late time cosmic acceleration. Using a more general and simple approach, the effect of the coupling constant and anisotropy on the cosmic dynamics have been investigated. In this study, it is found that cosmic anisotropy substantially affects cosmic dynamics.

MODIFIED GRAVITY THEORY DUE TO POSITIVE AS WELL AS NEGATIVE CURVATURE INDUCED ACCELERATION

2012 ◽  
Vol 21 (02) ◽  
pp. 1250012
Author(s):  
PRIYADARSHI MAJUMDAR
Keyword(s):  
Dark Energy ◽  
Modified Gravity ◽  
Negative Curvature ◽  
Gravity Theory ◽  
Cosmic Acceleration ◽  
Late Time ◽  
Negative Power ◽  
Modified Gravity Theory ◽  
Phase Q ◽  
The Universe

We formulate a modified gravity theory that eliminates the need for dark energy and is stable for a Lagrangian containing R, R2 as well as 1/R terms (i.e. nonlinear contributions of the Ricci curvature with a non-analytic model of f(R) at R = 0) without considering any matter-dominated era. The terms with positive powers (1, 2) of the curvature support the inflationary epoch while the terms with negative power (-1) serves as effective dark energy, supporting current cosmic acceleration. We present a few analytical solutions of evolution equation for the deceleration parameter q as a function of Hubble parameter H and time t; specially in one solution, the universe evolves continuously from q = 1 (a radiation-dominated epoch) to q = -1/2 (dark-energy-dominated late-time accelerating phase) when the universe is sufficiently old. The solution is supported by numerical results. The transition from the decelerated (q > 0) to the accelerated phase (q < 0) of expansion takes place smoothly without having to resort to a study of asymptotic behavior.

scholarly journals A Riccati equation based approach to isotropic scalar field cosmologies

2014 ◽  
Vol 23 (07) ◽  
pp. 1450063 ◽  
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
M. K. Mak
Keyword(s):  
Scalar Field ◽  
Evolution Equation ◽  
Interaction Potential ◽  
Arbitrary Function ◽  
Field Potential ◽  
Type Equation ◽  
Scalar Fields ◽  
Cosmological Models ◽  
Late Time ◽  
Field Equations

Gravitationally coupled scalar fields ϕ, distinguished by the choice of an effective self-interaction potential V(ϕ), simulating a temporarily nonvanishing cosmological term, can generate both inflation and late time acceleration. In scalar field cosmological models the evolution of the Hubble function is determined, in terms of the interaction potential, by a Riccati type equation. In the present work, we investigate scalar field cosmological models that can be obtained as solutions of the Riccati evolution equation for the Hubble function. Four exact integrability cases of the field equations are presented, representing classes of general solutions of the Riccati evolution equation. The solutions correspond to cosmological models in which the Hubble function is proportional to the scalar field potential plus a linearly decreasing function of time, models with the time variation of the scalar field potential proportional to the potential minus its square, models in which the potential is the sum of an arbitrary function and the square of the function integral, and models in which the potential is the sum of an arbitrary function and the derivative of its square root, respectively. The cosmological properties of all models are investigated in detail, and it is shown that they can describe the inflationary or the late accelerating phase in the evolution of the universe.

scholarly journals Scalar Field Models for an Accelerating Universe

2005 ◽  
Vol 201 ◽  
pp. 260-263
Author(s):  
Varun. Sahni
Keyword(s):  
Dark Matter ◽  
Scalar Field ◽  
Cold Dark Matter ◽  
High Redshift ◽  
Accelerating Universe ◽  
Late Time ◽  
Luminosity Distance ◽  
New Class ◽  
Scalar Field Models ◽  
Model Independent

I describe a new class of quintessence+CDM models in which late time scalar field oscillations can give rise to both quintessence and cold dark matter. Additionally, a versatile ansatz for the luminosity distance is used to reconstruct the quintessence equation of state in amodel independentmanner from observations of high redshift supernovae.

scholarly journals Dynamics of two-scalar-field cosmological models beyond the exponential potential

2017 ◽  
Vol 26 (14) ◽  
pp. 1750164 ◽  
Author(s):  
Yu Li
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Cosmological Models ◽  
The Other ◽  
Late Time ◽  
Exponential Potential ◽  
Multiple Attractors ◽  
Evolution Of The Universe ◽  
The Universe

In this paper, we discuss the dynamics of two- scalar-field cosmological models. Unlike in the situation of exponential potential, we find that there are late-time attractors in which one scalar field dominates the energy density of universe and the other one decay. We also discuss the possibility of multiple attractors model which is useful to realize the evolution of the universe from a scaling era to recent acceleration era. We also give the conditions of the existence of multiple attractors.

scholarly journals Integrable cosmological models with an additional scalar field

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Vsevolod R. Ivanov ◽  
Sergey Yu. Vernov
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Gravity Model ◽  
Modified Gravity ◽  
Field Model ◽  
Cosmic Time ◽  
Cosmological Models ◽  
Conformal Metric ◽  
General Solutions ◽  
Hubble Parameters

AbstractWe consider modified gravity cosmological models that can be transformed into two-field chiral cosmological models by the conformal metric transformation. For the $$R^2$$ R 2 gravity model with an additional scalar field and the corresponding two-field model with the cosmological constant and nonstandard kinetic part of the action, the general solutions have been obtained in the spatially flat FLRW metric. We analyze the correspondence of the cosmic time solutions obtained and different possible evolutions of the Hubble parameters in the Einstein and Jordan frames.

Generalized holographic dark energy and bouncing cosmology in Gauss–Bonnet gravity

2018 ◽  
Vol 15 (06) ◽  
pp. 1850096 ◽  
Author(s):  
Andrey N. Makarenko ◽  
Alexander N. Myagky
Keyword(s):  
Dark Energy ◽  
Holographic Dark Energy ◽  
Cosmological Models ◽  
Gravity Theory ◽  
Bonnet Gravity ◽  
Bouncing Cosmology

We found out that [Formula: see text] gravity theory can be rewritten in the holographic language at the level of background equivalence. The examples of the bouncing cosmological models in [Formula: see text] gravity are considered in details.

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