Energy exchange for homogeneous and isotropic universes with a scalar field coupled to matter

Abstract

We study the late time evolution of flat and negatively curved Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source and a scalar field arising in the conformal frame of $f(R)$ theories nonminimally coupled to matter. Under mild assumptions on the potential V we prove that equilibria corresponding to non-negative local minima for V are asymptotically stable, as well as horizontal asymptotes approached from above by V. We classify all cases of the flat model where one of the matter components eventually dominates. In particular for a nondegenerate minimum of the potential with zero critical value we prove in detail that if the parameter of the equation of state is larger than one, then there is a transfer of energy from the fluid to the scalar field and the later eventually dominates in a generic way.

18 pages, LaTeX, 1 figure

References in corpus (14)

• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Dynamics of Linear Perturbations in f(R) Gravity
• The (pseudo)issue of the conformal frame revisited
• Dynamics of $k$-essence
• Challenges for scaling cosmologies
• Classifying and avoiding singularities in the alternative gravity dark energy models
• Cosmological dynamics of Scalar--Tensor Gravity
• Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry
• Late-time oscillatory behaviour for self-gravitating scalar fields
• Decoupling of the general scalar field mode and the solution space for Bianchi type I and V cosmologies coupled to perfect fluid sources
• Constraining scalar-tensor quintessence by cosmic clocks
• Genericity of blackhole formation in the gravitational collapse of homogeneous self-interacting scalar fields
• The dynamical behaviour of homogeneous scalar-field spacetimes with general self-interaction potentials
• Gravitational collapse of homogeneous perfect fluid in HOG theories

Cited by in corpus (25)

• Dynamical behavior in $f(T,T_G)$ cosmology
• Dynamical behavior in mimetic F(R) gravity
• Barrow Entropy Cosmology: an observational approach with a hint of stability analysis
• Generalized Emergent Dark Energy: observational Hubble data constraints and stability analysis
• Cosmological dynamics in f(R) gravity
• FLRW metric $f(R)$ cosmology with a perfect fluid by generating integrals of motion
• Some remarks about non-minimally coupled scalar field models
• Non-minimally coupled scalar field cosmology with torsion
• Inflationary $\alpha$-attractor cosmology: A global dynamical systems perspective
• Coupled quintessence with double exponential potentials
• Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory
• Scalar field deformations of Lambda-CDM cosmology
• Time-averaging axion-like interacting scalar fields models
• Generalized scalar field cosmologies: theorems on asymptotic behavior
• Generalized Scalar Field Cosmologies: A Global Dynamical Systems Formulation
• Negative potentials and collapsing universes II
• Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally Symmetric Bianchi III and open Friedmann-Lemaître-Robertson-Walker models
• Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models
• Negative potentials and collapsing universes
• Cosmology in time asymmetric extensions of general relativity
• Higher Order Lagrangians inspired by the Pais-Uhlenbeck Oscillator and their cosmological applications
• Scalar field evolution at background and perturbation levels for a broad class of potentials
• Late time evolution of negatively curved FLRW models
• Observational constraints and dynamical analysis of Kaniadakis horizon-entropy cosmology
• Kaniadakis holographic dark energy: observational constraints and global dynamics