Dynamics of a self-interacting scalar field trapped in the braneworld for a wide variety of self-interaction potentials

Abstract

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped in the braneworld, for a wide variety of self-interaction potentials. We focus on RandallSundrum (RS) and on Dvali-Gabadadze-Porrati (DGP) braneworld models exclusively. These models are complementary to each other: while the RS brane produces ultra-violet (UV) corrections to general relativity, the DGP braneworld modifies Einstein's theory at large scales, i. e., produces infra-red (IR) modifications of general relativity. This study of the asymptotic properties of both braneworld models, shows -in the phase space -the way the dynamics of a scalar field trapped in the brane departs from standard general relativity behaviour.

Scalar-fluid interacting dark energy: Cosmological dynamics beyond the exponential potential

“…This potential was first introduced in [80]. For a canonical scalar field, it has been studied using dynamical systems techniques in [56,81], the cosmological dynamics of some alternative cosmological models using this potential has been also studied in [42,57]. For this potential, we have so that…”

“…We shall see that there are some critical points which exist for a general potential but which do not exist in the exponential potential case. This type of generalization has been done earlier in the context of braneworld theories [32,[57][58][59], tachyon field [60][61][62], quintom field [63], k-essence [42] and loop quantum gravity [64]. Moreover, for this type of analysis beyond the exponential potential, non-hyperbolic points (critical points whose stability matrix contains a vanishing eigenvalue) are usually obtained.…”

Some remarks about non-minimally coupled scalar field models

“…This method, that allows us to perform the whole analysis for a wide range of potentials, is a modification of the method first introduced in [140]. The original method was used for investigating flat FLRW scalar field cosmologies [31,140,141,142,143,144] and it was generalized to several cosmological contexts in [145,146,147,148]. As a drawback of the method of f -devisers it cannot be applied to some specific inflationary potentials like the logarithmic V (φ) ∝ φ p ln q (φ) [149] and the generalized exponential one V (φ) ∝ φ n exp (−λφ m ) [150] since the resulting f -functions are not single valued, then one should apply asymptotic techniques in order to extract the dominant branch at large φ-values as in [149,150].…”

Dark energy with a gradient coupling to the dark matter fluid: cosmological dynamics and structure formation

“…Apart from a mathematical point of view, the generalization to arbitrary scalar field potentials, is also well motivated by the low-energy limit of more fundamental high-energy theories, as well as by comparison with different phenomenological models of DE [12,13]. In order to analyze the cosmological dynamics for arbitrary potentials, we rely on the method developed in [46] for the quintessence field, and subsequently applied in the context of k-essence [47], braneworld theories [33,[48][49][50], tachyon fields [51][52][53], quintom fields [54] and loop quantum gravity [55]. We also discuss the stability of non-hyperbolic critical points (critical points whose Jacobian matrix present eigenvalues of vanishing real part), for which standard linear stability theory fails to determine their properties.…”