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 Randall-Sundrum (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.
We apply the dynamical systems tools to study the (linear) cosmic dynamics of a Dirac-Born-Infeld-type field trapped in the braneworld. We focus,exclusively, in Randall-Sundrum and in Dvali-Gabadadze-Porrati brane models. We analyze the existence and stability of asymptotic solutions for the AdS throat and the quadratic potential and a particular choice of the warp factor and of the potential for the DBI field ($f(ϕ)=1/V(ϕ)$). It is demonstrated, in particular, that in the ultra-relativistic approximation matter-scaling and scalar field-dominated solutions always arise. In the first scenario t…
We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a Randall-Sundrum brane. The simplest kinds of self-interaction potentials are investigated: a) constant potential, and b) exponential potential. It is shown that the dynamics of the Randall-Sundrum model significantly differs from the standard four-dimensional behavior at early times: in all cases of interest the (singular) empty universe is the past attractor for every trajectory in phase space, meanwhile the kinetic energy-dominated solution is always a saddle critical point. The …
A proposal to study the effect of interaction in an agegraphic dark energy model in DGP brane-world cosmology is presented in this manuscript. After explaining the details, we proceed to apply the dynamical system approach to the model to analyze its stability. We first, constrain model parameters with a variety of independent observational data such as cosmic microwave background anisotropies, baryon acoustic oscillation peaks and observational Hubble data. Then, we obtain the critical points related to different cosmological epochs. In particular, we conclude that in the presence of interact…
In this paper we investigate, from the dynamical systems perspective, the evolution of an scalar field with arbitrary potential trapped in a Randall-Sundrum's Braneworld of type II. We consider an homogeneous and isotropic Friedmann-Robertson-Walker (FRW) brane filled also with a perfect fluid. Center Manifold Theory is employed to obtain sufficient conditions for the asymptotic stability of de Sitter solution. We obtain conditions on the potential for the stability of scaling solutions as well for the stability of the scalar-field dominated solution. We prove the there are not late time attra…
In this paper we investigate, from the dynamical systems perspective, the evolution of an scalar field with arbitrary potential trapped in a Randall-Sundrum's Braneworld of type 2. We consider an homogeneous but anisotropic Bianchi I (BI) brane filled also with a perfect fluid. We also consider the effect of the projection of the five-dimensional Weyl tensor onto the three-brane in the form of a positive Dark Radiation term. Using the center manifold theory we obtain sufficient conditions for the asymptotic stability of de Sitter solution with standard 4D behavior. We also prove that there are…
We explore the cosmological aspects of interacting Tsallis holographic dark energy (THDE) in a $q$-modified DGP braneworld setup emerging from non-Gaussian statistical mechanics.To this end, three classes of superstatistics, that is, log-normal, inverse $χ^2$ and $χ^2$ superstatistics were incorporated into the model. We examined the implication of the three superstatistics on different cosmological parameters, namely, the dimensionless energy density and the equation-of-state (EoS) of THDE, along with the deceleration parameter and the squared speed of sound. As a result, we noted that the co…
We study motion of current-carrying string loops in the field of braneworld spherically symmetric black holes and naked singularities. The spacetime is described by the RN geometry with tidal charge b reflecting the non-local tidal effects coming from the external dimension; both positive and negative values of the spacetime parameter b are considered. We restrict attention to the axisymmetric motion of string loops when the motion can be fully governed by an appropriately defined effective potential related to the energy and angular momentum of the string loops. In dependence on these two con…
A unified model is developed within the context of the braneworld paradigm, where a single scalar field can act as both the inflaton field in the very early universe and also as strong, self-interacting dark matter in the post-inflationary universe. Reheating proceeds due to the overproduction and subsequent evaporation of primordial black holes. Observational constraints, most notably from gravitational waves, are satisfied if the probability of PBH formation is sufficiently high.
In the evolution of late universe, the main source of matter are Dark energy and Dark matter. They are indirectly detected only through their gravitational manifestations. So the possibility of interaction with each other without violating observational restrictions is not ruled out. With this motivation, we investigate the dynamics of DGP braneworld where source of dark energy is a scalar field and it interacts with matter source. Since observation favours phantom case more, we have also studied the dynamics of interacting phantom scalar field. In non interacting DGP braneworld there are no l…
We apply bulk holographic dark energy in general braneworld models with a Gauss-Bonnet term in the bulk and an induced gravity term and a perfect fluid on the brane. Without making any additional assumptions we extract the Friedmann equation on the physical brane and we show that a $ρ$-$ρ_Λ$ coupling arises naturally by the full 5D dynamics. The low-energy (late-time) evolution reveals that the effective 4D holographic dark energy behaves as ``quintom'', that is it crosses the phantom divide $w=-1$ during the evolution. In particular, the Gauss-Bonnet contribution decreases the present value o…
The illustration of cosmic acceleration under two interacting dark energy models (pilgrim dark energy with Granda and Oliveros cutoff and its generalized ghost version) in DGP braneworld framework is presented. In the current scenario, the equation of state parameter, deceleration parameter, $ω_{D}-ω'_{D}$ plane and statefinder diagnosis are investigated. The equation state parameter behave-like phantom era of the universe. The deceleration parameter depicts the accelerated expansion of the universe in both models. The cosmological planes like $ω_{D}-ω'_{D}$ and statefinder corresponds to $Λ$C…
Extremely Compact Stars (ECS) contain trapped null geodesics. When such objects enter the evolution period admitting geodetical motion of neutrinos, certain part of neutrinos produced in their interior will be trapped influencing their neutrino luminosity and thermal evolution. We study neutrino trapping in the braneworld ECS, assuming uniform distribution of neutrino emissivity and massless neutrinos. We give the efficiency of the neutrino trapping effects in the framework of the simple model of the internal spacetime with uniform distribution of energy density, and external spacetime describ…
We study localization properties of fundamental fields which are coupled to one another through the gauge mechanism both in the original Randall-Sundrum (RS) and in the modified Randall-Sundrum (MRS) braneworld models: scalar-vector, vector-vector, and spinor-vector configuration systems. For this purpose we derive conditions of localization, namely the finiteness of integrals over the extra coordinate in the action of the system considered. We also derive field equations for each of the systems and then obtain their solutions corresponding to the extra dimension by a separation of variable me…
In this work we present a phase space analysis of a quintessence field and a perfect fluid trapped in a Randall-Sundrum's Braneworld of type 2. We consider a homogeneous but anisotropic Bianchi I brane geometry. Moreover, we consider the effect of the projection of the five dimensional Weyl tensor onto the three-brane in the form of a negative Dark Radiation term. For the treatment of the potential we use the "Method of $f$-devisers" that allows investigating arbitrary potentials in a phase space. We present general conditions on the potential in order to obtain the stability of standard 4D an…
We investigate a model of brane cosmology to find a unified description of the radiation-matter-dark energy universe. It is of the interacting holographic dark energy with a bulk-holographic matter $χ$. This is a five-dimensional cold dark matter, which plays a role of radiation on the brane. Using the effective equations of state $ω^{\rm eff}_{\rm Λ}$ instead of the native equations of state $ω_{\rm Λ}$, we show that this model cannot accommodate any transition from the dark energy with $ω^{\rm eff}_{\rm Λ}\ge-1$ to the phantom regime $ω^{\rm eff}_{\rm Λ}<-1$. Furthermore, the case of interac…
We investigate the ghost model of dark energy in the framework of DGP braneworld. We explore the cosmological consequences of this model by determining the equation of state parameter, $ω_D$, the deceleration and the density parameters. We also examine the stability of this model by studying the squared of the sound speed in the presence/absence of interaction term between dark energy and dark matter. We find out that in the absence of interaction between two dark sectors of the Universe we have $ω_D\rightarrow -1$ in the late time, while in the presence of interaction $ω_D$ can cross the phan…
We study gravitational redshift of photons and neutrinos radiated by the braneworld neutron or quark stars that are considered in the framework of the simple model of the internal spacetime with uniform distribution of energy density, and the external spacetime described by the Reissner-Nordström geometry characterized by the braneworld "tidal" charge $b$. For negative tidal charges, the external spacetime is of the black-hole type, while for positive tidal charges, the external spacetime can be of both black-hole and naked-singularity type. We consider also extremely compact stars allowing ex…
The low energy regime of 5D braneworld models with a bulk scalar field is studied. The setup is rather general and includes the Randall-Sundrum and dilatonic braneworlds models as particular cases. We discuss the cosmological evolution of the system and conclude that, in a two brane system, the negative tension brane is generally expected to evolve towards a null warp-factor state. This implies, for late time cosmology, that both branes end up interacting weakly. We also analyze the observational constraints imposed by solar-system and binary-pulsar tests on the braneworld configuration. This …
We investigated the effects of the spacetime curvature and extra dimensions on the excitations of a self-interacting vector field known as the bumblebee field. The self-interacting quadratic potential breaks the gauge invariance and the vacuum expectation value (VEV) of the bumblebee field $b_M$ violates the local particle Lorentz symmetry. By assuming the bumblebee field living in a $AdS_{5}$ bulk, we found an exponential suppression of the self-interacting constant $λ$ and the bumblebee VEV along the extra dimension. The fluctuations of the bumblebee upon the VEV can be decomposed into trans…
Positively-curved, oscillatory universes have recently been shown to have important consequences for the pre-inflationary dynamics of the early universe. In particular, they may allow a self-interacting scalar field to climb up its potential during a very large number of these cycles. The cycles are naturally broken when the potential reaches a critical value and the universe begins to inflate, thereby providing a `graceful entrance' to early universe inflation. We study the dynamics of this behaviour within the context of braneworld scenarios which exhibit a bounce from a collapsing phase to …
The purpose of this paper is to study the Tsallis agegraphic dark energy with an interaction term between dark energy and dark matter in the DGP brane-world scenario. For this, we assume some initial conditions to obtain the dark energy density, deceleration, dark energy EoS, and total EoS parameters. Then, we analyze the statefinder parameters, $ω'{}_{DE}-ω_{DE}$ plots, and classical stability features of the model. The results state that the deceleration parameter provides the phase transition from decelerated to accelerated phase. The $ω_{DE}$ graphs show the phantom behavior, while the $ω_…
The braneworld model of gravity is well-known for several notable cosmological features such as self-acceleration originating from a geometric and not matter source, effective dark energy behavior with phantom characteristics but not leading to a Big-Rip singularity, rough resemblance to the $Λ$CDM evolution, etc. The dynamical system tools usually allow us to obtain generic conclusions on the global dynamics of a system over a wide range of initial conditions. With this motivation, in order to recover the important features of the braneworld model from a more global perspective, here, we inve…
