14437705
On the past asymptotic dynamics of non-minimally coupled dark energy
We apply dynamical system techniques to investigate cosmological models inspired in scalar?tensor theories written in the Einstein frame. We prove that if the potential and the coupling function are sufficiently smooth functions, the scalar field almost always diverges into the past. The dynamics of two important invariant sets are investigated in some detail. By assuming some regularity conditions for the potential and the coupling function, a dynamical system is constructed, well suited to investigating the dynamics where the scalar field diverges, i.e. near the initial singularity. The critical points therein are investigated and the cosmological solutions associated with them are characterized. We find that our system admits scaling solutions. Some examples are taken from the bibliography to illustrate the major results. Also we present asymptotic expansions for the cosmological solutions near the initial spacetime singularity, which extend, in a way, the previous results of other researchers.
118368853
Phase space analysis of quintessence fields trapped in a Randall-Sundrum braneworld: anisotropic Bianchi I brane with a positive dark radiation term
In this paper we investigate, from the dynamical systems perspective, the evolution of a scalar field with an arbitrary potential trapped in a Randall–Sundrum's braneworld of type 2. We consider a homogeneous but anisotropic Bianchi I (BI) brane filled with a perfect fluid. We also consider the effect of the projection of the five-dimensional (5D) 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 the de Sitter solution with standard 4D behavior. We also prove that there are no late-time de Sitter attractors with 5D modifications since they are always saddle-like. This fact correlates with a transient primordial inflation. We present here sufficient conditions on the potential for the stability of the scalar field–matter scaling solution, the scalar-field-dominated solution and the scalar field–dark radiation scaling solution. We illustrate our analytical findings using a simple f-deviser as a toy model. All these results are generalizations of our previous results obtained for FRW branes.
119272619
Phantom dark energy with varying-mass dark matter particles: Acceleration and cosmic coincidence problem
Abstract We investigate several varying-mass dark matter particle models in the framework of phantom cosmology. We examine whether there exist late-time cosmological solutions, corresponding to an accelerating universe and possessing dark energy and dark matter densities of the same order. Imposing exponential or power-law potentials and exponential or power-law mass dependence, we conclude that the coincidence problem cannot be solved or even alleviated. Thus, if dark energy is attributed to the phantom paradigm, varying-mass dark matter models cannot fulfill the basic requirement that led to their construction.
119111840
Phase-space analysis of teleparallel dark energy
We perform a detailed dynamical analysis of the teleparallel dark energy scenario, which is based on the teleparallel equivalent of General Relativity, in which one adds a canonical scalar field, allowing also for a nonminimal coupling with gravity. We find that the universe can result in the quintessence-like, dark-energy-dominated solution, or to the stiff dark-energy late-time attractor, similarly to standard quintessence. However, teleparallel dark energy possesses an additional late-time solution, in which dark energy behaves like a cosmological constant, independently of the specific values of the model parameters. Finally, during the evolution the dark energy equation-of-state parameter can be either above or below -1, offering a good description for its observed dynamical behavior and its stabilization close to the cosmological-constant value.
118018657
Cosmological Dynamical Systems
Preface xviiIntroduction 11 A bird’s eye view on cosmology and cosmological problems 131.1 Cosmological models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.1.1 Homogeneity and isotropy: the Roberson-Walker metric . . . . . 161.1.2 Dynamics: the Friedmann equations . . . . . . . . . . . . . . . . 171.1.3 Flat universes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.1.4 Including curvature . . . . . . . . . . . . . . . . . . . . . . . . . 211.1.5 Geometry, destiny and dark energy . . . . . . . . . . . . . . . . . 221.1.6 Scalar ﬁelds and Dark Energy . . . . . . . . . . . . . . . . . . . 232 Qualitative theory of dynamical systems 452.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.2 Qualitative theory of dynamical systems . . . . . . . . . . . . . . . . . . 482.2.1 Deﬁnitions and basic results . . . . . . . . . . . . . . . . . . . . 4 82.2.2 Desirable stability properties of nonlinear vector ﬁ elds . . . . . . 512.2.3 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.2.3.1 Linear stability theorem . . . . . . . . . . . . . . . . . 552.2.4 Flow for autonomous vector ﬁelds . . . . . . . . . . . . . . . . . 5 72.2.5 Invariant sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.2.5.1 Stable, Unstable and Center subspaces of singularpoints of linear autonomous vector ﬁelds . . . . . . . . 602.2.5.2 Stable, Unstable and Center manifolds of singularpoints of nonlinear autonomous vector ﬁelds . . . . . . 642.2.5.3 Center Manifold Theory . . . . . . . . . . . . . . . . . 662.2.5.4 Normal Forms . . . . . . . . . . . . . . . . . . . . . . 682.2.5.5 Asymptotic behavior . . . . . . . . . . . . . . . . . . . 712.3 Procedure for analyzing cosmological dynamical systems . . . . . . . . . 76i
119110648
PHASE SPACE OF ANISOTROPIC Rn COSMOLOGIES
We construct general anisotropic cosmological scenarios governed by an f(R) = Rn gravitational sector. Focusing then on some specific geometries, and modelling the matter content as a perfect fluid, we perform a phase-space analysis. We analyze the possibility of accelerating expansion at late times, and additionally, we determine conditions for the parameter n for the existence of phantom behavior, contracting solutions as well as of cyclic cosmology. Furthermore, we analyze if the universe evolves towards the future isotropization without relying on a cosmic no-hair theorem. Our results indicate that anisotropic geometries in modified gravitational frameworks present radically different cosmological behaviors compared to the simple isotropic scenarios.
118375869
Origin of Structure: Primordial Bispectrum without non-Gaussianities
The primordial bispectrum has been considered in the past decade as a powerful probe of the physical processes taking place in the early Universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that serves to discriminate among competing scenarios concerning the details of the origin of cosmological perturbations. However, all of the scenarios, based on the conventional approach to the so-called "quantum-to-classical transition" during inflation, lack the ability to point out the precise physical mechanism responsible for generating the inhomogeneity and anisotropy of our Universe starting from and exactly homogeneous and isotropic vacuum state associated with the early inflationary regime. In past works, we have shown that the proposals involving a spontaneous dynamical reduction of the quantum state provide plausible explanations for the birth of said primordial inhomogeneities and anisotropies. In the present letter, we show that, when considering single-field slow-roll inflation within the context of such proposals, the expected characteristics of the bispectrum turn out to be quite different from those found in the traditional approach. In particular, the statistical features corresponding to the primordial perturbations, which are normally associated with the bispectrum, are treated here in a novel way leading to rather different conclusions.
118523877
The slow-roll condition and the amplitude of the primordial spectrum of cosmic fluctuations: contrasts and similarities of the standard account and the 'collapse scheme'
The inflationary paradigm enjoys a very wide acceptance in the cosmological community, due largely to the fact that it is said to 'naturally account' for a nearly scale-independent power primordial spectrum of fluctuations which is in very good agreement with the observations. The expected overall scale of the fluctuations in most models turns out to be too large because it is inversely proportional to the slow-roll parameter, which is expected to be very small. This fact requires the fine tuning of the inflaton potential. In series of recent works it has been argued that the success of the inflationary picture is not fully justified in terms of the rules of quantum theory as applied to the cosmological setting and that an extra element, something akin to a self-induced collapse of the wavefunction, is required. There, it was suggested that the incorporation of such a collapse in the treatment might avoid the need for fine tuning of the potential that afflicts most inflationary models. In this paper we will discuss in detail the manner in which one obtains the estimation of the magnitude of the perturbations in the new scheme and that of the standard accounts, comparing one of the most popular among the latter and that corresponding to the new proposal. We will see that the proposal includes a collapse scheme that bypasses the problem, but we will see that the price seems to be a teleological, and thus unphysical, fine tuning of the characteristics of collapse.
54073503
Quantum origin of the primordial fluctuation spectrum and its statistics
The usual account for the origin of cosmic structure during inflation is not fully satisfactory, as it lacks a physical mechanism capable of generating the inhomogeneity and anisotropy of our Universe, from an exactly homogeneous and isotropic initial state associated with the early inflationary regime. The proposal in [A. Perez, H. Sahlmann, and D. Sudarsky, Classical Quantum Gravity, 23, 2317, (2006)] considers the spontaneous dynamical collapse of the wave function, as a possible answer to that problem. In this work, we review briefly the difficulties facing the standard approach, as well as the answers provided by the above proposal and explore their relevance to the investigations concerning the characterization of the primordial spectrum and other statistical aspects of the cosmic microwave background and large-scale matter distribution. We will see that the new approach leads to novel ways of considering some of the relevant questions, and, in particular, to distinct characterizations of the non-Gaussianities that might have left imprints on the available data.
118561121
Multiple quantum collapse of the inflaton field and its implications on the birth of cosmic structure
The standard inflationary account for the origin of cosmic structure is, without a doubt, extremely successful. However, it is not fully satisfactory as has been argued in Perez et al (2006 Class. Quantum Grav. 23 2317). The central point is that, in the standard accounts, the inhomogeneity and anisotropy of our universe seem to emerge, unexplained, from an exactly homogeneous and isotropic initial state through processes that do not break those symmetries. The proposal made there to address this shortcoming calls for a dynamical and self-induced quantum collapse of the original homogeneous and isotropic state of the inflaton. In this paper, we consider the possibility of a multiplicity of collapses in each one of the modes of the quantum field. As we will see, the results are sensitive to a more detailed characterization of the collapse than those studied in the previous works, and in this regard two simple options will be studied. We find important constraints on the model, most remarkably on the number of possible collapses for each mode.