119460309
Quintom cosmologies admitting either tracking or phantom attractors
Abstract In this Letter we investigate the evolution of a class of cosmologies fueled by quintom dark energy and dark matter. Quintom dark energy is a hybrid of quintessence and phantom which involves the participation of two real scalar fields playing the roles of those two types of dark energy. In that framework we examine, from a dynamical systems perspective, the possibility that those fields are coupled among them by considering an exponential potential with an interesting functional dependence similar but not identical to others studied before. The model we consider represents a counterexample to the typical behavior of quintom models with exponential potentials because it admits either tracking attractors ( w = 0 ), or phantom attractors ( w − 1 ).
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.
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.
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.
119264796
Quintom phase-space: beyond the exponential potential
Abstract We investigate the phase-space structure of the quintom dark energy paradigm in the framework of spatially flat and homogeneous universe. We have also included radiation and dark matter, both matter components are described as perfect fluids. Considering arbitrary decoupled potentials, we find certain general conditions under which the phantom-dominated solution is a late time attractor, generalizing previous results found for the case of an exponential potential. Center Manifold Theory is employed to obtain sufficient conditions for the instability of de Sitter solution either with phantom or quintessence potential dominance.
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.
119194137
The collapse of the wave function in the joint metric-matter quantization for inflation
It has been argued that the standard inflationary scenario suffers from a serious deficiency as a model for the origin of the seeds of cosmic structure: it can not truly account for the transition from an early homogeneous and isotropic stage to another one lacking such symmetries. The issue has often been thought as a standard instance of the “quantum measurement problem”, but as has been recently argued by some of us, that quagmire reaches a critical level in the cosmological context of interest here. This has lead to a proposal in which the standard paradigm is supplemented by a hypothesis concerning the self-induced dynamical collapse of the wave function, as representing the physical mechanism through which such change of symmetry is brought forth. This proposal was originally formulated within the context of semiclassical gravity. Here we investigate an alternative realization of such idea implemented directly within the standard analysis in terms of a quantum field jointly describing the inflaton and metric perturbations, the so called Mukhanov–Sasaki variable. We show that even though the prescription is quite different, the theoretical predictions include some deviations from the standard ones, which are indeed very similar to those found in the early studies. We briefly discuss the differences between the two prescriptions, at both, the conceptual and practical levels.
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.
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.
6373600
Novel possibility of nonstandard statistics in the inflationary spectrum of primordial inhomogeneities
Inflation is considered one of the cornerstones of modern cosmology. However, the account of the origin of cosmic structure, as provided by the standard inflationary paradigm, is not fully satisfactory. The fundamental issue is the inability of the usual account to point out the physical mechanism responsible for generating the inhomogeneity and anisotropy of our Universe, starting from the exactly homogeneous and isotropic vacuum state associated with the early inflationary regime. We briefly review this issue here together with the proposal to address this shortcoming in terms of a dynamical collapse of the vacuum state of the inflaton field, which has been considered in previous works. The main goal of this manuscript is to discuss certain statistical aspects associated with the collapse and its implications in the primordial spectrum, particularly those connected with the possible appearance of a novel type of unusual correlations.