118627594
Qualitative analysis of Kantowski-Sachs metric in a generic class of f(R) models
In this paper we investigate, from the dynamical systems perspective, the evolution of a Kantowski-Sachs metric in a generic class of f(R) models. We present conditions (i.e., differentiability conditions, existence of minima, monotony intervals, etc.) for a free input function related to the f(R), that guarantee the asymptotic stability of well-motivated physical solutions, specially, self-accelerated solutions, allowing to describe both inflationary- and late-time acceleration stages of the cosmic evolution. We discuss which f(R) theories allows for a cosmic evolution with an acceptable matter era, in correspondence to the modern cosmological paradigm. We find a very rich behavior, and amongst others the universe can result in isotropized solutions with observables in agreement with observations, such as de Sitter, quintessence-like, or phantom solutions. Additionally, we find that a cosmological bounce and turnaround are realized in a part of the parameter-space as a consequence of the metric choice.
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.
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.
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
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.
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.
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.
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.
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.