Matter and dynamics in closed cosmologies

To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal perfect fluid models, since such models exhibit a particularly rich dynamical structure and also illustrate typical features of more general cases. For these models, we recast Einstein's field equations into a regular system on a compact state space, which is the basis for our analysis. We prove that models expand from a singularity and recollapse to a singularity when the perfect fluid satisfies the strong energy condition. When the matter source admits Einstein's static model, we present a comprehensive dynamical description, which includes asymptotic behavior, of models in the neighborhood of the Einstein model; these results make earlier claims about ``homoclinic phenomena and chaos'' highly questionable. We also discuss aspects of the global asymptotic dynamics, in particular, we give criteria for the collapse to a singularity, and we describe when models expand forever to a state of infinite dilution; possible initial and final states are analyzed. Numerical investigations complement the analytical results

Homoclinic chaos and energy condition violation

In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be non-tilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density $\rho>0$ that evolve through the singularity and beyond as solutions with negative matter energy density $\rho<0$. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass.In addition, we discuss more general models: for solutions that are not locally rotionally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general.Comment: 4 pages, RevTe

New explicit spike solution -- non-local component of the generalized Mixmaster attractor

By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solution is part of the generalized Mixmaster attractor.Comment: Significantly revised. Colour figures simplified to accommodate non-colour printin

Dynamics of Bianchi type I elastic spacetimes

We study the global dynamical behavior of spatially homogeneous solutions of the Einstein equations in Bianchi type I symmetry, where we use non-tilted elastic matter as an anisotropic matter model that naturally generalizes perfect fluids. Based on our dynamical systems formulation of the equations we are able to prove that (i) toward the future all solutions isotropize; (ii) toward the initial singularity all solutions display oscillatory behavior; solutions do not converge to Kasner solutions but oscillate between different Kasner states. This behavior is associated with energy condition violation as the singularity is approached.Comment: 28 pages, 11 figure

Perfect fluids and generic spacelike singularities

We present the conformally 1+3 Hubble-normalized field equations together with the general total source equations, and then specialize to a source that consists of perfect fluids with general barotropic equations of state. Motivating, formulating, and assuming certain conjectures, we derive results about how the properties of fluids (equations of state, momenta, angular momenta) and generic spacelike singularities affect each other.Comment: Considerable changes have been made in presentation and arguments, resulting in sharper conclusion

Asymptotic silence-breaking singularities

We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and non-generic singularities that break asymptotic silence. The emphasis in this paper is on the latter class which have not been previously discussed. We illustrate the above aspects and concepts by describing the singularities of a number of representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure

Monotonic functions in Bianchi models: Why they exist and how to find them

All rigorous and detailed dynamical results in Bianchi cosmology rest upon the existence of a hierarchical structure of conserved quantities and monotonic functions. In this paper we uncover the underlying general mechanism and derive this hierarchical structure from the scale-automorphism group for an illustrative example, vacuum and diagonal class A perfect fluid models. First, kinematically, the scale-automorphism group leads to a reduced dynamical system that consists of a hierarchy of scale-automorphism invariant sets. Second, we show that, dynamically, the scale-automorphism group results in scale-automorphism invariant monotone functions and conserved quantities that restrict the flow of the reduced dynamical system.Comment: 26 pages, replaced to match published versio

Bianchi type I models with two tilted fluids

In this paper we investigate expanding Bianchi type I models with two tilted fluids with linear equations of state. Individually the fluids have non-zero energy fluxes w.r.t. the symmetry surfaces, but these cancel each other because of the Codazzi constraint. Asymptotically toward the past the solutions approach Kasner states if the speeds of sound are less than that of light. If one of the fluids has a speed of sound that is less or equal to 1/3 of the speed of light (radiation) then the models isotropize toward the future, but if both fluids are stiffer than radiation then the final state is anisotropic with non-zero Hubble-normalized shear. The significance of these results is discussed in a broader context.Comment: 19 pages, 2 figure

Use of Antihypertensives, Blood Pressure, and Estimated Risk of Dementia in Late Life: An Individual Participant Data Meta-Analysis

Importance: The utility of antihypertensives and ideal blood pressure (BP) for dementia prevention in late life remains unclear and highly contested. Objectives: To assess the associations of hypertension history, antihypertensive use, and baseline measured BP in late life (age >60 years) with dementia and the moderating factors of age, sex, and racial group. Data Source and Study Selection: Longitudinal, population-based studies of aging participating in the Cohort Studies of Memory in an International Consortium (COSMIC) group were included. Participants were individuals without dementia at baseline aged 60 to 110 years and were based in 15 different countries (US, Brazil, Australia, China, Korea, Singapore, Central African Republic, Republic of Congo, Nigeria, Germany, Spain, Italy, France, Sweden, and Greece). Data Extraction and Synthesis: Participants were grouped in 3 categories based on previous diagnosis of hypertension and baseline antihypertensive use: healthy controls, treated hypertension, and untreated hypertension. Baseline systolic BP (SBP) and diastolic BP (DBP) were treated as continuous variables. Reporting followed the Preferred Reporting Items for Systematic Review and Meta-Analyses of Individual Participant Data reporting guidelines. Main Outcomes and Measures: The key outcome was all-cause dementia. Mixed-effects Cox proportional hazards models were used to assess the associations between the exposures and the key outcome variable. The association between dementia and baseline BP was modeled using nonlinear natural splines. The main analysis was a partially adjusted Cox proportional hazards model controlling for age, age squared, sex, education, racial group, and a random effect for study. Sensitivity analyses included a fully adjusted analysis, a restricted analysis of those individuals with more than 5 years of follow-up data, and models examining the moderating factors of age, sex, and racial group. Results: The analysis included 17 studies with 34 519 community dwelling older adults (20 160 [58.4%] female) with a mean (SD) age of 72.5 (7.5) years and a mean (SD) follow-up of 4.3 (4.3) years. In the main, partially adjusted analysis including 14 studies, individuals with untreated hypertension had a 42% increased risk of dementia compared with healthy controls (hazard ratio [HR], 1.42; 95% CI 1.15-1.76; P = .001) and 26% increased risk compared with individuals with treated hypertension (HR, 1.26; 95% CI, 1.03-1.53; P = .02). Individuals with treated hypertension had no significant increased dementia risk compared with healthy controls (HR, 1.13; 95% CI, 0.99-1.28; P = .07). The association of antihypertensive use or hypertension status with dementia did not vary with baseline BP. There was no significant association of baseline SBP or DBP with dementia risk in any of the analyses. There were no significant interactions with age, sex, or racial group for any of the analyses. Conclusions and Relevance: This individual patient data meta-analysis of longitudinal cohort studies found that antihypertensive use was associated with decreased dementia risk compared with individuals with untreated hypertension through all ages in late life. Individuals with treated hypertension had no increased risk of dementia compared with healthy controls

Use of Antihypertensives, Blood Pressure, and Estimated Risk of Dementia in Late Life

ImportanceThe utility of antihypertensives and ideal blood pressure (BP) for dementia prevention in late life remains unclear and highly contested.ObjectivesTo assess the associations of hypertension history, antihypertensive use, and baseline measured BP in late life (age &amp;amp;gt;60 years) with dementia and the moderating factors of age, sex, and racial group.Data Source and Study SelectionLongitudinal, population-based studies of aging participating in the Cohort Studies of Memory in an International Consortium (COSMIC) group were included. Participants were individuals without dementia at baseline aged 60 to 110 years and were based in 15 different countries (US, Brazil, Australia, China, Korea, Singapore, Central African Republic, Republic of Congo, Nigeria, Germany, Spain, Italy, France, Sweden, and Greece).Data Extraction and SynthesisParticipants were grouped in 3 categories based on previous diagnosis of hypertension and baseline antihypertensive use: healthy controls, treated hypertension, and untreated hypertension. Baseline systolic BP (SBP) and diastolic BP (DBP) were treated as continuous variables. Reporting followed the Preferred Reporting Items for Systematic Review and Meta-Analyses of Individual Participant Data reporting guidelines.Main Outcomes and MeasuresThe key outcome was all-cause dementia. Mixed-effects Cox proportional hazards models were used to assess the associations between the exposures and the key outcome variable. The association between dementia and baseline BP was modeled using nonlinear natural splines. The main analysis was a partially adjusted Cox proportional hazards model controlling for age, age squared, sex, education, racial group, and a random effect for study. Sensitivity analyses included a fully adjusted analysis, a restricted analysis of those individuals with more than 5 years of follow-up data, and models examining the moderating factors of age, sex, and racial group.ResultsThe analysis included 17 studies with 34 519 community dwelling older adults (20 160 [58.4%] female) with a mean (SD) age of 72.5 (7.5) years and a mean (SD) follow-up of 4.3 (4.3) years. In the main, partially adjusted analysis including 14 studies, individuals with untreated hypertension had a 42% increased risk of dementia compared with healthy controls (hazard ratio [HR], 1.42; 95% CI 1.15-1.76; P = .001) and 26% increased risk compared with individuals with treated hypertension (HR, 1.26; 95% CI, 1.03-1.53; P = .02). Individuals with treated hypertension had no significant increased dementia risk compared with healthy controls (HR, 1.13; 95% CI, 0.99-1.28; P = .07). The association of antihypertensive use or hypertension status with dementia did not vary with baseline BP. There was no significant association of baseline SBP or DBP with dementia risk in any of the analyses. There were no significant interactions with age, sex, or racial group for any of the analyses.Conclusions and RelevanceThis individual patient data meta-analysis of longitudinal cohort studies found that antihypertensive use was associated with decreased dementia risk compared with individuals with untreated hypertension through all ages in late life. Individuals with treated hypertension had no increased risk of dementia compared with healthy controls