Averaging generalized scalar field cosmologies II: locally rotationally symmetric Bianchi I and flat Friedmann–Lemaître–Robertson–Walker models

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic equation of state (EoS) with barotropic index $$\gamma $$ γ for the locally rotationally symmetric (LRS) Bianchi I and flat Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $$\gamma $$ γ , the late-time attractors of physical interests are flat quintessence dominated FLRW universe and Einstein-de Sitter solution. With this approach, the oscillations entering the system through the Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble parameter H – acting as time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behavior.

On the existence of marginally trapped tubes in spacetimes with local rotational symmetry

Let M be a locally rotationally symmetric spacetime with at least one of the rotation or spatial twist being non-zero. It is proved that M cannot admit a non-minimal marginally trapped tube of the form $$\chi =X(t)$$ χ = X ( t ) .

Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open Friedmann–Lemaître–Robertson–Walker models

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $$\gamma $$ γ for locally rotationally symmetric (LRS) Bianchi III metric and open Friedmann–Lemaître–Robertson–Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic index $$\gamma $$ γ late-time attractors of physical interests for LRS Bianchi III metric are Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de Sitter, quintessence or zero acceleration solutions) and matter-curvature scaling solution. For open FLRW metric late-time attractors are a matter dominated FLRW universe and Milne solution. With this approach, oscillations entering nonlinear system through Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble factor H – acting as a time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behaviour.

Κοσμολογία στη Θεωρία Einstein - Aether

Στην διατριβή αυτή παρουσιάζουμε αρχικά τον χώρο λύσεων των εξισώσεων πεδίου της θεωρίας Eistein-Aether για την περίπτωση του χωρόχρονου FLRW καθώς και για την περίπτωση του χωρόχρονου Locally Rotationally Symmetric (LRS) Bianchi Type III . Στην περίπτωση του FLRW βρίσκουμε ανηγμένες Λαγκρανζιανές που αναπαράγουν σωστά τις εξισώσεις κίνησης. Οι εξισώσεις αυτές δεν επιδέχονται λύσεις για όλο τον χώρο των αρχικών παραμέτρων. Οι ανηγμένες Λαγκρανζιανές συνάγονται μέσω ολοκλήρωσης των μη ουσιωδών συντεταγμένων στην ολική δράση και περιγράφουν σωστά την δυναμική οποτεδήποτε υπάρχουν λύσεις των εξισώσεων. Τελικά στην FLRW περίπτωση υπάρχει μια ανωμαλία καμπυλότητας, ενώ στην περίπτωση του Bianchi Type III υπάρχουν επιλογές του εύρους των παραμέτρων για τις οποίες δεν υπάρχει ανωμαλία καμπυλότητας. Στην συνέχεια παρουσιάζουμε τον χώρο λύσεων για τις εξισώσεις πεδίου της θεωρίας Eistein-Aether για την περίπτωση του χωρόχρονου vacuum Bianchi Type V . Βρίσκουμε τμήματα του πεδίου ορισμού των αρχικών παραμέτρων για τα οποία οι ανηγμένες εξισώσεις πεδίου δεν επιδέχονται καμία λύση. Οποτεδήποτε υπάρχουν λύσεις εξετάζεται η φυσική τους ερμηνεία μέσα απο την συμπεριφορά των βαθμωτών Ricci και Kretschmann, καθώς επίσης και η ταυτοποίηση του τελεστή ενέργειας-ορμής σε σχέση με ένα ιδανικό ρευστό. Υπάρχουν περιπτώσεις όπου δεν παρατηρείται καμία ανωμαλία και άλλες όπου το ενεργό ρευστό είναι ισοτροπικό.

Geometric properties of a certain class of compact dynamical horizons in locally rotationally symmetric class II spacetimes

In this paper, we study the geometry of a certain class of compact dynamical horizons with a time-dependent induced metric in locally rotationally symmetric class II spacetimes. We first obtain a compactness condition for embedded [Formula: see text]-manifolds in these spacetimes, satisfying the weak energy condition, with non-negative isotropic pressure [Formula: see text]. General conditions for a [Formula: see text]-manifold to be a dynamical horizon are imposed, as well as certain genericity conditions, which in the case of locally rotationally symmetric class II spacetimes reduces to the statement that “the weak energy condition is strictly satisfied or otherwise violated”. The compactness condition is presented as a spatial first-order partial differential equation in the sheet expansion [Formula: see text], in the form [Formula: see text], where [Formula: see text] is the Gaussian curvature of [Formula: see text]-surfaces in the spacetime and [Formula: see text] is a real number parametrizing the differential equation, where [Formula: see text] can take on only two values, [Formula: see text] and [Formula: see text]. Using geometric arguments, it is shown that the case [Formula: see text] can be ruled out and the [Formula: see text] ([Formula: see text]-dimensional sphere) geometry of compact dynamical horizons for the case [Formula: see text] is established. Finally, an invariant characterization of this class of compact dynamical horizons is also presented.