Milne Spacetime Research Articles

Global Stability of the Open Milne Spacetime

Global Stability of the Open Milne Spacetime

The Stability of Relativistic Fluids in Linearly Expanding Cosmologies

Abstract In this paper, we study cosmological solutions to the Einstein–Euler equations. We first establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations on fixed linearly expanding cosmological spacetimes with a linear equation of state $p=K \rho $ for the parameter values $K \in (0,1/3)$. This removes the restriction to irrotational perturbations in earlier work [ 15] and relies on a novel transformation of the fluid variables that is well-adapted to Fuchsian methods. We then apply this new transformation to show the global regularity and stability of the Milne spacetime under the coupled Einstein–Euler equations, again with a linear equation of state $p=K \rho $, $K \in (0,1/3)$. Our proof requires a correction mechanism to account for the spatially curved geometry. In total, this is indicative that structure formation in cosmological fluid-filled spacetimes requires an epoch of decelerated expansion.

Milne spacetime with conical defect: Some holographic studies

We initiate a holographic study of field theory in a time-dependent background with a conical defect. We focus on the Milne spacetime to which, in the absence of cosmological constant, at late time any hyperbolic Friedmann-Robertson-Walker metric flows. When the Milne vacuum is represented by the adiabatic one, we are able to compute the two point correlators of operators which are dual to the massive scalars in the bulk AdS-Milne spacetime background with a defect. We find, for both twisted and untwisted operators, the correlators can be represented as the sum over images. This sum can be carried out explicitly to write the results in compact forms.

Detecting the massive bosonic zero-mode in expanding cosmological spacetimes

We examine a quantised massive scalar field in $(1+1)$-dimensional spatially compact cosmological spacetimes in which the early time and late time expansion laws provide distinguished definitions of Fock "in" and "out" vacua, with the possible exception of the spatially constant sector, which may become effectively massless at early or late times. We show, generalising the work of Ford and Pathinayake, that when such a massive zero mode occurs, the freedom in the respective "in" and "out" states is a family with two real parameters. As an application, we consider massive untwisted and twisted scalar fields in the $(1+1)$-dimensional spatially compact Milne spacetime, where the untwisted field has a massive "in" zero mode. We demonstrate, by a combination of analytic and numerical methods, that the choice of the massive "in" zero mode state has a significant effect on the response of an inertial Unruh-DeWitt detector, especially in the excitation part of the spectrum. The detector's peculiar velocity with respect to comoving cosmological observers has the strongest effect in the "in" vacuum of the untwisted field, where it shifts the excitation and de-excitation resonances towards higher values of the detector's energy gap.

Cosmological solutions with gravitational particle production and nonzero curvature

In a homogeneous and isotropic universe with non-zero spatial curvature we consider the effects of gravitational particle production in the dynamics of the universe. We show that the dynamics of the universe in such a background is characterized by a single nonlinear differential equation which is significantly dependent on the rate of particle creation and whose solutions can be dominated by the curvature effects at early times. For different particle creation rates we apply the singularity test in order to find the analytic solutions of the background dynamics. We describe the behavior of the cosmological solutions for both open and closed universes. We also show how the effects of curvature can be produced by the presence of a second perfect fluid with an appropriate equation of state. By combining that results with the analysis of the critical points we find that our consideration can be related with the pre-inflationary era. Specifically we find that for negative spatial curvature small changes of the Milne spacetime leads to a de Sitter universe.

Spinorial wave equations and stability of the Milne spacetime

The spinorial versions of the conformal vacuum Einstein field equations are used to construct a system of quasilinear wave equations for the various conformal fields. As a part of the analysis we also show how to construct a subsidiary system of wave equations for the zero quantities associated to the various conformal field equations. This subsidiary system is used, in turn, to show that under suitable assumptions on the initial data a solution to the wave equations for the conformal fields implies a solution to the actual conformal Einstein field equations. The use of spinors allows for a more unified deduction of the required wave equations and the analysis of the subsidiary equations than similar approaches based on the metric conformal field equations. As an application of our construction we study the nonlinear stability of the Milne Universe. It is shown that sufficiently small perturbations of initial hyperboloidal data for the Milne Universe gives rise to a solution to the Einstein field equations which exists towards the future and has an asymptotic structure similar to that of the Milne Universe.

The symmetries and conservation laws of some Gordon-type equations in Milne space-time

In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented and analysed. Using the Lie point symmetries, it is showed how to reduce Gordon-type wave equations using the method of invariants, and to obtain exact solutions corresponding to some boundary values. The Noether point symmetries and conservation laws are obtained for the Klein–Gordon equation in one case. Finally, the existence of higherorder variational symmetries of a projection of the Klein–Gordon equation is investigated using the multiplier approach.

Diversity in the phoenix universe

It has recently been argued by Copeland et al. that in eleven dimensions two orbifold planes can collide and bounce in a regular way, even when the bulk metric is perturbed away from Milne spacetime to a Kasner solution. In this paper, we point out that as a consequence the global "phoenix" structure of the cyclic universe is significantly enriched. Spatially separated regions, with different density fluctuation amplitudes as well as different non-gaussian characteristics, are all physically realized. Those regions containing by far the most structure are specified by a fluctuation amplitude of Q ~ 10^{-4.5} and local non-gaussianity parameters f_{NL} ~ O(+/- 10) and g_{NL} ~ O(-10^3), in agreement with current observations.

Perturbations of generic Kasner spacetimes and their stability

This article investigates the stability of a generic Kasner spacetime to linear perturbations, both at late and early times. It demonstrates that the perturbation of the Weyl tensor diverges at late time in all cases but in the particular one in which the Kasner spacetime is the product of a two-dimensional Milne spacetime and a two-dimensional Euclidean space. At early times, the perturbation of the Weyl tensor also diverges unless one imposes a condition on the perturbations so as to avoid the most divergent modes to be excited.

The axially symmetric p-modes of Maxwell radiation in Milne spacetime

The aim of this work is to give a fully covariant treatment of the ( l = 1 , m = 0 ) -electromagnetic excitations into the linearly expanding ( k = - 1 ) -Universe. For the corresponding radiating dipole, the closed form solutions, in the axially symmetric Lorentz–Coulomb gauge, are derived in terms of the Legendre associated functions. In order to get completeness in the physical interpretation, we have turned to hypergeometric functions and compute, in the far-field region, the observables of the entirely radiating field and the effective power.

A relationship between scalar Green functions on hyperbolic and Euclidean Rindler spaces

We derive a formula connecting in any dimension the Green function on the (D + 1)-dimensional Euclidean Rindler space and the one for a minimally coupled scalar field with a mass m in the D-dimensional hyperbolic space. The relation takes a simple form in the momentum space where the Green functions are equal at the momenta (p0, p) for Rindler and for hyperbolic space with a simple additive relation between the squares of the mass and the momenta. The formula has applications to finite temperature Green functions, Green functions on the cone and on the (compactified) Milne spacetime. Analytic continuations and interacting quantum fields are briefly discussed.

Classical propagation of strings across a big crunch/big bang singularity

One of the simplest time-dependent solutions of M theory consists of nine-dimensional Euclidean space times $1+1$-dimensional compactified Milne space-time. With a further modding out by ${Z}_{2}$, the space-time represents two orbifold planes which collide and re-emerge, a process proposed as an explanation of the hot big bang [J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Phys. Rev. D 64, 123522 (2001).][P. J. Steinhardt and N. Turok, Science 296, 1436 (2002).][N. Turok, M. Perry, and P. J. Steinhardt, Phys. Rev. D 70, 106004 (2004).]. When the two planes are near, the light states of the theory consist of winding M2-branes, describing fundamental strings in a particular ten-dimensional background. They suffer no blue-shift as the M theory dimension collapses, and their equations of motion are regular across the transition from big crunch to big bang. In this paper, we study the classical evolution of fundamental strings across the singularity in some detail. We also develop a simple semiclassical approximation to the quantum evolution which allows one to compute the quantum production of excitations on the string and implement it in a simplified example.

COVARIANT ANALYSIS OF NEWTONIAN MULTI-FLUID MODELS FOR NEUTRON STARS II: STRESS–ENERGY TENSORS AND VIRIAL THEOREMS

The 4-dimensionally covariant approach to multiconstituent Newtonian fluid dynamics presented in the preceding paper of this series is developed by construction of the relevant 4-dimensional stress–energy tensor whose conservation in the non-dissipative variational case is shown to be interpretable as a Noether identity of the Milne spacetime structure. The formalism is illustrated by the application to homogeneously expanding cosmological models, for which appropriately generalized local Bernoulli constants are constructed. Another application is to the Iordanski type generalization of the Joukowski formula for the Magnus force on a vortex. Finally, at a global level, a new (formally simpler but more generally applicable) version of the "virial theorem" is obtained for multiconstituent — neutron or other — fluid star models as a special case within an extensive category of formulae whereby the time evolution of variously weighted mass moment integrals is determined by corresponding space integrals of stress tensor components, with the implication that all such stress integrals must vanish for any stationary equilibrium configuration.

COVARIANT ANALYSIS OF NEWTONIAN MULTI-FLUID MODELS FOR NEUTRON STARS I: MILNE–CARTAN STRUCTURE AND VARIATIONAL FORMULATION

This is the first of a series of articles showing how 4 dimensionally covariant analytical procedures developed in the context of General Relativity can be usefully adapted for application in a purely Newtonian framework where they provide physical insights (e.g. concerning helicity currents) that are not so easy to obtain by the traditional approach based on a 3+1 spacetime decomposition. After an introductory presentation of the relevant Milne spacetime structure and the associated Cartan connection, the essential principles are illustrated by application to the variational formulation of simple barotropic perfect fluid models. This variational treatment is then extended to conservative multiconstituent self-gravitating fluid models of the more general kind that is needed for treating the effects of superfluidity in neutron stars.

Bellert's general relativity theory

In this paper, new ideas from our previous paper (Rydzynska, 1989)-i.e., problems connected with the new equivalence principle-have been developed. It is conformed, that certain static particles from Bellert's space-time are equivalent to a free particle from classic Milne's space-time. Mention is made of the algebraic structure of Bellert's space-time from (Rydzynska, 1990b). The space-time interval in this space-time, and its connection with a probability and the physical meaning of this interval and probability, has been defined. In the last section we derive dynamical equations for Bellert's space-time, i.e., we do the foundations of Bellert's general relativity theory.