Critical Robertson-Walker universes

Abstract

The integral of the energy density function $\mathfrak{m}$ of a closed Robertson-Walker (RW) spacetime with source a perfect fluid and cosmological constant $\Lambda$ gives rise to an action functional on the space of scale functions of RW spacetime metrics. This paper studies closed RW spacetimes which are critical for this functional, subject to volume-preserving variations (critical RW spacetimes). A complete classification of critical RW spacetimes is given and explicit solutions in terms of Weierstrass elliptic functions and their degenerate forms are computed. The standard energy conditions (weak, dominant, and strong) as well as the cyclic property of critical RW spacetimes are discussed.

arXiv comment18 pages, LaTex

References in corpus (22)

• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• The Application of Weierstrass elliptic functions to Schwarzschild Null Geodesics
• Massive spinning particles and the geometry of null curves
• Bounce universe from string-inspired Gauss-Bonnet gravity
• Corrected Entropy of Friedmann-Robertson-Walker Universe in Tunneling Method
• Apparent horizon and gravitational thermodynamics of the Universe: Solutions to the temperature and entropy confusions, and extensions to modified gravity
• Geometrical particle models on 3D null curves
• Complete Integrability for Lagrangian Dependent on Acceleration in a Space-Time of Constant Curvature
• Particle with torsion on 3d null-curves
• Hamiltonian flows on null curves
• Closed trajectories of a particle model on null curves in anti-de Sitter 3-space
• Reduction for constrained variational problems on 3D null curves
• Conformal geometry of timelike curves in the (1+2)-Einstein universe
• The geometric Cauchy problem for the membrane shape equation
• Quantization of the conformal arclength functional on space curves
• Supersymmetry of FRW barotropic cosmologies
• The Weierstrass Criterion and the Lemaitre-Tolman-Bondi Models with Cosmological Constant λ
• Reconstruction of the equation of state for the cyclic universes in homogeneous and isotropic cosmology
• Lorentzian manifolds with transitive conformal group
• Parametric solution of certain nonlinear differential equations in cosmology
• Geometric phases and cyclic isotropic cosmologies
• Applications of Elliptic and Theta Functions to Friedmann-Robertson-Lemaitre-Walker Cosmology with Cosmological Constant