Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant

Abstract

We consider solutions to the Einstein-massless-scalar field system with a positive cosmological constant, arising from sufficiently regular, near-FLRW, initial data. We establish global existence in the future direction and derive their precise asymptotic behavior towards infinity. As a corollary, we infer that, unlike the FLRW background, the perturbed solutions do not describe a regular irrotational stiff fluid with linear equation of state $p=\rho$, for general asymptotic data at infinity. The reason for the breakdown of this interpretation is that the gradient of the scalar field stops being timelike at large times, eventually becoming null and then spacelike near infinity. Our results hold for open sets of initial data in Sobolev spaces without symmetries.

final version published in JMP

References in corpus (3)

• Stable Big Bang formation for Einstein's equations: The complete sub-critical regime
• On the initial value problem for the wave equation in Friedmann -- Robertson -- Walker space-times
• A conformal approach to the stability of Einstein spaces with spatial sections of negative scalar curvature

Cited by in corpus (4)

• On the stability of relativistic perfect fluids with linear equations of state $p=K\rho$ where $1/3<K<1$
• Future instability of FLRW fluid solutions for linear equations of state $p=K\rho$ with $1/3<K<1$
• Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state $p=K\rho$ with $0\le K<1/3$
• Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant