When is stability in the eye of the beholder\? Comments on a singular initial-value problem for a nonlinear differential equation arising in semiclassical cosmology

Mathematics – Logic

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Scientific paper

A mathematical phenomenon discovered by Suen for the vacuum solution of the semiclassical Einstein equation is shown to occur also for the equation of motion of a free particle, recast in strange variables. Consequently, this instability may not necessarily be a physical pathology of semiclassical cosmological theory. Solutions with reasonable initial values for both the Hubble constant and a quantity related to the deceleration parameter are stable. The physical significance of the instability therefore hinges on which variables can be regarded as ``controllable'' by observations.

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