Dark energy states from quantization of Klein-Gordon equation on
an
accelerating space-time
The world has been shaken by the discovery, in the last ten years, that
Although it is spatially flat, the universe is not only expanding but accelerating,
at least 75% of the universe’s energy density, inferred from galactic dynamics, is ‘dark energy’ in a form associated with neither particulate matter nor known oscillatory forms of radiation.
I will discuss a self-consistent explanation in terms of quantum field theory. When one quantizes an unstable dynamical system, the spectrum of the Hamiltonian energy operator is continuous and unbounded below. In quantum field theory, if one quantizes a classical field with unstable modes (defined by some relativistically invariant hyperbolic PDE), the consequence is that some modes have no associated invariant Boson number operators, and the concept of particle number and vacuum is irrelevant.
The simplest universe with acceleration is the isotropic FLRW universe that expands exponentially. In quantum mechanics, the simplest relativistically invariant extension of the Schroedinger equation is the Klein Gordon equation. In quantum field theory, its space of complex solutions that are twice differentiable in time, and square integrable in space, is considered to be the ‘single particle space’ for the wave function of a scalar spinless Boson field. If we extend this equation in the simplest manner to an accelerating space-time background, we find that the classical massless scalar field has unstable modes but at the current time, only at extremely low wave numbers. The analysis shows that as time progresses, energy is transferred from the oscillatory particle modes to unstable quantum jelly modes at progressively higher wave numbers. The total dark energy increases in proportion to the volume of the universe, leading to a positive cosmological constant in Einstein’s gravitational field equations.
In quantum field theory, there are infinitely many inequivalent (up to unitary equivalence) irreducible representations of the Weyl algebra of observable quantities. So far, useful calculations have been made by using the Fock representation. With expanding modes, there is no vacuum or Fock representation. I indicate how the appropriate representation may be chosen.