Oscillators and repellers in an expanding accelerating universe

"The domain of quantum phenomena has long been recognised to be at the atomic scale. For more than 50 years after the invention of quantenmechanik in the 1902s [I], it was preposterous to consider quantum feld effects at cosmological scales. However by the wave-particle duality that was first encountered theoretically in de Broglie’s matter waves, and experimentally in the photoelectric effect and the Compton scattering, particle 4 momentum is directly related to frequency and wave number of the matter wave even though the unambiguous oscillatory nature of a field requires an observer to be in an inertial reference frame that is, according to Mach’s principle, defined by the overall structure of the universe at large. Two discoveries of the matters meant that an in-tandem study of large-scale gravitation and quantum effects could not be avoided. The first was the Hawking effect of black hole evaporation [2]. The second, the Unruh effect, came from studying the Hawking effect at a fundamental level: A vacuum state in an inertial frame contains particles in an accelerating reference frame, with a thermal black-body distribution of particle energies [2] at a Boltzmann temperature kBT = _a. The Hawking spectrum is the special case when acceleration a is the gravitational acceleration at a Schwarzschild surface. This gives a beautifully simple relationship involving the speed of light, Planck’s constant, Boltzmann’s constant and the universal gravitational constant. Now there are several monographs on quantum fields in curved space, the earliest [2] having an Australian connection."