Equivalence principle, de-Sitter space, and cosmological twistors

TL;DR

This paper explores how a positive cosmological constant influences the relationship between the equivalence principle and quantum mechanics, highlighting ambiguities in wave function phases and connecting symmetries to cosmological twistor space.

Contribution

It introduces a novel perspective on the impact of the cosmological constant on quantum principles and links non-relativistic symmetries to cosmological twistor structures.

Findings

Identifies phase ambiguity in wave functions due to cosmological effects

Connects Newton-Hooke algebra to non-relativistic limits of cosmological twistor space

Relates the Penrose and Unruh effects to cosmological phenomena

Abstract

I discuss the impact of the positive cosmological constant on the interplay between the equivalence principle in general relativity, and the rules of quantum mechanics. At the non--relativistic level there is an ambiguity in the definition of a phase of a wave function measured by inertial and accelerating observes. This is the cosmological analogue of the Penrose effect, which can also be seen as a non--relativistic limit of the Unruh effect. The symmetries of the associated Schr\"odinger equation are generated by the Newton--Hooke algebra, which arises from a non--relativistic limit of a cosmological twistor space.