2014/04/30 by C. Wetterich · 3 citations
Mathematics · Physics and Astronomy · #Astrophysics #Big Bang (financial markets) #Big Bounce #Big Crunch #Big Rip #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Dark energy #De Sitter universe #Galaxies: Formation, Evolution, Phenomena #Geometry #Inflation (cosmology) #Initial singularity #Massless particle #Mathematical physics #Mathematics #Metric expansion of space #Observable #Particle horizon #Physical cosmology #Physics #Quantum mechanics #Singularity #Steady State theory #Theoretical physics #Ultimate fate of the universe #Universe #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.90.043520
published as Phys. Rev. D 90, 043520 (2014) · Extended discussion of physical time, map between frames, limitation of proper time, incomplete geodesics in the Sitter space, graviton scattering, 17 pages, 2 figures
arxiv created 2014/05/19 · openalex publication_date 2014/08/18 · arxiv updated 2014/08/27 · openalex created_date 2020/07/02 · openalex updated_date 2026/08/05
We discuss cosmological models for an eternal Universe. Physical observables show no singularity from the infinite past to the infinite future. While the Universe is evolving, there is no beginning and no end---the Universe exists forever. The early state of inflation is described in two different, but equivalent pictures. In the freeze frame the Universe emerges from an almost static state with flat geometry. After entropy production it shrinks and ``thaws'' slowly from a ``freeze state'' with extremely low temperature. The field transformation to the second ``big bang picture'' (Einstein frame) is singular. This ``field singularity'' is responsible for an apparent singularity of the big bang. Furthermore, we argue that past-incomplete geodesics do not necessarily indicate a singularity or beginning of the Universe. Proper time ceases to be a useful concept for physical time if particles become massless. We propose to define physical time by counting the number of zeros of a component of the wave function. This counting is independent of the choice of coordinates and frames, and applies to massive and massless particles alike.