Teaching cosmology with special relativity: Piecewise inertial frames as a model for cosmic expansion

This article presents a simple model that reproduces key concepts of modern cosmology within the framework of special relativity, at a level that is suitable for an undergraduate or high school setting. The model includes cosmic expansion governed by a universal scale factor, the Hubble relation, proper distances between galaxies and the associated recession speeds, comoving coordinates, angular and luminosity distances, and the relation between the cosmic scale factor and the cosmological redshift. It allows for a pedagogical discussion of the role of superluminal recession speeds of galaxies, the applicability of the special-relativistic Doppler formula to describe the cosmological redshift, and the validity of energy conservation for the redshifted photons. The model can be viewed as a toy version of the Milne universe.Comment: 20 pages, 4 figure

Energy conservation in explicit solutions as a simple illustration of Noether's theorem

Noether's theorem is widely regarded as one of the most elegant results in theoretical physics. The article presents two simple examples that can be used to demonstrate the basic idea behind Noether's theorem, by deriving a relation between translational symmetry in the time coordinate and energy conservation in a way that is accessible to beginning students.Comment: 3 page