Can Matter be Created or Destroyed?

[Alex K]

Mass is simply the measure of how much energy of any form is contained in an object (*). Energy is conserved at short time spans, but can be converted and in particular, energy which appears as mass, can be freed from its confines and converted into other types. However, cosmic expansion removes energy from the universe via the redshift.

(*) This holds always. For example, a spring under tension has more mass than a relaxed one, precisely differing by the stored energy divided by c^2

I thought Friedman equations shows energy is conserved in the entire expanding universe despite the red shifting of the photons.

I don't immediately see how the Friedman equations say something about that, but maybe you can be more specific. They tell us how the scale factor of the universe changes with time for a given amount of energy density in the universe. They have to be supplemented by the equations of state which tell us how the energy density changes with the scale factor. Nonrelativistic matter is diluted by the increasing volume ~a^3 and its energy density therefore goes with a^-3, dark energy has constant density, and relativistic matter ("radiation") is diluted as well as redshifted and goes with a^-4. If we assume for now that the universe is finite in size, the total amounts of both dark energy and radiation change as the universe expands, i.e. the scale factor a gets larger: dark energy increasing its total energy with a factor a^3, and radiation decreasing with a factor a^-1.

The question is now whether one can extend our notion of energy such that it is conserved again. People have thought about whether maybe geometry itself can be assigned an energy density (roughly, but not quite, curvature being a form of energy), and one result is the Landau-Lifshitz-Pseudotensor, which provides a notion of energy stored in the geometry. The Landau-Lifshitz contribution plus all the matter and dark energy and radiation jointly, are conserved again. But matter and energy alone, in the conventional sense, as far as I know, aren't. But I'm happy to hear more points of view on this very subtle topic.