The question whether energy is conserved in an expanding universe remains one of the central conceptual issues of relativistic cosmology. The absence of a global timelike Killing vector and the lack of a local gravitational energy density often lead to the conclusion that cosmological redshift represents a genuine violation of energy conservation. In this work we reconsider this problem within the framework of Brown-York quasilocal energy and its associated balance law. For comoving spherical boundaries in Friedmann–Lemaître–Robertson–Walker spacetimes we show that the ordinary stress-energy flux through the boundary vanishes identically for arbitrary perfect fluids, while the unreferenced Brown-York energy evolves entirely due to a purely geometrical boundary contribution. We further demonstrate that the timelike boundary world tube possesses a natural dynamical reference geometry. The corresponding reference subtraction removes the universal background contribution of the unreferenced Brown-York energy and leads to a quasilocal energy whose leading nontrivial term exactly reproduces the enclosed matter energy. For radiation dominated cosmologies, the resulting expansion is $E_{\mathrm{BY}}=H^2{R}^3/2-H^4{R}^5/8+\mathcal{O}(R^7)$, where the leading term coincides precisely with the energy of the enclosed radiation responsible for cosmological redshift. Higher-order contributions naturally possess the structure expected for gravitational self-energy corrections. These results suggest that cosmological redshift can be understood within a fully quasilocal conservation framework. The apparent loss of photon energy therefore need not indicate a breakdown of energy conservation but may instead reflect the fundamentally quasilocal character of gravitational energy in general relativity.

Close

PrevNext

View figure in article

• 

• General relativity equations & solutions
• Relativistic aspects of cosmology