# cosmological conservation

03 May 2023Can you show that the adiabatic relation \(\mathrm{d}(a^3\rho)/\mathrm{d}a = -p\mathrm{d}(a^3)/\mathrm{d}a\) in cosmology follows from covariant energy-momentum conservation \(\nabla^\mu T_{\mu\nu} = 0\) under the FLRW-symmetry assumptions for ideal fluids?