Energy balance in an expanding Universe

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Problem 1: Newtonian interpretation

Show that the first Friedman equation can be treated as the energy conservation law in Newtonian mechanics. Use this equation to classify the solutions describing different dynamics of the Universe.

Problem 2: thermodynamic derivation

Obtain the conservation equation for the expanding Universe using only thermodynamical considerations.

Problem 3: the lost energy of the Universe

A photon's wavelength is redshifted due to the Universe' expansion. Estimate the rate of change of the energy of the Universe due to this process.