The authors derive the Friedmann equations and their first-order perturbations from Newtonian mechanics and thermodynamics, and show the perturbed equations coincide with general relativity at linear order.
Centenary of Alexander Friedmann's Prediction of the Universe Expansion and the Quantum Vacuum
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abstract
We review the main scientific pictures of the universe developed from ancient times to Albert Einstein and underline that all of them treated the universe as a stationary system with unchanged physical properties. In contrast to this, 100 years ago Alexander Friedmann predicted that the universe expands starting from the point of infinitely large energy density. We briefly discuss the physical meaning of this prediction and its experimental confirmation consisting of the discovery of redshift in the spectra of remote galaxies and relic radiation. After mentioning the horizon problem in the theory of the hot universe, the inflationary model is considered in connection with the concept of quantum vacuum as an alternative to the inflaton field. The accelerated expansion of the universe is discussed as powered by the cosmological constant originating from the quantum vacuum. The conclusion is made that since Alexander Friedmann's prediction of the universe expansion radically altered our picture of the world in comparison with the previous epochs, his name should be put on a par with the names of Ptolemy and Copernicus.
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On the perturbed Friedmann equations in Newtonian Gauge
The authors derive the Friedmann equations and their first-order perturbations from Newtonian mechanics and thermodynamics, and show the perturbed equations coincide with general relativity at linear order.