I have some misunderstanding about Fridman models of University.(adsbygoogle = window.adsbygoogle || []).push({});

Friedman equation:

## \begin{array}{l}

{\left( {\frac{{\dot a}}{a}} \right)^2} = \frac{{8\pi G}}{3}\rho - \frac{{k{c^2}}}{{{a^2}}}\\

\frac{1}{a}\frac{{{d^2}a}}{{d{t^2}}} = - \frac{{4\pi G}}{3}\left( {\rho + \frac{{3p}}{{{c^2}}}} \right)

\end{array} ##

with equation of state ##p=\omega\rho##

Functional dependence on the scale factor ##a## for the energy density of matter ##\rho_m \propto \frac{1}{a^3}## / radiation ##\rho_r \propto \frac{1}{a^4}## / dark energy ##\rho_{\Lambda} =const## we know from some other assumptions. Parameter ##k## - determined from observations.

Thus, from the first Friedmann equation we find the dependence of the scale factor ##a(t)## of time.

The quastion is: Why do we need the second equation? What other information can you get?

It turns out that the system of equations is overdetermined.

Moreover, from Newtonian cosmology is known that the first equation - the energy conservation law, the second - the equation of motion. Integrating the second equation we obtain the first. From the perspective of Newtonian cosmology rather the law of conservation of energy and density considerations depending on the scale factor Moreover, from Newtonian cosmology is known that the first equation - the energy conservation law, the second - the equation of motion. Integrating the second equation we obtain the first. From the perspective of Newtonian cosmology rather the law of conservation of energy and density considerations depending on the scale factor to find ##a(t)##.

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# About completeness of the Friedmann equations

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