Modern Physics: Friedmann equation

In summary, the Friedmann equation is a mathematical equation first derived by Alexander Friedmann in 1922 that describes the expansion of the universe. It is a key component of the Big Bang theory and helps to explain the observed redshift of galaxies and the overall structure of the universe. The equation involves several key variables, including the scale factor, Hubble parameter, and energy density, and is used in modern physics to study the large-scale structure of the universe and make predictions about its future expansion. Its implications have solidified the Big Bang theory and support the existence of dark energy and dark matter.
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Homework Statement
Consider a flat expanding universe with no cosmological constant and no curvature (k=0 in the Friedmann equation). Show that if the Universe is made of "dust", so the energy density scales like 1/R^3 , then the scale factor, R(t), grows as t^(2/3). Show if it is made of radiation (so the energy density scales as 1/R^4 -- the extra factor of R comes from the redshift), then it grows as t^(1/2). In both cases, show that for early times, the scale factor grows faster than light. Is this a problem?
Relevant Equations
(adot/a)^2 = 8*pi*G*rho/3 (because k=0)
I was shown that adot^2/a^2 = c/a^3, adot = c / √(a), then da/dt = c / √(a) . Then I was told that I have to integrate this, but I don't understand where to go from there or how this will show me that the scale factor grows as t^(2/3).
 
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1. What is the Friedmann equation?

The Friedmann equation is a mathematical equation used in modern physics to describe the expansion of the universe. It was first developed by Alexander Friedmann in 1922 and has been refined and expanded upon by numerous scientists since then. The equation relates the rate of expansion of the universe to the density and energy content of the universe, as well as the curvature of space.

2. How does the Friedmann equation relate to the Big Bang theory?

The Friedmann equation is a key component of the Big Bang theory. It helps to explain how the universe has expanded and evolved since the initial explosive event of the Big Bang. The equation shows that the expansion of the universe is not constant, but rather has changed over time due to the changing density and energy content of the universe.

3. What are the assumptions made in the Friedmann equation?

The Friedmann equation is based on a few key assumptions, including the homogeneity and isotropy (uniformity) of the universe on large scales, and the principles of general relativity. It also assumes a flat or nearly flat universe, meaning that the curvature of space is negligible. These assumptions have been supported by various observations and experiments.

4. How does dark energy affect the Friedmann equation?

Dark energy, which is believed to make up about 68% of the total energy content of the universe, has a significant impact on the Friedmann equation. It is thought to be responsible for the current acceleration of the expansion of the universe, and is included as a term in the equation. Understanding dark energy and its effects is an active area of research in modern physics.

5. Can the Friedmann equation be used to predict the future of the universe?

Yes, the Friedmann equation can be used to make predictions about the future of the universe. By using various values for the density and energy content of the universe, scientists can determine the fate of the universe. Depending on these values, the universe may continue to expand forever, eventually stop expanding and reach a maximum size, or collapse in a "Big Crunch" scenario. However, the exact fate of the universe is still unknown and subject to ongoing research and debate.

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