While Einstein introduced his cosmological constant to get a static universe, he was never satisfied with it. This wasn’t merely due to the aesthetics of imposing such a solution. A significant problem with his cosmological constant was that while it made the universe static, it also made it unstable. To illustrate this, consider Einstein’s static universe to be comprised only of non-relativistic matter with mass density ρ, and a cosmological constant, Λ = 4πGρ. Suppose, now, that some of the non-relativistic matter is converted into radiation (e.g., by stars). Will the universe start to expand or contract ?
Problem 1. While Einstein introduced his cosmological constant to get a static universe, he was never satisfied
with it. This wasn’t merely due to the aesthetics of imposing such a solution. A significant problem with his
cosmological constant was that while it made the universe static, it also made it unstable. To illustrate this,
consider Einstein’s static universe to be comprised only of non-relativistic matter with mass density ρ, and a
cosmological constant, Λ = 4πGρ. Suppose, now, that some of the non-relativistic matter is converted into
radiation (e.g., by stars). Will the universe start to expand or contract ? You must show calculations justifying
your answer;
Given that,
the mass density is
cosmological constant is
From the Friedmann equation
where a is the scale factor, G is the gravitational constant, c is the speed of light, P is the pressure, and is the energy density
This equation is also known as the acceleration equation.
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