Expansion of Universe, do we know the equation?

[magnetoman]

Our acceleration universe due to 'dark energy'. Do we have a mathematical equation to describe this? I want to know if it is linear, exponential, asymptotic or something else. Is amount of 'dark energy' increasing or staying the same?

 

[Nabeshin]

Hello and welcome to PF!

The expansion of the universe, in a universe completely dominated by dark energy alone, is exponential in character. Since our universe is not 100% dark energy, our real universal expansion is slightly more complicated.

Now, the density of dark energy does not dilute as the volume of the universe increase. Think of a box with a finite number of particles in it, say N. Now if I expand the box, the density of particles, N/V, decreases. This does not happen with dark energy. As the volume of the box increases, density stays constant. So while the density of normal matter is falling as our universe expands, the density of dark energy is constant! This means that eventually dark energy will be the main component of the universe, simply because while everything else is decreasing it stays the same.

P.S: The mathematical equations describing the evolution of the universe are known as the Friedmann equations:
http://en.wikipedia.org/wiki/Friedmann_equations

 

[mysearch]

Our acceleration universe due to 'dark energy'. Do we have a mathematical equation to describe this? I want to know if it is linear, exponential, asymptotic or something else. Is amount of 'dark energy' increasing or staying the same?

I don't know if this thread would be of any help.
There is a specific equation in post #5 that is used in the Ned Wright cosmic calculator.
https://www.physicsforums.com/showthread.php?t=267808

 

[BillSaltLake]

If we take the present value of dark energy being 73% of the total density, then a/a₀ = .715[sinh(1.28t/t₀)]^2/3. This is a pretty good approximation that ignores only "light" energy (photons, neutrinos), which is less than 1% now and is decreasing. The subscribt "₀" represents the present.
(This is the LCDM model.)