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.)

 

[sardar]

I can confirm that there is a mathematical equation to describe the expansion of the universe. This equation is known as the Friedmann equations, which are a set of equations that describe the evolution of the universe based on the theory of general relativity.

The acceleration of the universe due to dark energy is currently believed to be described by the Lambda-CDM model, which includes a cosmological constant term (lambda) to account for the observed acceleration. This model is based on the assumption that dark energy is a constant, meaning that the amount of dark energy in the universe remains the same over time.

However, there are ongoing studies and research to better understand the nature of dark energy and its effects on the expansion of the universe. Some theories suggest that the amount of dark energy may be increasing, while others propose alternative explanations for the observed acceleration. Therefore, the exact nature of dark energy and its impact on the expansion of the universe is still a topic of active research and debate in the scientific community.

In terms of the behavior of the expansion of the universe, the Friedmann equations predict that it is currently in a phase of accelerated expansion, but this may change in the future depending on the amount and nature of dark energy. The exact form of the expansion (linear, exponential, etc.) is still being studied and is dependent on the specific model used to describe the universe.

In conclusion, while we do have a mathematical equation to describe the expansion of the universe and its acceleration due to dark energy, there is still much to learn and understand about this phenomenon. Further research and advancements in technology will continue to improve our understanding of the expansion of the universe and its underlying mechanisms.