There are minor fluctuations, like parts in a million, that correspond to density fluctuations in the universe.

The fluctuations are a part in 100,000.

But there will also be large fluctuations.

We talk about several different types of density fluctuations. The most commonly used ones are so called, adiabatic fluctuations.

However, after recombination fluctuations can grow and essentially baryons fall into the potential wells defined by the dark matter fluctuations.

Isothermal fluctuations where the photons are unperturbed does the equal temperature, but there are underlying fluctuations in the regular matter.

During the radiation dominated era, fluctuations do not grow.

And thus, they would start the raising the fluctuations.

And those fluctuations were stretched to astronomical sizes, and those fluctuations eventually are the things we see in the cosmic microwave background.

Next, we will talk about primordial density spectrum of fluctuations, which is a descriptor of how many fluctuations, of what size they are.

However, after the matter domination begins, the fluctuations could grow.

Dark matter fluctuations can grow before baryons can actually follow.

The energy of empty space brings to life quantum fluctuations.

Or large scale fluctuations lifting the small ones even further.

When we observe the physical world, we find random fluctuations everywhere.

I don't want currency fluctuations to barge in on us here.

Those are fluctuations that go beyond the horizon, and here's the spectrum.

So next time we will talk about cosmology Cosmic microwave background fluctuations.

So, if all of the fluctuations of different frequencies have same amplitude.

Next time we will talk more how the fluctuations grow in time.

And the predictions are that the fluctuations that make us are minimal.

Now in reality, the density fluctuations are unlikely to be perfect spheres.

On the hand there could be proto voids which are negative fluctuations.

There will be density fluctuations, in the early universe, and those that are leftover from the quantum fluctuations, from even earlier times, in the history of the universe.

It started with tiny quantum mechanical fluctuations, but expanding at a tremendous rate.

Price fluctuations in economic markets can be fruitfully viewed as an algorithmic process.

We can generate truly random numbers by measuring random fluctuations known as noise.

Let us now take a closer look at the collapse of density fluctuations.

Lets take just, exaggerated density cut through a density field in your universe and you can think of it as small scale fluctuations riding on top of large scale fluctuations.

So we believe that the original fluctuations came from quantum fluctuations in the early universe that you know due to fluctuations in the number of density of particles and then they're inflated through the inflationary era to the large scale structures or are the seeds of large scale structures.

Recall also that initially it's just the fluctuations in the dark matter that matter because baryons are coupled to photons and they only participate in growth of fluctuations after the recombination.

And you do get to the point where there's some wild fluctuations with Bitcoin.

Essentially, the pressure suppresses collapse of fluctuations at all scales smaller than Jeans Length.

In the early universe there will be density fluctuations as residual of quantum processes.

The dark matter fluctuations have grown already relative to those in baryons and photons.

Nearest you might be looking at 1 or 2 signal fluctuations to see which.

So far we've discussed how a collapse of primordial density fluctuations would lead to formations of structures in the universe, but the fluctuations will have a spectrum of different sizes or masses.

Consider the fate of fluctuations of different amplitude, here shown with thin black lines and dashed red lines the highest fluctuations say 5 sigma lines will evolve fastest, they will reach higher values sooner, the lower contract fluctuations will get there eventually but takes longer time Now if the structures form according to the biased contrast, then as you look back is you'll be looking at different type of fluctuations.

There is damping mechanisms, say photon diffusion or sound waves. They raise small scale fluctuations.

So for a long time, cosmologists tried to measure these fluctuations, and finally they succeeded.

At certain intervals, there are fluctuations in the node that cause the signal to reappear.

That the density fluctuations are dominated with the dark matter which, as you recall is several times more by density of regular baryons and those fluctuations grow even before the micro background is released.

If you note any fluctuations, let the customer know they may have some reason for concern

Because of this reason, the different mechanisms dominating erasure of small scale fluctuations with different efficiency.

The small scale fluctuations are damp, but not nearly as efficiently. So, some power does exist.