How was the fractal-like anisotropy of the cosmic microwave background born?

http://www.astro.ucla.edu/~wright/CMB-DT.html

https://www.physicsoverflow.org/19466/why-is-the-cmb-nearly-scale-invariant

The differences in temperature are in the range 25 - 70 microkelvins if we measure a feature size between 0.2 degrees and 20 degrees in the sky. The overall temperature is 3 K.

The features are roughly "scale-invariant" in the sense that a magnified map shows similar-looking anisotropies to an unmagnified map.

The inflation hypothesis and the patterns of the microwave background

The inflation hypothesis explains the scale invariance by "random quantum fluctuations" which were inflated to a cosmic scale by the rapid expansion of the universe. There is a huge amount of energy in the anisotropies, even though the temperature difference is just around 1 / 100,000.

The energy had to come from somewhere. In the inflation hypothesis, the expansion of the universe produces energy from nothing to a scalar inflaton field. In our previous blog post we remarked that the non-conservation of energy may contradict basic principles of quantum mechanics. New energy quanta would pop up from nothing.

In classical physics, turbulence of, say hot smoke which rises from a smoke stack, creates a fractal-like structure. But it is hard to see how an expanding universe would have turbulence. In the case of the smoke, the turbulence is a result of the hot smoke colliding with cool, static air.

In a Big Bang model without inflation, there are roughly 6,000 points in the night sky which were not in a causal contact at the time when the microwave backround was born. Such points are roughly at a distance 3 degrees from each other.

How can the patterns of the anisotropies be coordinated over 20 degrees of the sky if there was no causal contact between different parts of that area? The inflation hypothesis solves this by asssuming a very fast expansion phase which caused a pattern to expand faster than light.

Could there be a mechanism which produces large patterns without a causal contact?

In a big bounce model, the causal contact would have occurred in the contraction phase.

Is there any other way to explain the large patterns? Maybe the original signal is at a constant temperature, but the space between the signal and us contains a fractal-like phenomenon which can change the apparent temperature. But how do we explain galaxy formation in that case? The fractal-like phenomenon should cause matter to collapse into galaxy clusters.

Yet another explanation is that, for an unknown reason, the matter in the Big Bang was created into a fractal-like structure. Since the Big Bang is beyond our understanding, there is no reason why the original matter content should have been smooth. If there was some process which created the original Big Bang universe, and that process was not constrained by the light speed in our universe, then the fractal-like structure could be a result of that process.

Why there are no "domain walls" or other defects in the visible universe?

It is assumed that the symmetry breaking of various fields, for example, the Higgs field and the electroweak field caused the universe to form "crystals" where a certain field has a constant value. The value in the neighbor crystal may be different.

We have not found domain walls in the visible universe. It looks like the whole visible universe is inside a single crystal.

Here we again have the problem how the whole visible universe is inside a single crystal if different parts have not been in a causal contact since the Big Bang.

The inflation hypothesis solves the problem by assuming that every crystal expanded immensely during the inflation.

Big bounce models might assume that the large crystal formed in the contraction phase.

We might also imagine that the original creation process of the Big Bang universe already had the symmetries broken, and the corresponding fields have a single value throughout the universe.

The quantum measurement problem and "quantum fluctuations" in the inflaton field

In standard quantum mechanics, if we try to measure the energy content of some object, we will get varying values because of the uncertainty principle. Some people call these varying values "quantum fluctuations".

In a measurement, the measuring apparatus interacts with the object. If we claim that the variations of temperature in the sky are "quantum fluctuations", what is the measuring apparatus in that case? Is the scalar field itself and the metric a "measuring apparatus" which measures the energy content of the scalar field?

An analogous process is crystallization of a cooled liquid. If the temperature happens to drop within a small group of molecules, they will form a small initial crystal, a seed, which will grow larger. The measuring apparatus of the temperature is the liquid itself. A small random variation of the temperature downward will start a cascading process where at the end, it is the large crystal which interacted with the original temperature variation. The crystal is the measuring apparatus.

But is the inflaton field really analogous to crystal formation? A crystal is formed from a finite number of atoms. What are the "atoms" in the case of the inflaton field?