2.2 The Multiverse Theory Review

summary

When inflation lasts forever in certain regions, the multiverse is produced.

The initial infinitesimal patch can have different physical regions. You can think of these regions as different colored hexagons on the surface of a small soccer ball.
Inflation stretches each of these regions to be arbitrarily large. Each region becomes so large that none have any influence over any other. A hypothetical inhabitant of any given region would not recognize the existence of any other region.
Physical laws don’t necessarily need to be the same from one region to another—a scientist living in the “blue” region might define laws of physics to explain why they observe only blue around them; a red region scientist’s laws might be totally different.
The pessimist’s viewpoint: If each part of the multiverse is so large, we will never see its other parts and so it is impossible to prove that we live in the multiverse. Conversely, the optimist would say that it is impossible to disprove the theory.

Quantum fluctuations can account for the multiverse.

The graph of the potential energy has the shape of a large hill. Smaller hills are generated on the surface of this hill from quantum fluctuations, and even smaller hills on top of those, continuing endlessly.
Quantum fluctuations can cause the size of these hills to either increase or decrease. The larger the energy, the faster the exponential growth of the corresponding region. This causes inflation to reproduce itself an arbitrary number of times.
With the quantum fluctuations defining the energy, inflation responds to the landscape of these hills, inflating some regions while ending in others. The combination of quantum fluctuations and inflation is what generates the multiverse.
We live in one region, where the hills are small. The inhomogeneities we observe in the CMB radiation arise from the quantum fluctuations of the scalar field, stretched out by inflationary expansion. In eternal inflation, there are many other regions, separate and independent from ours.

There are two theories of inflationary perturbations.

Scalar perturbations—perturbations of the scalar field, of density, or temperature.
Tensor perturbations—gravitational waves, deformations of space-time, and B-modes.
Gravitational waves can tell us much about the early universe, and were predicted to exist even before inflation was.
The Planck satellite has mapped small-scale temperature fluctuations on the order of 10⁻⁵ K across the observable universe.
These temperature variations arose from quantum fluctuations—produced 10⁻³⁵ seconds after the Big Bang—that were stretched by inflation, making them cosmologically observable.
Comparing the Planck results to the predictions made by the inflationary theory, there is significant agreement, the universe is flat with accuracy 10⁻², and the spectrum of perturbations is nearly flat.

When we look into space, we can use it as a time machine.

As we look further and further, we are seeing stars and galaxies as they were hundreds, millions, and even billions of years ago.
Eventually, we reach the cosmic microwave background—energy dispatched approximately 400,000 years after the Big Bang.
This is the limit of how far back we can see, because the universe at that time was non-transparent (to electromagnetic radiation).
Inflation posits that the universe became hot only after the end of inflation. In the period of inflation, energy was sitting in this scalar field. When the scalar field oscillated, it produced normal particles, which interacted with each other and became hot. It was at this point that energy was released in the form of photons, which we observe as the CMB radiation.
If the Big Bang is defined as the moment the universe became hot, then chronologically we should think of the history of the universe with inflation first, and then a hot Big Bang.