Comments about Inflation (cosmology) in Wikipedia

Introduction

At the beginning of this paragragh we read:

Inflation answers the classic conundrum of the Big Bang cosmology: why does the universe appear flat, homogeneous and isotropic in accordance with the cosmological principle when one would expect, on the basis of the physics of the Big Bang, a highly curved, heterogeneous universe?

This text raises two questions:

1. Why should one expect that based on the physics of the Big Bang the Universe should be inhomogeneous while based on observations the Univerese is homogeneous.
2. Why do we need inflation to switch from inhomogeneous to homogeneous ? Maybe the evolution of the Universe was always a rather continuous process, specific the part of the Univerese that is Observable.

Overview

This paragragh starts with the text:

While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such constraint in general relativity.

The physical question exist can objects have a speed larger than the speed of light. The speed measured with two clocks and a ruler all at rest in the frame of the Milky Way (Back Ground radiation)
If this sentence has something to do with the concepts local and global (In the sense of: locally they can not move faster than the speed of light but globally there is not such a constraint) than there is an issue when local ends and global begins.

An expanding universe generally has a cosmological horizon, and like a black hole event horizon, this marks the boundary to the part of the universe that an observer can see. The horizon is the boundary beyond which objects are moving away too fast to be visible from Earth.

Any observer using a telescope can only see a certain part of the Universe. The more accurate the telescope the more he or she can see. With the same telescope the observer will always see the same distance i.e. volume of space.
When the univerese is expanding the observer will see less in the future because galaxies are moving outside this volume of space.
Next we read:

There are two ways to describe a spacetime with a horizon: global and local.
The global picture includes regions beyond the horizon, which are invisible to us, while the local picture is the picture from one point of view only. These two perspectives are related by a process of extension, wherever there is a horizon, a solution of General Relativity can go on by assuming that nothing special happens there.

What has General Relativity to do with this ? Next we Read:

The local and global points of view have a different notion of time. From the local point of view, time stops at the horizon. From the global point of view, time marches on, and surfaces of constant time cross the horizon. Ignoring quantum mechanics, the two pictures are equivalent: any statement can be translated freely back and forth.

The above text has no physical contents.
Next we read:

For cosmology in the global point of view, the observable universe is one causal patch of a much larger unobservable universe; there are parts of the universe which cannot communicate with us yet. These parts of the universe are outside our current cosmological horizon.

The human point of view has nothing to do with the evolution of the Universe. Next we read:

In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view.

New regions you will see when you have a better telescope. Next we read:

As we see these regions for the first time, they look no different from any other region of space we have already seen: they have a background radiation which is at nearly exactly the same temperature as the background radiation of other regions, and their space-time curvature is evolving lock-step with ours.

The background radiation you will see more accurate when you have a better telescope. Next we read:

This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They couldn't have learned it by getting signals, because they were not in communication with our past light cone before.

The easiest explanation of a rather uniform distribution is that apparently the cooling process happened relatif slow and uniform in the course of time together with local mixing. Our light cone has nothing to do with this. Next we read:

Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put.

You can not use a cosmological constant in order to explain the physical evolution of the Universe.

For any one observer, the distance to the cosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communications. In the global point of view, the spatial slices are expanding very fast to cover huge volumes. In the local point of view, things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous very quickly.

IMO you can not use expanding space in order to explain that an inhomogeneous state changed into a homogeneous state (With or without a cosmological horizon).
They use the wording everything becomes homogeneous. You can call the background radiation homogeneous, but is not true for all the galaxies in the Universe. Galaxy evolution requires inhomogeneous events.

Reflection

The Background radiation is a relic of cooling events that started millions years ago. This radiation is all around us, which maybe also explains why it is homogeneous.
The Big Bang is a single extremely powerfull event.
One major problem of the Big Bang is to deduce, based on observations which represents a sequence of pictures in the past, the evolution and the present state of the Universe. The problem is you have almost nothing to compare it with. The best way is to compare it with a supernova of a blackhole.

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