Explanation on how inflation solves the horizon and flatness problem

In summary, during inflation, the energy density remains constant while the scale factor increases rapidly. This leads to the density parameter, |\Omega-1|, being driven towards zero, making the universe flat. This also solves the horizon problem by greatly reducing the comoving Hubble length, allowing regions that were previously in causal contact to become out of contact. The particle horizon is also affected by inflation, as the rapid increase in scale factor makes the curvature less dominant. This all makes sense and is explained by physicist Alan Guth in a lecture on YouTube.
  • #1
trv
73
0
Hi, I'm totally lost on how inflation solves the horizon and flatness problem.


Flatness Problem

Explanation I have
d/dt(1/Ha)<0

and therefore

[itex]
|\Omega-1|
[/itex]

is driven towards zero rather than away from it.

My Confusion
Doesn't inflation increase the volume of the universe, and hence wouldn't the density decrease rather than increase? Or am I misunderstanding the density parameter here?

Horizon Problem

Explanation I have

The quantity 1/Ha is the comoving Hubble length, and determines which two regions can communicate now. The particle horizon on the other hand, separates two regions that could never have communicated. The horizon problem is solved by the possibility of greatly reducing the comoving Hubble length. Hence, regions that cannot communicate today were in causal contact early.

My Understanding
The way I understand this is that, the comoving Hubble length gets smaller with time. Therefore region that were within the comoving Hubble length earlier and hence could communicate and affect each other, are now out of contact. So even though we look at space and see regions that can't communicate now, there was a time when they could do so.

Does what I have just said make sense?

My Confusion
Finally my question on this part is, how does the particle horizon bit come into the picture? Can someone try and explain?
 
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  • #2
Hi trv,

During inflation the energy density of the inflaton field is constant while the scale factor a increases very rapidly. The argument on Wikipedia writes the Friedmann equation in the form,

[tex] (\Omega^{-1} -1) \rho a^2 = \frac{-3kc^2}{8 \pi G} [/tex]

All the factors on the RHS are constant so as [tex] \rho a^2 [/tex] increases [tex] \Omega^{-1} -1 [/tex] must decrease. This can only happen if [tex] \Omega [/tex] goes towards 1 which makes the Universe flat.

There is a very good lecture by Alan Guth (who came up with inflation) on YouTube
 
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  • #3
Curvature goes as one over the scale factor squared. The stuff that drives inflation is nearly independent of scale. Therefore, as inflation progressed, the stuff that drove inflation came to dominate over the curvature (and anything else that happened to be around).
 

1. What is the horizon problem?

The horizon problem, also known as the homogeneity problem, is a major issue in cosmology where the universe appears to be uniform and isotropic on large scales, yet different regions of the universe are not causally connected. This means that there has not been enough time since the beginning of the universe for these regions to interact and reach a state of thermal equilibrium.

2. What is the flatness problem?

The flatness problem is a cosmological puzzle related to the geometry of the universe. It refers to the observation that the universe appears to be very close to flat, with a curvature parameter of almost exactly zero. However, this is highly unlikely to occur by chance, leading to the question of why the universe is so finely tuned to be flat.

3. How does inflation solve these problems?

Inflation is a theory that proposes a rapid and exponential expansion of the universe in its early stages, which can solve the horizon and flatness problems. The inflationary period allows different regions of the universe to come into causal contact, resulting in a more homogenous and flat universe. Additionally, the rapid expansion smooths out any irregularities in the curvature of the universe, explaining its near-flatness.

4. Can inflation be proven?

While there is strong evidence for inflation, such as the uniformity of the cosmic microwave background radiation, it is difficult to directly prove the theory. However, ongoing observations and experiments, such as those conducted by the European Space Agency's Planck satellite, continue to support the predictions of inflation.

5. Are there any alternative explanations for the horizon and flatness problem?

There are other proposed solutions to the horizon and flatness problems, such as the cosmic strings theory or the cyclic universe model. However, inflation remains the most widely accepted theory due to its ability to explain not only these two problems, but also other observed phenomena such as the large-scale structure of the universe and the origin of cosmic perturbations.

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