Some questions about Cosmic Inflation

[PainterGuy]

Hi,

I have some questions about the cosmic inflation. As I tried to find the answers, I got little more confused. I have mentioned all the quotes from relevant articles which I found confusing. I understand that there are quite a few questions but they are all related to each other and I thought that asking them together might be a good idea so you can see where I'm having the difficulty.

Also please keep in mind that I'm only trying to understand it from basic layman point of view.

Thank you for your time and help, in advance!Quote 1:
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from 10−36 seconds after the conjectured Big Bang singularity to some time between 10−33 and 10−32 seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago).[1]
https://en.wikipedia.org/wiki/Inflation_(cosmology)

Quote 2:
Detailed measurements of the expansion rate of the universe place the Big Bang singularity at around 13.8 billion years ago, which is thus considered the age of the universe.[6]
https://en.wikipedia.org/wiki/Big_Bang

Quote 3:
Immediately after the Big Bang, the universe was a hot, dense plasma of photons, leptons, and quarks: the quark epoch. At 10−6 seconds, the Universe had expanded and cooled sufficiently to allow for the formation of protons: the hadron epoch. This plasma was effectively opaque to electromagnetic radiation due to Thomson scattering by free electrons, as the mean free path each photon could travel before encountering an electron was very short. This is the current state of the interior of the Sun. As the universe expanded, it also cooled. Eventually, the universe cooled to the point that the formation of neutral hydrogen was energetically favored, and the fraction of free electrons and protons as compared to neutral hydrogen decreased to a few parts in 10,000.
https://en.wikipedia.org/wiki/Recombination_(cosmology)

Quote 4:
Extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past.[20] This irregular behavior, known as the gravitational singularity, indicates that general relativity is not an adequate description of the laws of physics in this regime. Models based on general relativity alone can not extrapolate toward the singularity—before the end of the so-called Planck epoch.[5]

This primordial singularity is itself sometimes called "the Big Bang",[21] but the term can also refer to a more generic early hot, dense phase[22][notes 2] of the universe.
https://en.wikipedia.org/wiki/Big_Bang#Singularity

Quote 5:
The earliest phases of the Big Bang are subject to much speculation, since astronomical data about them are not available. In the most common models the universe was filled homogeneously and isotropically with a very high energy density and huge temperatures and pressures, and was very rapidly expanding and cooling. The period from 0 to 10−43 seconds into the expansion, the Planck epoch, was a phase in which the four fundamental forces — the electromagnetic force, the strong nuclear force, the weak nuclear force, and the gravitational force, were unified as one.[25] In this stage, the characteristic scale length of the universe was the Planck length, 1.6×10−35 m, and consequently had a temperature of approximately 1032 degrees Celsius. Even the very concept of a particle breaks down in these conditions. A proper understanding of this period awaits the development of a theory of quantum gravity.[26][27] The Planck epoch was succeeded by the grand unification epoch beginning at 10−43 seconds, where gravitation separated from the other forces as the universe's temperature fell.[25]

At approximately 10−37 seconds into the expansion, a phase transition caused a cosmic inflation, during which the universe grew exponentially, unconstrained by the light speed invariance, and temperatures dropped by a factor of 100,000. Microscopic quantum fluctuations that occurred because of Heisenberg's uncertainty principle were amplified into the seeds that would later form the large-scale structure of the universe.[28] At a time around 10−36 seconds, the electroweak epoch begins when the strong nuclear force separates from the other forces, with only the electromagnetic force and weak nuclear force remaining unified.[29]

Inflation stopped at around the 10^−33 to 10^−32 seconds mark, with the universe's volume having increased by a factor of at least 1078. Reheating occurred until the universe obtained the temperatures required for the production of a quark–gluon plasma as well as all other elementary particles.[30][31] Temperatures were so high that the random motions of particles were at relativistic speeds, and particle–antiparticle pairs of all kinds were being continuously created and destroyed in collisions.[4] At some point, an unknown reaction called baryogenesis violated the conservation of baryon number, leading to a very small excess of quarks and leptons over antiquarks and antileptons—of the order of one part in 30 million. This resulted in the predominance of matter over antimatter in the present universe.[32]
https://en.wikipedia.org/wiki/Big_Bang#Inflation_and_baryogenesis

Quote 6:
According to inflation theory, during the inflationary epoch about 10−32 of a second after the Big Bang, the universe suddenly expanded, and its volume increased by a factor of at least 10^78 (an expansion of distance by a factor of at least 1026 in each of the three dimensions). This would be equivalent to expanding an object 1 nanometer (10−9 m, about half the width of a molecule of DNA) in length to one approximately 10.6 light years (about 10^17 m or 62 trillion miles) long. A much slower and gradual expansion of space continued after this, until at around 9.8 billion years after the Big Bang (4 billion years ago) it began to gradually expand more quickly, and is still doing so. Physicists have postulated the existence of dark energy, appearing as a cosmological constant in the simplest gravitational models, as a way to explain this late-time acceleration. According to the simplest extrapolation of the currently favored cosmological model, the Lambda-CDM model, this acceleration becomes more dominant into the future. In June 2016, NASA and ESA scientists reported that the universe was found to be expanding 5% to 9% faster than thought earlier, based on studies using the Hubble Space Telescope.[2]
https://en.wikipedia.org/wiki/Expansion_of_the_universe
Question 1:
It's related to the first paragraph of Quote 4.

What does it mean when it's said that all the present physics theories break down if they try to explain what happened before the Planck epoch, i.e. from 0 seconds to 10^-43 seconds. This is also said that the theory of quantum gravity will be able to explain it one day. For example, to put in perspective, I think I understand how at small scale the theory of general relativity fails, one of the reasons from a layman perspective, is that the location of a particle is not fixed at microscopic scale and hence is the curvature of space-time is also not fixed to one location.

Question 2:
During the inflation, the space was able to expand at faster than the speed of light, at almost 3.3 x 10^40 times the speed of light as shown in the "Calculation" below. But how did whatever the 'material' that non-inflated space contained within it before the inflation was able to keep pace with the inflated space. Did the material the space contained in it also inflated at the same rate?

Calculation:
As the Wikipedia article, Quote 6, says that during inflation 1 nm distance expanded to 62 trillion miles over the period of 10^-32 second (assuming inflation lasted from10^-36 second to 10^-32 second).

62 (10^12) miles
62 (10^12) miles / 10^-32 second
62 (10^44) miles/second
speed of light 186000 miles/second
3.3 x 10^40 times the speed of light

Question 3:
You can access the hi-res copy of the table here: https://photos.app.goo.gl/jS3apBR5gQ2SuDFv9
The copy of it is attached as well.
Table source: https://en.wikipedia.org/wiki/Chronology_of_the_universe#Tabular_summary

For the epoch titled "Inflationary epoch, Electroweak epoch" between 10^-36 to 10^-32 seconds, in green highlight it says, "Cosmic inflation expands space by a factor of the order of 10^26 over a time of the order of 10^−36 to 10^−32 seconds".

For the epoch titled "Electroweak epoch ends" around 10^-12 second, in yellow highlight, it says "The sphere of space that will become the observable universe is approximately 300 light-seconds in radius at this time".

This part has confused me a lot. As it is said the universe was infinite to start with, then the big bang happened everywhere. The visible universe is a subset of the whole universe. If the visible universe is compressed back, it would result into a singularity. Informally speaking at the time of big bang, such singularities were present everywhere in the universe. At the time of big bang, all those singularities exploded.

If the universe was really infinite to start with then how it can expand by a factor of 10^26. Is it infinity expanding by a factor of the order of 10^26?! If it's been estimated that it expanded by a factor of 10^26 then the size of universe at the beginning should have been known.

Question 4:
Under Quote 5, under third paragraph, it says, "Inflation stopped at around the 10^−33 to 10^−32 seconds mark, with the universe's volume having increased by a factor of at least 1078. Reheating occurred until the universe obtained the temperatures required for the production of a quark–gluon plasma as well as all other elementary particles".

How did the reheating occur? I understand that as the universe expanded, its temperature should have dropped. But then how did it reheat itself?

Question 5:
If you look under the column titled "Epoch" of the table, there is a row labelled "Electroweak epoch end" around 10^-12 seconds after the big bang. It seems like induvial particles such bosons and fermions started coming into existence around that time. I've highlighted the terms in blue.

The photons came into existence during the epoch titled "Quark epoch" which occurred between 10^-12 second to 10^-5 second after the big bang.

Do you think I'm understanding it correctly as a layman?

You can access the hi-res copy of the table here: https://photos.app.goo.gl/jS3apBR5gQ2SuDFv9
The copy of it is attached as well.
Table source: https://en.wikipedia.org/wiki/Chronology_of_the_universe#Tabular_summary

Question 6:
It's just a general question.

Under Quote 1, in first paragraph, it says, "Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago)".

It means that the expansion was taking place but it was getting slow, then the acceleration stared happening as the influence of dark energy started becoming dominant. Do I have it correct?Helpful pictures:
1: https://i.pinimg.com/originals/48/1d/23/481d23ef05001a866efe128f6b955197.jpg
2: https://www.ctc.cam.ac.uk/images/contentpics/outreach/cp_universe_chronology_large.jpg
3: http://cdn.sci-news.com/images/enlarge/image_2469_2e-Cosmic-Microwave-Background.jpg
4: http://cdn.sci-news.com/images/enlarge/image_2469_2e-Cosmic-Microwave-Background.jpg

 

[Ibix]

What does it mean when it's said that all the present physics theories break down if they try to explain what happened before the Planck epoch,

You can recover Newtonian gravity from relativity by making the assumption that some parts of the equation are "small". "Small" in that case turns out to mean things like all velocities being very much less than $c$ - because some terms involve $v/c$, and when that's a tiny number that term doesn't matter. The terms you're left with turn out to be Poisson's form of Newtonian gravity. In general, future theories must simplify to current theories in some limit because they have to explain all the experiments we've done to date, so they must look like the current theories because those fit the data.

An educated guess for when GR breaks down (i.e., when whatever the extra terms in quantum gravity are become large enough we can't neglect them) is when curvature constants (which have dimension of length raised to minus some power) approach the Planck length raised to the appropriate negative power. In the case of the cosmological model this is the Planck Epoch.

Note that referring to the Planck Epoch as an amount of time after the singularity is a bit weird because the whole point is that we expect that general relativity doesn't work there and there is no singularity. So what it means is something like "the first $10^{-43}\mathrm{s}$ of the model are probably invalid".

During the inflation, the space was able to expand at faster than the speed of light

Neither inflation nor the later expansion is sensibly measured with a speed. Nearby points separate more slowly than further apart points - you need to use something like the Hubble constant, which measures the rate at which the distance growth increases with distance. In the inflationary phase the growth rate is very very high, but even now there are points receding from us faster than light.

It isn't a question of matter "keeping up with space". The idea that "nothing can travel faster than light" is only a universal truth in special relativity. In curved spacetime you need a more general definition, such as looking at the shapes of light cones.

If the universe was really infinite to start with then how it can expand by a factor of 10^26.

The quote doesn't talk about the whole universe. It talks about the size increase of a finite region (the observable universe), and it is referring to the time between $10^{-32}\mathrm{s}$ and $10^{-12}\mathrm{s}$, which does not include the singularity so there's no issues with scale.

How did the reheating occur?

There was a phase transition and a lot of energy condensed out of the inflaton field into matter and radiation. It's analogous to how you can end up with serious burns from steam - steam at 100 C turning into water at 100 C releases energy even though its temperature doesn't change, and that energy is available to heat stuff up.

It means that the expansion was taking place but it was getting slow, then the acceleration stared happening as the influence of dark energy started becoming dominant. Do I have it correct?

More or less. The rate of expansion depends on the mix of various kinds of thing - radiation, matter, dark energy, etc, and since the energy density of all of those changes at different rates as expansion proceeds, the expansion rate changes. In the early universe the mix was such that the expansion rate decreased, but now the mix has changed and the rate is accelerating.

 

[kimbyd]

An educated guess for when GR breaks down (i.e., when whatever the extra terms in quantum gravity are become large enough we can't neglect them) is when curvature constants (which have dimension of length raised to minus some power) approach the Planck length raised to the appropriate negative power. In the case of the cosmological model this is the Planck Epoch.

GR might also break down at or near the event horizon of a black hole, even though the curvature is not at all extreme at that location. This is suggested by the existence of Hawking radiation, which is not predicted by General Relativity (it's a fundamentally quantum phenomenon). If this were to be the case, then in all likelihood the event horizon of a black hole would not be a "true" horizon, and something else would be going on. This is unknown at present, but future observations of black holes could, in principle, differ from General Relativity's predictions by some amount. I believe current observations put some significant constraints on how much black holes can differ from GR's prediction, but I don't think they're that strong just yet.

For more on this, you can read up on the proposed Firewall phenomenon and the fuzzball hypothesis (I believe this is currently an unsettled debate in physics).

 

[PainterGuy]

Thank you very much for the help!Related to Question 1:

You can recover Newtonian gravity from relativity by making the assumption that some parts of the equation are "small". "Small" in that case turns out to mean things like all velocities being very much less than c - because some terms involve v/c, and when that's a tiny number that term doesn't matter. The terms you're left with turn out to be Poisson's form of Newtonian gravity. In general, future theories must simplify to current theories in some limit because they have to explain all the experiments we've done to date, so they must look like the current theories because those fit the data.

An educated guess for when GR breaks down (i.e., when whatever the extra terms in quantum gravity are become large enough we can't neglect them) is when curvature constants (which have dimension of length raised to minus some power) approach the Planck length raised to the appropriate negative power. In the case of the cosmological model this is the Planck Epoch.

Note that referring to the Planck Epoch as an amount of time after the singularity is a bit weird because the whole point is that we expect that general relativity doesn't work there and there is no singularity. So what it means is something like "the first 10^−43s of the model are probably invalid".

I'm still struggling with it. Anyway, before the end of Planck epoch gravity was not a distinct force so that could be the reason application of the theory of general relativity doesn't make sense. Please check below.

In physical cosmology, assuming that nature is described by a Grand Unified Theory, the grand unification epoch was the period in the evolution of the early universe following the Planck epoch, starting at about 10^−43 seconds after the Big Bang... During this period, three of the four fundamental interactions—electromagnetism, the strong interaction, and the weak interaction—were unified as the electronuclear force. Gravity had separated from the electronuclear force at the end of the Planck era.

https://en.wikipedia.org/wiki/Grand_unification_epoch

Also, before the end of Planck epoch, the size of universe was comparable to Planck length therefore distance also loses its meaning. That could also be the reason that GR doesn't hold.Related to Question 2:

Neither inflation nor the later expansion is sensibly measured with a speed. Nearby points separate more slowly than further apart points - you need to use something like the Hubble constant, which measures the rate at which the distance growth increases with distance. In the inflationary phase the growth rate is very very high, but even now there are points receding from us faster than light.

It isn't a question of matter "keeping up with space". The idea that "nothing can travel faster than light" is only a universal truth in special relativity. In curved spacetime you need a more general definition, such as looking at the shapes of light cones.

I'm sorry but I don't follow you.

In the present universe, the speed of light is the speed of causality. (I'm using the term "present universe" because I don't know if the speed of causality has been the same). Nothing can move faster than the speed of light but this rule is not applicable to the space itself. That's the reason that some parts of space are expanding at faster than the speed of light.

So, when the inflation occurred, did everything expanded at the same rate? By the way, does it even make sense to speak of space as a distinct entity during that time period? It might have been something completely different - some kind of stuff made up entities we now call space, energy and whatever.

I'd request you to check Question 5 from my previous post since it could be relevant here. BTW, you forgot to address Question 5 in your message. :)Related to Question 3:

The quote doesn't talk about the whole universe. It talks about the size increase of a finite region (the observable universe), and it is referring to the time between 10^−32s and 10^−12s, which does not include the singularity so there's no issues with scale.

I don't think I was able to state my confusion clearly in my previous message.

Quote 6: (from my previous post)

According to inflation theory, during the inflationary epoch about 10^−32 of a second after the Big Bang, the universe suddenly expanded, and its volume increased by a factor of at least 10^78 (an expansion of distance by a factor of at least 10^26 in each of the three dimensions). This would be equivalent to expanding an object 1 nanometer (10^−9 m, about half the width of a molecule of DNA) in length to one approximately 10.6 light years (about 10^17 m or 62 trillion miles) long.

https://en.wikipedia.org/wiki/Expansion_of_the_universeNow using the table for two paragraphs below. Chronology of the universe: https://photos.app.goo.gl/jS3apBR5gQ2SuDFv9

For the epoch titled "Inflationary epoch, Electroweak epoch" between 10^-36 to 10^-32 seconds, in green highlight it says, "Cosmic inflation expands space by a factor of the order of 10^26 over a time of the order of 10^−36 to 10^−32 seconds".

For the epoch titled "Electroweak epoch ends" around 10^-12 second, in yellow highlight, it says "The sphere of space that will become the observable universe is approximately 300 light-seconds in radius at this time".What confuses me is that the radius of 300 light-seconds (or, diameter of 600 light-seconds) seems quite small. As it says above, "an expansion of distance by a factor of at least 10^26 in each of the three dimensions".

Let's check it. I'm going to use 600 light-second diameter for the observable universe.

600 light-second = 1.8 x 10^8 km
y x 10^26 = 1.8 x 10^8 km
y = 1.8 x 10^8 / 10^26
y = 1.8 x 10^-18 km
y = 1.8 x 10^-15 m
y = 1.8 x 10^-6 nm

For comparison:
radius of proton: 8.8 x 10^-16 m
diameter of proton: 18 x 10^-16 m

So, before the inflation, the diameter of observable universe was almost 1.8 x 10^-6 nm. Do you think I'm correct?Note to self:
In my first post I forgot to mention that I also used some material from the documentary How did the Universe Begin 2021, part of the series Secrets of the Universe by Curiosity.
documentary

 

[Orodruin]

Anyway, before the end of Planck epoch gravity was not a distinct force

There is no way that you could possibly know that.

You are missing the huge caveat in the beginning of the text you quoted which presumes the existence of a grand unified theory. Obviously GR breaks down at (if not before) the GUT scale in that case.

Nothing can move faster than the speed of light but this rule is not applicable to the space itself. That's the reason that some parts of space are expanding at faster than the speed of light.

This is wrong. Please stop saying that ”space expands faster than light”. As was already pointed out, the expansion of space is a rate, not a speed. Consider an ant moving on an inflating baloon (please forget the third dimension and just consider the surface itself). The expansion of space is how the baloon’s surface is being stretched. The speed of light is the maximal speed that the ant can move on that surface.

So, when the inflation occurred, did everything expanded at the same rate? By the way, does it even make sense to speak of space as a distinct entity during that time period? It might have been something completely different - some kind of stuff made up entities we now call space, energy and whatever.

Experimentally we obviously don’t know. Theoretically, spacetime is fine during inflation for the most part.

As to question 5:

Do you think I'm understanding it correctly as a layman?

No. No layman is going to really understand that part correctly as doing so requires a quite advanced knowledge of quantum field theory.

So, before the inflation, the diameter of observable universe was almost 1.8 x 10^-6 nm. Do you think I'm correct?

It says at least a factor 10^26. It could be more. But you should not be surprised to find very small numbers here. It is in the nature of inflation.