I have some somewhat detailed questions about inflation, curvature, and entropy

[ocsis2]

I posted these on Reddit but some questions weren't answered so I was wondering if people here could help:

First Part

Is the energy of the universe now the same as it was at the Big Bang, more, or less?

At the Big Bang there was very low volume (infinitesimal?), very high temperature/pressure (fuzzy on which it would be), and very low entropy. (And a certain amount of energy)

The increase in volume of the universe (big bang, expansion, etc) resulted in the temperature decreasing, entropy increasing, and energy staying constant?

I was informed that the universe did actually exponentially gain energy during inflation and perhaps other periods of its development.

So how does this affect the entropy and energy relation above?

I assumed since the change in energy is equal to the temperature times the change in entropy that the universe started off as having very low volume, very high temperature/pressure, and low entropy. The high pressure drove the expansion in volume which caused temperatures to decrease and entropy to increase.

So that's wrong.

But if the inflationary period came with an exponential growth of energy, how did the universe get colder? Was this compensated by a massively exponential increase in entropy?

Why do we need something with negative pressure to be responsible for inflation. Wouldn't the extremely high positive pressure with low volume of the initial Big Bang conditions be enough to drive inflation?

Second Part

I'm a little confused by this:

http://en.wikipedia.org/wiki/Flatness_problem

Which seems to imply the universe is more curved now than it was soon after the Big Bang. Look at the graph on the right side. It's not drawn to scale but clearly implies that with continued expansion the mass-energy density to critical density ratio (Omega) will change which should mean a difference in curvature... no?

In other words the term |Ω − 1| is currently less than 0.01, and therefore must have been less than 10−62 at the Planck era.

So while it's still close to flat, it was closer to flat in the early period of the universe than it is now? And this is due to the mass-energy density decreasing quicker (due to expansion) than the curvature?

- And this is a problem because this implies the curvature had to be closer to flat (Omega had to be closer to 1) very early on, and this low level of curvature could not have contributed enough to the expansion of the universe to match the contribution of the mass-energy density? When they should have matched? Implying curvature was being governed by some other factor? (Assuming one didn't go the philosophical route of invoking the anthropic principle)

- OR am I reading the Wiki's language incorrectly and it merely says that curvature and mass-energy density should match but they don't as mass-energy density decreases faster than curvature which implies curvature in the past approaches the necessary value for the critical density? Which then implies that curvature is being affected by more than just mass-energy density?

So the inflationary model says there's an inflaton field which drove the sharp exponential inflation during the early period of the universe which quickly flattened out the universe (overriding the effect of mass-energy density?) and then the curvature began to deviate away again slowly as the universe continued to expand?

So now the curvature will increase slightly to match our current Omega which is slightly off the critical density? Should this not then mean that the universe is actually not flat but spherical (due to omega slightly greater than one) and soon to be hyperbolic because of the decreasing energy density? (due to expansion driven by dark energy)?

And this explains how the universe lasted long enough to reach its current (relatively) highly differentiated stage at local levels (due, I suppose, to its advanced age and gravitation) while simultaneously holding global equilibrium (i.e, homogeneity and thermal equilibrium) rather than collapse almost as soon as it had began? Or additionally is it that this explains how the universe grew as much as it did in as short a time period as it did? Were we expecting a smaller size for the universe's age or something which also influenced the development of inflationary theory? (You can ignore this last paragraph if it doesn't make sense, I'm not too sure what I'm going on about either)

But even then, if it's not perfectly flat, it gets progressively less flat with time.

Does this mean that it's slowly gaining curvature? Will it eventually become spherical or perhaps hyperbolic?

Does the expansion from dark energy affect flatness?

I thank you all in advance for any help you can provide in clearing up my confusion!

Third Part

Regarding this thread:

https://www.physicsforums.com/showthread.php?t=506985

Why is the idea that the total energy in the universe "zero" so popular (re: Laurence Krauss) and why is the flatness of the universe used to back this up when, according to that post, an open universe would not conserve energy so the total energy of the universe cannot be "zero", can it? What's the energy being defined as zero and why is that energy used to predict things about the universe when "the" energy (as the term is used in that post) is not zero?

 

[Mark M]

I posted these on Reddit but some questions weren't answered so I was wondering if people here could help:

Hi ocsis, glad you came here.

First Part

I was informed that the universe did actually exponentially gain energy during inflation and perhaps other periods of its development.

Well, this is mostly correct. The universe initially gained an enormous amount of energy as inflation began, but it cooled dramatically during inflation. After it ended, the field that drove inflation, the inflaton field, decayed into a hot bath of particles, reheating the universe.

So how does this affect the entropy and energy relation above?

As the universe gains volume, entropy increases, and temperatures decrease. Energy is unaffected, density just decreases. But remember, inflation had a large effect on the energy in the universe, I addressed that above. Normal expansion does not.

But if the inflationary period came with an exponential growth of energy, how did the universe get colder? Was this compensated by a massively exponential increase in entropy?

After inflation ended, the universe began to cool.

Why do we need something with negative pressure to be responsible for inflation. Wouldn't the extremely high positive pressure with low volume of the initial Big Bang conditions be enough to drive inflation?

Remember, positive energy/mass/pressure cause attractive gravity, which is the positive curvature of space. Negative pressure, on the other hand, causes repulsive gravity, the expansion of space.

Second Part



I thank you all in advance for any help you can provide in clearing up my confusion!

An increase in curvature applies only is the universe is closed or open. If it is exactly flat, it will remain so forever. If it began closed, it will become more and more positively curved. If it is open, it will become more and more negatively curved.

Third Part

Regarding this thread:

https://www.physicsforums.com/showthread.php?t=506985

Why is the idea that the total energy in the universe "zero" so popular (re: Laurence Krauss) and why is the flatness of the universe used to back this up when, according to that post, an open universe would not conserve energy so the total energy of the universe cannot be "zero", can it? What's the energy being defined as zero and why is that energy used to predict things about the universe when "the" energy (as the term is used in that post) is not zero?

If the universe is closed, it would have a net positive amount of energy. If it is open, it would have a net negative energy. If it is flat, the total energy of everything in the universe would be offset by the negative gravitational energy, resulting in the universe having zero total energy, the ultimate 'free lunch', as Alan Guth calls it.

 

[ocsis2]

Will the negative pressure of dark energy which is driving current and future expansion also "flatten" the universe? Why?

 

[Mark M]

Will the negative pressure of dark energy which is driving current and future expansion also "flatten" the universe? Why?

The expansion due to dark energy is far weaker than that of inflation. As far as I know, it does not flatten the universe.

 

[TheTechNoir]

Also I'd like to point out that the big bang theory does not require that the universe was small at the time of the big bang, in fact many if not most cosmologists don't believe this view of an infinitesimally small/dense state of the universe.

 

[ocsis2]

Also I'd like to point out that the big bang theory does not require that the universe was small at the time of the big bang, in fact many if not most cosmologists don't believe this view of an infinitesimally small/dense state of the universe.

Well it had to be pretty dense and small if:

The basic answer, however, is quite simple. Nothing can travel faster than the speed of light through space. This does not, however, limit the speed at which space can expand. In the first 1E-35 seconds (that is 0.00..(34 zeroes)..01 seconds after the big bang the universe expanded to a diameter of something like 1 meter carrying all matter with it.

Dick Plano, Professor of Physics emeritus, Rutgers University

http://www.Newton.dep.anl.gov/askasci/phy00/phy00990.htm

Also, from Wiki,

Prior to the expansion period, the inflaton field was at a higher energy state. Random quantum fluctuations triggered a phase transition whereby the inflaton field released its potential energy as matter and radiation as it settled to its lowest energy state. This action generated a repulsive force that drove the portion of the universe that is observable to us today to expand from approximately 10−50 metres in radius at 10−35 seconds to almost 1 metre in radius at 10−34 seconds.

 

[ocsis2]

The expansion due to dark energy is far weaker than that of inflation. As far as I know, it does not flatten the universe.

Thanks for your help here! One more question, how did inflation add energy to the universe? What mechanism did this occur by? In other words, where did that energy come from? Was it due to the quantum fluctuation (or that scalar field rolling down a potential energy hill) to a lower, more stable energy state? This energy then manifested as exponential expansion, and then switched from expansion into heating (by filling up the universe with hot quark-gluon plasma)? Do we know the mechanism for this expansion->reheating switch?

 

[Mark M]

Well it had to be pretty dense and small if:



Also, from Wiki,

Well it was very, very dense, but defining distance of a global scale is a difficult matter. Simply because, if the universe is finite, it wraps back on itself like the surface of a balloon, there is no boundary. If you define the distance as being in between points where the universe began to repeat (in the case of the balloon analogy, the circumference), then it could have been small, but not necessarily. Just small relative to today's universe.

Also, the quote you posted is of the observable universe, what we can see.

 

[TheTechNoir]

Well it had to be pretty dense and small if:

"The basic answer, however, is quite simple. Nothing can travel faster than the speed of light through space. This does not, however, limit the speed at which space can expand. In the first 1E-35 seconds (that is 0.00..(34 zeroes)..01 seconds after the big bang the universe expanded to a diameter of something like 1 meter carrying all matter with it.

Dick Plano, Professor of Physics emeritus, Rutgers University

http://www.Newton.dep.anl.gov/askasc...0/phy00990.htm"

Not so. It was very dense yes, but we have no strong evidence that says it had to be small. This quotation applies to the observable universe, considering we do not know for certain the size of the universe or if it is even finite or not, we simply don't know it's size in the first 1E-35 seconds. Anywhere from small to infinitely large.

EDIT: Mark got it - thanks.

 

[ocsis2]

Not so. It was very dense yes, but we have no strong evidence that says it had to be small. This quotation applies to the observable universe, considering we do not know for certain the size of the universe or if it is even finite or not, we simply don't know it's size in the first 1E-35 seconds. Anywhere from small to infinitely large.

EDIT: Mark got it - thanks.

This brings up a related thing I've often wondered about. Do we have any evidence for the existence of an unobservable universe at the Big Bang?

Or even now? I figure if stuff disappears beyond the cosmological horizon it would qualify as unobservable universe which developed after the Big Bang. Have we observed that yet?

 

[TheTechNoir]

This brings up a related thing I've often wondered about. Do we have any evidence for the existence of an unobservable universe at the Big Bang?

Or even now? I figure if stuff disappears beyond the cosmological horizon it would qualify as unobservable universe which developed after the Big Bang. Have we observed that yet?

Prior to 300,000 years after the big bang the entire universe was unobservable.

I suggest reading this section of this article: http://en.wikipedia.org/wiki/Observable_universe#The_universe_versus_the_observable_universe

Your question was worded a bit wrong/funny but I understand what you're asking so no: in principal it is impossible to know anything with certainty that has and will forever remain outside of the observable universe so the answer is no we don't have evidence of that, but none on the contrary either and multiple reputable or leading models make predictions that suggest a large or infinite size at those earliest moments.

 

[ocsis2]

Prior to 300,000 years after the big bang the entire universe was unobservable.

I suggest reading this section of this article: http://en.wikipedia.org/wiki/Observable_universe#The_universe_versus_the_observable_universe

Your question was worded a bit wrong/funny but I understand what you're asking so no: in principal it is impossible to know anything with certainty that has and will forever remain outside of the observable universe so the answer is no we don't have evidence of that, but none on the contrary either and multiple reputable or leading models make predictions that suggest a large or infinite size at those earliest moments.

Which models are those?

 

[Mark M]

Thanks for your help here! One more question, how did inflation add energy to the universe? What mechanism did this occur by? In other words, where did that energy come from? Was it due to the quantum fluctuation (or that scalar field rolling down a potential energy hill) to a lower, more stable energy state? This energy then manifested as exponential expansion, and then switched from expansion into heating (by filling up the universe with hot quark-gluon plasma)? Do we know the mechanism for this expansion->reheating switch?

Sorry, for missing these questions, I'll answer them now.

Inflation added energy in two ways, I'll explain them both.

First, was the enormous deposit of energy just as inflation began. Imagine that two spaceships are held together by a rubber band. If the spaceships continue to pull away, the rubber band will get tighter and tighter. As it does so, the kinetic energy from the spaceships is transferred to the rubber band, which will build up a large store of energy.

Similarly, a gravitational field can do the same thing. It can 'store' energy when large objects curve spacetime. (these usually come into effect as gravitational waves)

So, remember, inflation was an enormous burst of repulsive gravity. So, instead of storing energy, it dumped massive amounts of energy into the universe. And I mean massive. In chaotic inflation, this is what creates the 10³² degree temperatures during the Planck time.

Once inflation got underway, however, the universe began to cool as it expanded. It cooled down to approximately 10²⁸ degrees. After inflation ended, the inflaton field decayed into an extraordinarily hot bath of radiation, reheating the universe. This radiation, along with the heat from inflation, soon gave birth to quark-gluon plasma through particle pair production. It still remains a mystery how matter managed to outnumber anti-matter. Supersymmetry provides an explanation in which leptons could be converted to Baryons, which would have thrown off the balance.

Which models are those?

Eternal inflation actually allows for finite 'bubble universes' that form when inflation ends to become infinite in size. This is because of how dramatically inflation warps time, opposite of the effect on objects orbiting a black hole.