Quantum tunneling and the universe

[Rational T]

Alexander Vilenkin has a model of cosmic origins which describes the universe coming into being as a quantum tunneling event. The problem that I see with this, is that this requires the universe to be closed. However, we know the universe is probably flat with a margin of error of less than 1%. Does this mean, the model is a dud? Or, is there some way around it?

 

[Maui]

Everyone on the planet entertains some model of the beginning. Why is his model more plausible than the other million or so?

 

[Naty1]

The shape of the universe is still an open debate:

http://en.wikipedia.org/wiki/Closed_universe#Closed_Universe

I suspect a majority believe the universe is close to Ω = 1...and that seems reasonable
so far; but if history is any guide, that may not be very important.

 

[Rational T]

Well, of course science at this point is not absolute, anything can potentially be proven wrong. The point is, based on all available evidence we have, the universe is most likely flat.

 

[Mark M]

Alexander Vilenkin has a model of cosmic origins which describes the universe coming into being as a quantum tunneling event. The problem that I see with this, is that this requires the universe to be closed. However, we know the universe is probably flat with a margin of error of less than 1%. Does this mean, the model is a dud? Or, is there some way around it?

Well, the key is 'within one percent'. The mainstream view is that the early universe underwent an incredibly rapid expansion called inflation. One effect of inflation is make any region of the universe enormous. So, after inflation, any spatial curvature would become undetectable. Therefore, measuring the universe is close to flat may just mean that inflation made the universe large enough that no curvature can be detected with our current measurements. So, Vilenkin's model is perfectly valid.

 

[Rational T]

Well, the key is 'within one percent'. The mainstream view is that the early universe underwent an incredibly rapid expansion called inflation. One effect of inflation is make any region of the universe enormous. So, after inflation, any spatial curvature would become undetectable. Therefore, measuring the universe is close to flat may just mean that inflation made the universe large enough that no curvature can be detected with our current measurements. So, Vilenkin's model is perfectly valid.

One percent is a pretty good margin of error I would say. Also, if any spatial curvature could not be detected anyway, then why does NASA and other websites claim it is flat wuth such accuracy? What is the point of this discovery which if one could just say "It's just as likely it is closed, but we just can't detect the evidence". Also, doesn't that assumption violate Occam's Razor? Doesn't it make more sense to say the universe is most likely flat based on all available evidence, until evidence contradicts it?

Regardless, if the universe is really closed then it would have a net energy which is negative. This would mean the universe doesn't really have a net energy of zero, which means Alexander's model fails. Only if the universe has a net energy of zero could it have possibly come from "nothing". Alexander Vilenkin claims that the positive and negative energy balance out, but this is only true under the assumption of a flat universe. With a closed universe, isn't there a negative net energy?

"The universe is neither spherical shaped, like the shape of a ball. That would be positive curvature, having net negative energy" - Neil deGrasse Tyson

"The gravitational energy which is always negative exactly compensates the positive energy of matter. So the energy of a closed universe is always zero" - Alexander Vilenkin

Can you explain how Alexander Vilenkin can get away with claiming a zero energy universe, if it is closed? Conventional wisdom is that a closed universe has a net negative energy based on what I have read, not a net energy of zero like in a flat universe.

 

[Chalnoth]

Alexander Vilenkin has a model of cosmic origins which describes the universe coming into being as a quantum tunneling event. The problem that I see with this, is that this requires the universe to be closed. However, we know the universe is probably flat with a margin of error of less than 1%. Does this mean, the model is a dud? Or, is there some way around it?

It only requires that the universe be slightly closed. This is perfectly compatible with measuring near-flatness. It may even be compatible with measuring very slightly negative curvature, as we can only measure the curvature of our observable region, but the statement about a universe from a quantum tunneling event being closed is a global statement that doesn't necessarily rule out some sub-regions within the universe being open.

 

[Rational T]

It only requires that the universe be slightly closed. This is perfectly compatible with measuring near-flatness. It may even be compatible with measuring very slightly negative curvature, as we can only measure the curvature of our observable region, but the statement about a universe from a quantum tunneling event being closed is a global statement that doesn't necessarily rule out some sub-regions within the universe being open.

How can the universe have a total energy of zero, if the universe is closed though? I thought that conventional wisdom told us that only provided the universe is flat, does the net energy equal zero. If it doesn't equal zero, then one is forced to ask where that little spark of energy came form. Thus, I still fail to see how Alexander's model works by assuming a closed universe. I'm not saying you are wrong, but would you please clarify your position? Thank you.

 

[Rational T]

It only requires that the universe be slightly closed. This is perfectly compatible with measuring near-flatness. It may even be compatible with measuring very slightly negative curvature, as we can only measure the curvature of our observable region, but the statement about a universe from a quantum tunneling event being closed is a global statement that doesn't necessarily rule out some sub-regions within the universe being open.

Basically, Alexander Vilenkin can say the universe came from "nothing" if the total energy of the universe is zero (I guess this makes sense, because "nothing" would have a net energy of zero as well). This is what he does in fact claim. However, in a closed universe, there is a net negative energy based on what I have researched, and only in a flat universe do you get a net energy of zero.

 

[Chalnoth]

How can the universe have a total energy of zero, if the universe is closed though?

It is only for a closed universe that it is possible (so far as we are aware) to define a total energy such that the total energy is zero. I don't know where you got the idea that this result is for a flat universe.

 

[Rational T]

It is only for a closed universe that it is possible (so far as we are aware) to define a total energy such that the total energy is zero. I don't know where you got the idea that this result is for a flat universe.

"Alan Guth's term of inflation, which causes our universe to be flat, like inflating a ball decreases its surface curvature and makes it flat. Another factor proposed by Guth which should be considered is that in such a flat universe, the total gravitational energy equals zero." - http://news.softpedia.com/news/Zero-Energy-and-the-Flat-Universe-98861.shtml

"A gravitational field has negative energy. Matter has positive energy. The two values cancel out provided the universe is completely flat. In that case the universe has zero energy and can theoretically last forever." - http://en.wikipedia.org/wiki/Zero-energy_universe

Everything I have researched, concludes that if the universe is flat it has a net energy of zero, and if it is closed, it has a net negative energy.

"The universe is neither spherical shaped, like the shape of a ball. That would be positive curvature, having net negative energy." - Neil deGrasse Tyson ()

 

[Chalnoth]

"Alan Guth's term of inflation, which causes our universe to be flat, like inflating a ball decreases its surface curvature and makes it flat. Another factor proposed by Guth which should be considered is that in such a flat universe, the total gravitational energy equals zero." - http://news.softpedia.com/news/Zero-Energy-and-the-Flat-Universe-98861.shtml

"A gravitational field has negative energy. Matter has positive energy. The two values cancel out provided the universe is completely flat. In that case the universe has zero energy and can theoretically last forever." - http://en.wikipedia.org/wiki/Zero-energy_universe

Everything I have researched, concludes that if the universe is flat it has a net energy of zero, and if it is closed, it has a net negative energy.

"The universe is neither spherical shaped, like the shape of a ball. That would be positive curvature, having net negative energy." - Neil deGrasse Tyson ()

The statement that the universe has zero total energy comes from what is known as the Hamiltonian formalism of General Relativity. See here:
http://arxiv.org/PS_cache/gr-qc/pdf/0605/0605063v3.pdf

Looks like I was part-wrong, in that it is also possible to define zero total energy for a flat universe.

That said, one of the main problems here is that the pseudo-tensor approach which leads to the zero-energy result is somewhat arbitrary: it depends explicitly upon the coordinates used. There isn't any absolute sense in which it is possible to state that any universe is or is not zero-energy, because there isn't any absolute way to define the total energy of a universe. To me, the zero-energy universe is just an interesting conceptual idea to understand how it is perfectly sensible for a universe to appear as a vacuum fluctuation, or for the apparent energy in matter fields to increase or decrease as the universe expands. It should not be taken as truth, or even as necessary. Because the simple fact of the matter is that in General Relativity, energy is not conserved.

 

[Rational T]

The statement that the universe has zero total energy comes from what is known as the Hamiltonian formalism of General Relativity. See here:
http://arxiv.org/PS_cache/gr-qc/pdf/0605/0605063v3.pdf

Looks like I was part-wrong, in that it is also possible to define zero total energy for a flat universe.

That said, one of the main problems here is that the pseudo-tensor approach which leads to the zero-energy result is somewhat arbitrary: it depends explicitly upon the coordinates used. There isn't any absolute sense in which it is possible to state that any universe is or is not zero-energy, because there isn't any absolute way to define the total energy of a universe. To me, the zero-energy universe is just an interesting conceptual idea to understand how it is perfectly sensible for a universe to appear as a vacuum fluctuation, or for the apparent energy in matter fields to increase or decrease as the universe expands. It should not be taken as truth, or even as necessary. Because the simple fact of the matter is that in General Relativity, energy is not conserved.

(i) A closed universe means positively curved, hence a negative net energy (no?). How can a closed universe have net energy zero? I am not saying you are wrong, but could you provide a source stating that a zero energy universe is also possible with with a closed universe? From what I have read, it is possible with a flat universe, but a closed universe would be negative (once more, I could be wrong)

(ii) I never said the zero-energy universe was absolute truth. However, with all the evidence we have it is entirely plausible, and an attractive idea on top of that.

(iii) How is energy not conserved? Isn't that the First Law of Thermodynamics?

 

[Rational T]

The statement that the universe has zero total energy comes from what is known as the Hamiltonian formalism of General Relativity. See here:
http://arxiv.org/PS_cache/gr-qc/pdf/0605/0605063v3.pdf

Looks like I was part-wrong, in that it is also possible to define zero total energy for a flat universe.

That said, one of the main problems here is that the pseudo-tensor approach which leads to the zero-energy result is somewhat arbitrary: it depends explicitly upon the coordinates used. There isn't any absolute sense in which it is possible to state that any universe is or is not zero-energy, because there isn't any absolute way to define the total energy of a universe. To me, the zero-energy universe is just an interesting conceptual idea to understand how it is perfectly sensible for a universe to appear as a vacuum fluctuation, or for the apparent energy in matter fields to increase or decrease as the universe expands. It should not be taken as truth, or even as necessary. Because the simple fact of the matter is that in General Relativity, energy is not conserved.

“If the shape of the universe were anything else [besides flat], positively curved or negatively curved, it would not have zero energy.” – Neil DeGrasse Tyson

"The gravitational energy which is always negative exactly compensates the positive energy of matter. So the energy of a closed universe is always zero" - Alexander Vilenkin

Basically, both of the above statements cannot be true. Neil says that a closed universe could not have a net energy of zero, but Alex says the energy of a closed universe could always be zero. Who do you agree with?

 

[Chalnoth]

(i) A closed universe means positively curved, hence a negative net energy (no?).

Not at all. I think you're mistaking the critical density for the density required for zero net energy. This isn't at all what that means.

How can a closed universe have net energy zero? I am not saying you are wrong, but could you provide a source stating that a zero energy universe is also possible with with a closed universe?

I did, in the very post you're quoting. You can see the mentions in the introduction, and the calculation in section 3C, on pages 8-9.

 

[Rational T]

Not at all. I think you're mistaking the critical density for the density required for zero net energy. This isn't at all what that meansI did, in the very post you're quoting. You can see the mentions in the introduction, and the calculation in section 3C, on pages 8-9.

“If the shape of the universe were anything else [besides flat], positively curved or negatively curved, it would not have zero energy.” – Neil DeGrasse Tyson

So basically, what you are saying, is Neil DeGrasse Tyson is mistaken?

Also, yes you did provide a link, I see it now. Thank you.

 

[Chalnoth]

“If the shape of the universe were anything else [besides flat], positively curved or negatively curved, it would not have zero energy.” – Neil DeGrasse Tyson

So basically, what you are saying, is Neil DeGrasse Tyson is mistaken?

Yes. Which is perfectly understandable. It's not quite his field. He's an astronomer. This is about cosmology. And while there is some overlap, it isn't as much as you'd think.

 

[Mark M]

Basically, Alexander Vilenkin can say the universe came from "nothing" if the total energy of the universe is zero (I guess this makes sense, because "nothing" would have a net energy of zero as well). This is what he does in fact claim. However, in a closed universe, there is a net negative energy based on what I have researched, and only in a flat universe do you get a net energy of zero.

This is false. The total energy of a closed universe is zero. A flat universe may have zero energy, if and only if it is finite in size. See MS Berman's derivation:

http://arxiv.org/pdf/gr-qc/0605063.pdf

 

[Rational T]

This is false. The total energy of a closed universe is zero. A flat universe may have zero energy, if and only if it is finite in size. See MS Berman's derivation:

http://arxiv.org/pdf/gr-qc/0605063.pdf

By finite in size, do you mean, not expanding forever? If so, how can this be? Doesn't a flat universe necessitate the expansion of the universe slowing down, but never quite stopping?

 

[Rational T]

Yes. Which is perfectly understandable. It's not quite his field. He's an astronomer. This is about cosmology. And while there is some overlap, it isn't as much as you'd think.

I find it weird this video was released then, without it being peer-reviewed:



However, what you are saying makes sense. Therefore, I thank you for answering my questions, you have been a big help!

 

[Chalnoth]

By finite in size, do you mean, not expanding forever? If so, how can this be? Doesn't a flat universe necessitate the expansion of the universe slowing down, but never quite stopping?

No. What is meant is that any individual time-slicing of the universe at a finite time is finite in size. The size of the universe at infinite time is not relevant for this statement.

 

[audioloop]

Vilenkin has a model of cosmic which describes the coming into being as a event. The problem that I see with this, is that this requires the to be closed. However, we know the is probably with a margin of error of less than 1%. Does this , the model is a dud? Or, is there some way around it?

for open tunneling universe

Quantum Cosmology and Open Universes
http://arxiv.org/pdf/gr-qc/9905056.pdf

...Restricting ourselves to the Tunneling boundary condition, and applying it in turn to each of these curvatures, it is shown that quantum cosmology actually suggests that the Universe be open, k = −1...Quantum Creation of an Open Inflationary Universe
http://arxiv.org/abs/gr-qc/9802038

If one uses the tunneling wave function for the description of creation of the universe, then in most inflationary models the universe should have Ω = 1, which agrees with the standard expectation that inflation makes the universe flat.Nonsingular instantons for the creation of open universes
Phys. Rev. D 59, 043509

We show that the instability of the singular Vilenkin instanton describing the creation of an open universe can be avoided using, instead of a minimally coupled scalar field, an axionic massless scalar field which gives rise to the Giddings-Strominger instanton.

 

[Rational T]

for open tunneling universe

Quantum Cosmology and Open Universes
http://arxiv.org/pdf/gr-qc/9905056.pdf

...Restricting ourselves to the Tunneling boundary condition, and applying it in turn to each of these curvatures, it is shown that quantum cosmology actually suggests that the Universe be open, k = −1...Quantum Creation of an Open Inflationary Universe
http://arxiv.org/abs/gr-qc/9802038

If one uses the tunneling wave function for the description of creation of the universe, then in most inflationary models the universe should have Ω = 1, which agrees with the standard expectation that inflation makes the universe flat.Nonsingular instantons for the creation of open universes
Phys. Rev. D 59, 043509

We show that the instability of the singular Vilenkin instanton describing the creation of an open universe can be avoided using, instead of a minimally coupled scalar field, an axionic massless scalar field which gives rise to the Giddings-Strominger instanton.

"If one uses the tunneling wave function for the description of creation of the universe, then in most inflationary models the universe should have Ω = 1, which agrees with the standard expectation that inflation makes the universe flat"
Ah but this presents another problem with quantum tunneling models. The universe is not in a supposition state. This means, an observer must have collapsed the wave-function of the universe (meaning the tunneling does not really happen "spontaneously"). Correct me if I'm wrong, but the collapse of wave-functions don't just happen, it requires an observer (correct?).

 

[Chalnoth]

Ah but this presents another problem with quantum tunneling models. The universe is not in a supposition state. This means, an observer must have collapsed the wave-function of the universe (meaning the tunneling does not really happen "spontaneously"). Correct me if I'm wrong, but the collapse of wave-functions don't just happen, it requires an observer (correct?).

Wave function collapse does not require an observer. Here is an experiment where they collapsed a wave function simply by bathing the system in photons, without ever looking at those photons:
http://prl.aps.org/abstract/PRL/v77/i24/p4887_1

 

[Rational T]

Wave function collapse does not require an observer. Here is an experiment where they collapsed a wave function simply by bathing the system in photons, without ever looking at those photons:
http://prl.aps.org/abstract/PRL/v77/i24/p4887_1

What could have possibly caused the collapse of the universal wave-function though? Photons wouldn't have existed if the universal wave-function hadn't of collapsed yet, and was in a supposition state. They would have had to exist outside the universe to cause the collapse of the universal wave-function. Thus, you can't use them an an explanation for why the universal wave-function collapsed. There would have been nothing to cause the collapse of the universal wave-function unless due to an external measurement. Thus, these quantum tunneling models explain nothing, it just begs the question of who/ what measured the wave-function of the universe to cause it to collapse.

 

[Chalnoth]

What could have possibly caused the collapse of the universal wave-function though?

Wave function collapse only requires interaction with a sufficiently-complex system. Once the wave function of the universe had become complex enough, it would have effectively collapsed.

 

[Rational T]

Wave function collapse only requires interaction with a sufficiently-complex system. Once the wave function of the universe had become complex enough, it would have effectively collapsed.

What external complex system could have interacted with the wave-function to cause it to collapse though? It seems that the tunneling models just beg for an explanation with regards to what external, complex system interacted with the wave-function to cause it to collapse. One would have to explain what complex system existed outside the universe while it was in a supposition state, to cause this collapse. How is this possible?

 

[audioloop]

"If one uses the tunneling wave function for the description of of the , then in most inflationary the universe should have Ω = 1, which agrees with the standard expectation that inflation the universe flat"



Ah but this presents another problem with . The universe is not in a supposition state. This , an observer must have collapsed the wave-function of the universe (meaning the tunneling does not really happen "spontaneously"). Correct me if I'm wrong, but the of wave-functions don't just happen, it requires an observer (correct?).

non-linear quantum mechanics.
no need of observers.

 

[Rational T]

non-linear quantum mechanics.
no need of observers.

So what collapsed the universal wave-function?

 

[Rational T]

Also, one last question. Isn't quantum tunneling dependent on space-time? If so, how could it explain the universe? Thank you all very much for your time. The people on this site have been really generous with regards to answering my questions. I deeply appreciate that.

 

[audioloop]

So what collapsed the wave-function?

you know what is a linear schrodinger equation and a non linear equation and what is a superposition ?

 

[Rational T]

you know what is a linear schrodinger equation and a non linear equation and what is a superposition ?

All I know, is that wave-function collapse is due to measurement/ observation. My question is, what could have possibly caused the wave-function of the universe to collapse while it was in a state of uncertainty? Thank you.

 

[audioloop]

All I know, is that wave-function is due to measurement/ observation. My is, what could have possibly caused the wave-function of to while it was in a of uncertainty? .

measurement/observation is in-herited from the Copenhagen interpretation
...The Copenhagen interpretation assumes a mysterious division between the microscopic world governed by quantum mechanics and a macroscopic world of apparatus and observers that obeys classical physics. During measurement the state vector of the microscopic system collapses in a probabilistic way to one of a number of classical states, in a way that is unexplained, and cannot be described by the time-dependent Schrodinger equation...cos in standard quantum mechanics schrodinger equation is linear i.e. ever in superposition,

and in the many world interpretation:...assumes that the state vector of the whole of any isolated system does not collapse, but evolves deterministically according to the time-dependent Schrodinger equation...

 

[Rational T]

measurement/observation is heredited from the Copenhagen interpretation.

...The Copenhagen interpretation assumes a mysterious division between the microscopic world governed by quantum mechanics and a macroscopic world of apparatus and observers that obeys classical physics. During measurement the state vector of the microscopic system collapses in a probabilistic way to one of a number of classical states, in a way that is unexplained, and cannot be described by the time-dependent Schrodinger equation...

cos in standard quantum mechanics schrodinger equation is linear i.e. ever in superposition,

and in the many world interpretation:

...assumes that the state vector of the whole of any isolated system does not collapse, but evolves deterministically according to the time-dependent Schrodinger equation...

Alexander Vilenkin's model of cosmic origins says the universe could have began acausally as a quantum tunneling event. If what you are saying is true, that only determinism can explain this, then this is contradictory. How can something deterministic explain an acausal event? Also, appealing to multiple universes is a violation of Parsimony...I think you see the problem here.

 

[Rational T]

measurement/observation is in-herited from the Copenhagen interpretation



...The Copenhagen interpretation assumes a mysterious division between the microscopic world governed by quantum mechanics and a macroscopic world of apparatus and observers that obeys classical physics. During measurement the state vector of the microscopic system collapses in a probabilistic way to one of a number of classical states, in a way that is unexplained, and cannot be described by the time-dependent Schrodinger equation...


cos in standard quantum mechanics schrodinger equation is linear i.e. ever in superposition,

and in the many world interpretation:


...assumes that the state vector of the whole of any isolated system does not collapse, but evolves deterministically according to the time-dependent Schrodinger equation...

If you cannot explain how the universe's wave-function collapsed without appealing to determinism and many worlds, then tunneling models are duds and explain nothing.

 

[audioloop]

Vilenkin's of cosmic says could have began acausally as a . If what you are saying is true, that only determinism can explain this, then this is contradictory. How can something deterministic explain an acausal ? Also, appealing to multiple universes is a violation of Parsimony...I think you see the problem here.

like you said, vilenkin...

i do not agree completely with him.

some time ago i asked him personally, why exist the universe and he answered "rather ask the dalai lama" and after
we laugh a while...

and respect to many world, i dislike.

 

[audioloop]

why you say determinism ?

 

[Rational T]

why you say determinism ?

"...assumes that the state vector of the whole of any isolated system does not collapse, but evolves deterministically according to the time-dependent Schrodinger equation..."

You said it. All I'm saying, is that it's simpler to assume an observer from the outside collapsed the wave-function of the universe, than to introduce many worlds to explain it. Many worlds seems like a violation of Parsimony and Occam's Razor, to try to avoid the conclusion that an observer caused the universal wave-function collapse. One observer is simply than many worlds.

 

[Rational T]

why you say determinism ?

My point is that quantum tunneling is presented as an acausal event by advocates like Vilenkin, this is impossible though because something must have caused the universal wave-function collapse. If you appeal to many worlds to solve the problem, then you violate Occam'z Razor.

 

[audioloop]

"...assumes that the vector of the whole of any isolated system does not , but evolves deterministically according to the time-dependent Schrodinger equation..."

You said it. All I'm saying, is that it's simpler to assume an observer from the collapsed the -function of , than to introduce many worlds to explain it. Many worlds seems like a violation of Parsimony and Occam's Razor, to try to avoid the conclusion that an observer caused the wave-function . One observer is simply than many worlds.

i dislike many worlds, i am no aduce from it.

 

[audioloop]

If you appeal to many worlds to solve the problem, then you violate Occam'z Razor.

not me.

in many world there is no collapse.

i advocate objective collapse models. i.e. nonlinear quantum mechanics.

 

[Rational T]

not me.

i dislike many worlds, i am no aduce from it.

So you agree that an observer must have collapsed the universal wave-function. Since you dislike the many worlds idea..

 

[audioloop]

So you agree that an observer must have collapsed the -function. Since you dislike the many worlds idea..

no observers, in objective collapse models there is no need of observers.

 

[Rational T]

no observers, in objective collapse models there is no need of observers.

So, are you saying that Alexander Vilenkin's model based on objective collapse? Also, if no observers are required, then what actually does collapse the wave-function?

 

[Chalnoth]

What external complex system could have interacted with the wave-function to cause it to collapse though?

It doesn't have to be external. It just needs enough disparate parts that are tightly-interacting to cause collapse. One way of thinking of this is to divide the wavefunction into two regions that are tightly-interacting. As long as each region has enough complexity, the other will be forced to effectively collapse.

 

[Rational T]

It doesn't have to be external. It just needs enough disparate parts that are tightly-interacting to cause collapse. One way of thinking of this is to divide the wavefunction into two regions that are tightly-interacting. As long as each region has enough complexity, the other will be forced to effectively collapse.

So basically, are you saying the wave-function of the universe self-collapsed? If so, how often does this really occur in the real world without external measurement being a necessary condition?

 

[Rational T]

It doesn't have to be external. It just needs enough disparate parts that are tightly-interacting to cause collapse. One way of thinking of this is to divide the wavefunction into two regions that are tightly-interacting. As long as each region has enough complexity, the other will be forced to effectively collapse.

Also, aren't quantum events contingent to space-time? Or, is it just as plausible for a quantum tunneling event to emerge from a state void of space-time? Thank you.

 

[Chalnoth]

Also, aren't quantum events contingent to space-time? Or, is it just as plausible for a quantum tunneling event to emerge from a state void of space-time? Thank you.

I think this is just an artifact of not knowing the correct theory of quantum gravity.

 

[Rational T]

Also, Alexander's model only works if the universe is closed:

"The only verifiable (in principle) prediction of the model is that the universe must be closed." - http://mukto-mona.net/science/physics/a_vilinkin/universe_from_nothing.pdf

However, the theory of inflation predicts the universe is flat:

"The current theoretical belief (because it is predicted by the theory of cosmic inflation) is that the universe is flat..." - http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question35.html

 

[Mark M]

Also, Alexander's model only works if the universe is closed:

"The only verifiable (in principle) prediction of the model is that the universe must be closed." - http://mukto-mona.net/science/physics/a_vilinkin/universe_from_nothing.pdf

However, the theory of inflation predicts the universe is flat:

"The current theoretical belief (because it is predicted by the theory of cosmic inflation) is that the universe is flat..." - http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question35.html

The first statement is right, but the second is false. Nothing inflation requires implies flatness, there are some models that work with a closed universe.