B Big Bang and Infinite Universe

[Jimmy87]

Hi,

I’m pretty new to cosmology and I’m trying to get my head around the Big Bang and the potential infinite extent of the universe as a whole.

There’s lots of misleading info out there but this forum and a few others have helped me and I just wanted to check I have the right idea.

The Big Bang was the creation of space and time. At this instant t=0 space was infinite in size but the scale factor was zero. I’m picturing it (hopefully correctly) like an excel spreadsheet with infinite cells. At t=0 the size of the cells is zero but space is still infinite - this is where the excel spreadsheet analogy breaks down as you would have nothing to see on the screen. However, mathematically speaking it’s possible to be infinite in extent despite a scale factor of zero right?

Our observable universe today (93 billion light years across) is just one of those excel cells? So when people like Alan Guth say the universe went from the size of proton to the size of a grapefruit during inflation - he means the observable universe right? Since the universe is (possibly - let’s assume it is) infinite it would have been infinite at the Big Bang? This confused me initially to have a finite size in an infinite universe until I realise people mean the observable patch we are in?

Intelligent life on the same level as humans is debated from what I can tell in terms of it existing elsewhere. Some use the Drake equation to say there probably is such intelligent life but some are more skeptical.

My main question is that if intelligent life exists in our excel cell and there are at least a vast number of these observable universe cells then it has to unequivocally contain intelligent life right? Even if the universe were just very large and not infinite? (Since infinite by definition must contain such life elsewhere). Why are some people still skeptical of intelligent life elsewhere when the best cosmological models at least predict a vast number other observable universe size patches? Or is that because strictly scientists can only comment on what they can observe in their own patch?

 

[Jaime Rudas]

The Big Bang was the creation of space and time. At this instant t=0 space was infinite in size but the scale factor was zero.

No, we don't know the characteristics of the universe at time t=0.

However, mathematically speaking it’s possible to be infinite in extent despite a scale factor of zero right?

I think not, because that would imply that the distance between any two points would also be zero

So when people like Alan Guth say the universe went from the size of proton to the size of a grapefruit during inflation - he means the observable universe right? Since the universe is (possibly - let’s assume it is) infinite it would have been infinite at the Big Bang?

Yes, they possibly refer to the observable universe, because if the universe is infinite, it has been so since its beginning.

 

[PeterDonis]

The Big Bang was the creation of space and time.

Sort of.

At this instant t=0 space was infinite in size but the scale factor was zero.

No. The "instant t=0" is not part of spacetime.

 

[Jimmy87]

No, we don't know the characteristics of the universe at time t=0.


I think not, because that would imply that the distance between any two points would also be zero

Yes, they possibly refer to the observable universe, because if the universe is infinite, it has been so since its beginning.

You said we don’t know the characteristics at t = 0 so you said no to the infinity of space but then you said it must have been infinite since the beginning? t = 0 is not the beginning then?

 

[PeroK]

At this instant t=0 space was infinite in size but the scale factor was zero.

The Big Bang Theory goes from the current state of the universe backwards to a time where the universe was in a "hot, dense state". At some point our current theories of General Relativity and Quantum Mechanics break down. This is at some time $t > 0$. The theory doesn't go all the way back to $t = 0$ and a scale factor of zero. Although, this is quite a common claim by those presenting cosmology as a popular science.

Our observable universe today (93 billion light years across) is just one of those excel cells? So when people like Alan Guth say the universe went from the size of proton to the size of a grapefruit during inflation - he means the observable universe right? Since the universe is (possibly - let’s assume it is) infinite it would have been infinite at the Big Bang? This confused me initially to have a finite size in an infinite universe until I realise people mean the observable patch we are in?

There is a lot of unnecessary confusion caused by people using the word universe for the observable universe.

Note that although the best model of the universe is that it is spatially infinite, you must be careful of reaching too many conclusions on the basis of this. That doesn't mean that it definitely is spatially infinite.

My main question is that if intelligent life exists in our excel cell and there are at least a vast number of these observable universe cells then it has to unequivocally contain intelligent life right?

Not necessarily. The probability that intelligent life evolves on a planet is unknown. The Earth had only single-cell organisms for most of its evolution. It may be the case that the evolution of complex life, let alone intelligent life, is extremely rare.

It's true that if you assume a spatially infinite, homogeneous universe, then you can deduce an infinite number of planets identical to Earth. But, see my note above about drawing conclusions. There is no proof that the universe is infinite.

Even if the universe were just very large and not infinite? (Since infinite by definition must contain such life elsewhere). Why are some people still skeptical of intelligent life elsewhere when the best cosmological models at least predict a vast number other observable universe size patches? Or is that because strictly scientists can only comment on what they can observe in their own patch?

It's both. First, see my comment above. The probability of the evolution of intelligent life on a planet might be commensurately low. And, until we have some evidence of what happens on other planets, there is too much guesswork for some people.

A better question may be to ask how many advanced civilisations there are (or have been) in the Milky Way? Any answer to that is a guess. Just saying there are lots of stars and lots of planets doesn't give you a number. It could be 1 (us); it could be 10; it could be 100; or, it could be thousands. We don't know and we have no evidence of how many there are.

The problem is that you can conjure whatever number you are looking for by making the appropriate assumptions. Perhaps this is more agnostic than sceptical, although that may be simply playing with words. I wouldn't be surprised if we found intelligent life in the Milky Way. But, we can't say with any certainty that we are not alone.

Beyond that, intergalactic communication may be impossible within the lifespan of an advanced civilisation. So, if we are alone in the Milky Way, we may never know for sure that there is intelligent life in other galaxies.

 

[PeroK]

It was professor Kipling who clarified my thinking on this:

 

[Ibix]

The Big Bang was the creation of space and time.

You seem to be using "Big Bang" to mean the singularity. Some sources use it to mean the first few hundred thousand years when the universe was not transparent to light, so beware.

The singularity is a prediction of our models, and the existence of singularities is one of the reasons we suspect those models aren't quite right. Furthermore, the point about a singularity is that it's an "edge" of a model, a place or time where the model stops predicting. So the singularity is the beginning of our model of spacetime, but by its nature doesn't let us talk about "at or before" the singularity. So it might not be the beginning in reality.

I’m picturing it (hopefully correctly) like an excel spreadsheet with infinite cells.

As long as you keep on mind that the cells are a grid you imagined drawing and nothing real, OK. Also keep in mind that you can't always draw a Cartesian grid - it depends on the geometry of space.

However, mathematically speaking it’s possible to be infinite in extent despite a scale factor of zero right?

The point is that the singularity is where the maths breaks down, and contradictions are part of that. As Peter says, singularities aren't part of spacetime - they're its boundary.

So when people like Alan Guth say the universe went from the size of proton to the size of a grapefruit during inflation - he means the observable universe right?

Yes, unless they're talking about a closed universe model when there is sense to a finite size for the universe.

My main question is that if intelligent life exists in our excel cell and there are at least a vast number of these observable universe cells then it has to unequivocally contain intelligent life right?

No. Further to PeroK's comment above we had a long thread recently about the related topic of whether an infinite universe must contain all possible configurations of matter in finite patches, to which the answer was also no. I'll see if I can find it.

 

[FlorianR]

Your main question is a very good one: "if intelligent life exists in our excel cell and there are at least a vast number of these observable universe cells then it has to unequivocally contain intelligent life right?". Not 100% certainly. There is the statistical analysis (the Fermi paradox) which is why perhaps a majority of people today believe that the likelihood of complex biological life is high (Because there are sooooo many planets out there, that it almost seems inevitable that we are not the only one with life). But at the same time, it is possible that complex life like ours, is an extremely rare (very low probability) outcome. So it is actually not impossible that we are alone in the universe, but that idea is quite scary :) so it's often less discussed. The gist is that we can't know for certain until we actually find alien life somewhere. Until then, it's perhaps more likely then not that there is something else out there, but it's also not impossible that we are the only ones looking up at the stars.

 

[Orodruin]

if intelligent life exists in our excel cell

Does it though?

 

[Jimmy87]

Does it though?

Ha ha, good point. By the end of the century for certain I reckon but in silicon form……..

 

[Jimmy87]

The Big Bang Theory goes from the current state of the universe backwards to a time where the universe was in a "hot, dense state". At some point our current theories of General Relativity and Quantum Mechanics break down. This is at some time t>0. The theory doesn't go all the way back to t=0 and a scale factor of zero. Although, this is quite a common claim by those presenting cosmology as a popular science.

So since the Big Bang in the singularity sense marks the boundary of our current theories then it is only accurate to say our observable universe started with some very small finite size which was hot and dense? Is it better to use the start of inflation as the origin of the observable universe since current theories do not take us before this? Is it true that the universe is actually cold (not hot and dense at the start of inflation) - only after inflation?

 

[Jimmy87]

Here is a screenshot taken from the website listed below:

https://www.icc.dur.ac.uk/~tt/Lectures/Galaxies/LocalGroup/Back/bigbang.html

If you go to the web page and watch the animation - do you think it is a reasonable analogy of the Big Bang and how it unfolded?

 

[PeroK]

So since the Big Bang in the singularity sense marks the boundary of our current theories then it is only accurate to say our observable universe started with some very small finite size which was hot and dense? Is it better to use the start of inflation as the origin of the observable universe since current theories do not take us before this? Is it true that the universe is actually cold (not hot and dense at the start of inflation) - only after inflation?

The hot dense state was before inflation. You could model the universal expansion without inflation, but then you have what is called the flatness problem. The preferred solution is an initial period of very rapid inflation, which has been included in the overall Big Bang Theory. :

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

 

[Bandersnatch]

The hot dense state was before inflation.

After, surely. During inflation the density is dominated by the scalar field, and as such there's no matter to be hot or dense. Only when the 'reheating' triggers, and standard model particles are created from the scalar field, the (bubble) universe enters the classical big bang cosmology.

 

[PeroK]

After, surely. During inflation the density is dominated by the scalar field, and as such there's no matter to be hot or dense. Only when the 'reheating' triggers, and standard model particles are created from the scalar field, the (bubble) universe enters the classical big bang cosmology.

You're right. As far as I understand it:

The inflation phase occurs before the original Hot Big Bang Theory, and ends with the original hot, dense state.

The new initial state (before inflation) is dominated by a cosmological constant, which results in the rapid, exponential expansion of space. The universe, however, must have been in thermal equilibrium before inflation (that's one of the reasons for postulating an inflation phase). So, it must have been hot? And, density would have been scalar-field energy density, rather than mass or radiation density?

 

[javisot]

After, surely. During inflation the density is dominated by the scalar field, and as such there's no matter to be hot or dense. Only when the 'reheating' triggers, and standard model particles are created from the scalar field, the (bubble) universe enters the classical big bang cosmology.

Even though inflation isn't a thermal process, one can still define an effective temperature based on the quantum fluctuations of the inflaton field and the de Sitter horizon.

I'm going to look for who said the following, I think it was Alan Guth himself in a video, "inflation is the mechanism that explains how the universe goes from an initial singularly hot and dense state to a later non-singular state of temperature and density.

 

[PeterDonis]

The universe, however, must have been in thermal equilibrium before inflation

In some models, such as eternal inflation, there is no "before inflation". Inflation goes back an infinite time to the past of the Big Bang reheating event where inflation ends in our particular "bubble".

(that's one of the reasons for postulating an inflation phase).

It is? Can you be more specific (and possibly give a reference)?

So, it must have been hot?

"Thermal equilibrium" does not imply "hot". It can exist at any temperature.

 

[PeroK]

It is? Can you be more specific (and possibly give a reference)?

Liddle includes the isotropy of the CMBR as a problem for the Big Bang Model:

"This means that a small patch of the universe, small enough to achieve thermalization before inflation can to be much larger than ... the observable universe."

"Thermal equilibrium" does not imply "hot". It can exist at any temperature.

Yes, I meant that temperature was a valid concept during inflation.

Note that Liddle gives everything for $t < 10^{-10}s$ as "open to speculation".

 

[PeterDonis]

Liddle includes the isotropy of the CMBR as a problem for the Big Bang Model:

Ah, ok. But inflation solves that problem without there having to have been any thermal equilibrium before inflation (in models where there is a "before inflation" at all). Inflation solves the problem by smoothing out everything by a huge number of orders of magnitude by the time of the Big Bang, so it doesn't matter whether the pre-inflation state was in thermal equilibrium or not.

Yes, I meant that temperature was a valid concept during inflation.

It is. But its physical interpretation in the inflating "false vacuum" state is very different from what we're all used to. "Zero temperature" in the "false vacuum" state means that there are zero fluctuations around the "false vacuum", not the "true vacuum" that's the vacuum state after the end of inflation. So you can have a "false vacuum" state that's at zero temperature everywhere (and so is technically in "thermal equilibrium") but has a huge energy density that's not reflected in the temperature. That goes against our usual intuitions.

 

[Jimmy87]

It was professor Kipling who clarified my thinking on this:

Thanks for this - it was very interesting and I thoroughly enjoyed it. I’ve never thought about this idea before. I also did some further reading and found that it ties into the Great Filter concept. I calculated roughly that human intelligence has existed for just 0.005% of Earth’s habitable lifespan, despite life itself starting very early — within the first few percent of that habitable phase. That suggests some truly astonishing prerequisites. And given that the Doomsday Clock is now set to 90 seconds to midnight, that’s a vanishingly small window too. I suppose, depending on whether we’ve already passed the Filter or not, intelligent life is either incredibly rare and ephemeral — or inevitably just fleeting.

 

[javisot]

My main question is that if intelligent life exists in our excel cell and there are at least a vast number of these observable universe cells then it has to unequivocally contain intelligent life right? Even if the universe were just very large and not infinite? (Since infinite by definition must contain such life elsewhere). Why are some people still skeptical of intelligent life elsewhere when the best cosmological models at least predict a vast number other observable universe size patches? Or is that because strictly scientists can only comment on what they can observe in their own patch?

I notice your main question isn't cosmology. You want to know whether the argument "the universe is finite" or "it's infinite" influences the probability of life existing in the universe.

We don't know the probability of life existing somewhere in the universe depends on the size of the universe. You could even make exact calculations based on the assumption that the amount of life in the universe depends on its size, but we don't know if that's true.