B The Universe without Cosmic Inflation?

[Arman777]

I don't know this question makes sense or not but;

Respect to the two possible size universe models (finite and infinite) how would be the evolution of the universe without the cosmic inflation?

 

[Jorrie]

You can investigate such hypothetical scenarios by using a cosmological calculator. The one I link to in my sig below allows Lambda to be set to a very small value and the total density smaller or larger than critical, to look at the evolution of expansion over time.

Oh, sorry - I see you were asking about inflation, not the late time expansion. The calculator does not cater for inflation.

 

[Arman777]

You can investigate such hypothetical scenarios by using a cosmological calculator. The one I link to in my sig below allows Lambda to be set to a very small value and the total density smaller or larger than critical, to look at the evolution of expansion over time.

Oh, sorry - I see you were asking about inflation, not the late time expansion. The calculator does not cater for inflation.

I see, well thanks anyway

 

[Chronos]

You need an infinitie, or really big wrap around universe to explain a temporally finite and homogenous universe without inflation.

 

[Arman777]

You need an infinitie, or really big wrap around universe to explain a temporally finite and homogenous universe without inflation.

But in these cases, as you said, the universe will be unstable (either it will collapse or expand so much faster. Even if the universe is infinite.

I think it's not possible to have a finite universe without the inflation. It doesn't matter how big it the universe is.

Without the inflation, either the universe is finite or inifite, it would collapse (for finite case) or expand in much more rapidly (for infinite case) than the current universe.

 

[timmdeeg]

Respect to the two possible size universe models (finite and infinite) how would be the evolution of the universe without the cosmic inflation?

I think without inflation means without a cosmological constant. Then the universe would expand decelerated and collapse finally. It would be finite in this case.

 

[Arman777]

Why would it be collapse ? (If you are thinking matter dominated universe). I think the universe would have a hyperbolic geometry and it would expand forever.

We need cosmological constant for a flat/infinite universe.

I might be mistaken too.

 

[timmdeeg]

We need cosmological constant for a flat/infinite universe.

Yes, i agree. But then the universe begins matter dominated with no empty epoch before. Because in an empty universe a cosmological constant generates inflation.

 

[Jorrie]

Why would it be collapse ? (If you are thinking matter dominated universe). I think the universe would have a hyperbolic geometry and it would expand forever.

We need cosmological constant for a flat/infinite universe.

I don't think we need a cosmological constant for a flat/infinite universe, just standard inflation without Lambda would do. After that, you just need critical matter density for a flat/infinite universe. It will of course not give us the observed (late) accelerated expansion.

Nor would the cosmological parameters have been what we have today (as 'best buy' values), e.g. the present cosmic clock would have been at less than 10 Gyr after inflation. BTW, this type of thing you can get out of most cosmological calculators, without them knowing about inflation.

 

[timmdeeg]

I don't think we need a cosmological constant for a flat/infinite universe, just standard inflation without Lambda would do. After that, you just need critical matter density for a flat/infinite universe.

Inflation means that the universe expands exponentially. To my understanding the Friedmann equations show that this requires Lambda.

 

[PeterDonis]

Inflation means that the universe expands exponentially. To my understanding the Friedmann equations show that this requires Lambda.

No, that's not correct. The Friedmann equation shows that for exponential expansion, you need $p = - \rho$. A positive cosmological constant is one of the ways to get that, but not the only one. The usual assumption in inflation models is a scalar field (the "inflaton" field), which also has this property.

 

[Arman777]

I don't think we need a cosmological constant for a flat/infinite universe, just standard inflation without Lambda would do. After that, you just need critical matter density for a flat/infinite universe. It will of course not give us the observed (late) accelerated expansion.

Nor would the cosmological parameters have been what we have today (as 'best buy' values), e.g. the present cosmic clock would have been at less than 10 Gyr after inflation. BTW, this type of thing you can get out of most cosmological calculators, without them knowing about inflation.

Well yes, I agree. In my mind, I fixed the baryonic density parameter as it's observed value, $Ω_b=0.04$, but yes for a $Ω_b=1$ and with the cosmic inflation the universe can be stable I guess, without the cosmological constant.

 

[Jorrie]

Well yes, I agree. In my mind, I fixed the baryonic density parameter as it's observed value, $Ω_b=0.04$, but yes for a $Ω_b=1$ and with the cosmic inflation the universe can be stable I guess, without the cosmological constant.

I think we could perhaps make do with $Ω_b=0.04$, but then we needed dark matter $Ω_{dm}=0.96$. I think that this is ruled out observationally.

 

[Arman777]

I think we could perhaps make do with $Ω_b=0.04$, but then we needed dark matter $Ω_{dm}=0.96$. I think that this is ruled out observationally.

Yes exactly

 

[timmdeeg]

No, that's not correct. The Friedmann equation shows that for exponential expansion, you need $p = - \rho$. A positive cosmological constant is one of the ways to get that, but not the only one. The usual assumption in inflation models is a scalar field (the "inflaton" field), which also has this property.

Ah I see. And are these inflation models also consistent with the observed accelerated expansion? If so, then there seems no necessity to assume a cosmological constant at all.

 

[Arman777]

If so, then there seems no necessity to assume a cosmological constant at all.

We can treat like, the cosmological constant caused the cosmic inflation. But in that case the cosmological constant that caused the inflation must be much higher than the current observational one. Approximately it should be $10^{107}$ times larger.

Ryden, B. (2006). Introduction to cosmology (p. 244).
[For more information you can look the book]

In this case, I don't think we can just say that the cosmological constant caused the inflation (as @PeterDonis pointed out). And another problem is that in the old inflationary model reheating seemed to never occur. So after this problem, they changed it and slow-roll inflation model introduced. Which in this case inflation ends after a time and reheating occurs.

The second thing is without the cosmological constant the total density of the universe would be $Ω=0.31$. But we know that for a flat universe total density should be equal to $1$ (to consist with the observational data). If we think our observable universe and rule out the cosmological constant we should have seen a much different type of universe, first of all, it wouldn't be flat at all due to presence density matter in the OU.

 

[bapowell]

Ah I see. And are these inflation models also consistent with the observed accelerated expansion? If so, then there seems no necessity to assume a cosmological constant at all.

Inflation and the cc are distinct epochs that have nothing to do with one another. The term “inflation” is usually taken to refer to the accelerated expansion of the universe in its earliest moments. Inflation gave way to the hot Big Bang cosmology, which in its latter years became Lambda (or vacuum)-dominated.

 

[timmdeeg]

Inflation and the cc are distinct epochs that have nothing to do with one another. The term “inflation” is usually taken to refer to the accelerated expansion of the universe in its earliest moments. Inflation gave way to the hot Big Bang cosmology, which in its latter years became Lambda (or vacuum)-dominated.

If we assume the cosmological constant today (instead of dark energy) doesn’t this require Lambda all the time including the inflation epoch?

 

[timmdeeg]

We can treat like, the cosmological constant caused the cosmic inflation. But in that case the cosmological constant that caused the inflation must be much higher than the current observational one. Approximately it should be $10^{107}$ times larger.

Ryden, B. (2006). Introduction to cosmology (p. 244).
[For more information you can look the book]

Interesting, unfortunately I don’t have this book. So according to our observation the cc didn’t cause the inflation. I think this follows also considering that the cc can’t be the cause for the reheating epoch.

 

[Arman777]

Interesting, unfortunately I don’t have this book. So according to our observation the cc didn’t cause the inflation. I think this follows also considering that the cc can’t be the cause for the reheating epoch.

There is an online pdf version of it.

Yes cc can't be the cause of inflation. As you said "Inflation should end" so that reheating can occur. In this sense if cc truly caused the inflation its value should decrease by the factor of $10^{107}$.

 

[bapowell]

If we assume the cosmological constant today (instead of dark energy) doesn’t this require Lambda all the time including the inflation epoch?

Sure, but it was irrelevant to the process of primordial inflation. That's what I'm trying to say.

 

[bapowell]

Interesting, unfortunately I don’t have this book. So according to our observation the cc didn’t cause the inflation. I think this follows also considering that the cc can’t be the cause for the reheating epoch.

Right. Inflation could not have been driven by a constant because, well, it *ended*! Of course, during slow roll inflation the universe undergoes near-exponential expansion, closely approximating expansion under a constant vacuum density. Because inflation was dynamic (with very special dynamics at that) and because it was much higher energy than today's possibly cosmological constant-driven acceleration, it is generally considered a separate process.

 

[timmdeeg]

Ok, thanks to all.

So, coming back to the question of the OP, “without Cosmic Inflation” but with a cosmological constant the matter density of the universe would be zero and hence it would de Sitter like (or Milne like in case the cc is zero too).

 

[Arman777]

Ok, thanks to all.

So, coming back to the question of the OP, “without Cosmic Inflation” but with a cosmological constant the matter density of the universe would be zero and hence it would de Sitter like (or Milne like in case the cc is zero too).

I don't think so. One of the crucial points in the inflation theory is that it solves flatness problem. Without the inflation Even there's CC I think the universe cannot be stable. Respect to the densities of the materials in the universe, either it would collapse immediately or it will expand much faster that universe would cool much faster in seconds.

I didn't understand why you think matter density would be zero?

 

[PeterDonis]

“without Cosmic Inflation” but with a cosmological constant the matter density of the universe would be zero

Huh? There are FRW models with a cosmological constant and nonzero matter density.

 

[PeterDonis]

Without the inflation Even there's CC I think the universe cannot be stable.

I don't understand what you mean by "stable".

The general answer to the question you ask in the OP is that we can model such a universe using the standard FRW models without inflation. The two key characteristics of those models are the universe's spatial geometry (sphere, flat, or hyperbolic), and whether the universe expands forever or recollapses to a Big Crunch.

Without a cosmological constant, these two key characteristics are correlated: spherical spatial geometry == universe recollapses, flat or hyperbolic spatial geometry == universe expands forever.

With a cosmological constant, however, all combinations of the two key characteristics are possible, by tuning the value of the cosmological constant appropriately. Also, it becomes possible to have a static universe (the Einstein static universe) which neither expands nor collapses. However, the static universe is like a pencil balanced on its point: a small perturbation will cause it to either expand forever or collapse to a Big Crunch.

 

[timmdeeg]

I didn't understand why you think matter density would be zero?

I was assuming that you are discussing our universe (mentioning the flatness problem), not a arbitrary FRW model. Then if you drop the inflation which produces matter wherelse should matter density come from?

 

[timmdeeg]

Huh? There are FRW models with a cosmological constant and nonzero matter density.

Yes I’m aware of that. Please see post #27.

 

[Arman777]

I don't understand what you mean by "stable".

The general answer to the question you ask in the OP is that we can model such a universe using the standard FRW models without inflation. The two key characteristics of those models are the universe's spatial geometry (sphere, flat, or hyperbolic), and whether the universe expands forever or recollapses to a Big Crunch.

Without a cosmological constant, these two key characteristics are correlated: spherical spatial geometry == universe recollapses, flat or hyperbolic spatial geometry == universe expands forever.

With a cosmological constant, however, all combinations of the two key characteristics are possible, by tuning the value of the cosmological constant appropriately. Also, it becomes possible to have a static universe (the Einstein static universe) which neither expands nor collapses. However, the static universe is like a pencil balanced on its point: a small perturbation will cause it to either expand forever or collapse to a Big Crunch.

Of course, they are all possible as you said. I was just referring to the flat universe by saying "stable"

Without the inflation, I don't think we can ever achieve a flat universe. Because total denisty of the universe should be exactly $1$ for a flat universe and for such tuning we need inflation.

 

[Arman777]

I was assuming that you are discussing our universe (mentioning the flatness problem), not a arbitrary FRW model. Then if you drop the inflation which produces matter wherelse should matter density come from?

Hmm that's a good question.

 

[PeterDonis]

I was just referring to the flat universe by saying "stable"

Why do you think a flat universe is the only kind that can be "stable"?

 

[PeterDonis]

I’m aware of that. Please see post #27.

Ah, got it.

 

[Arman777]

Why do you think a flat universe is the only kind that can be "stable"?

Because flat case happens only $Ω=1$ and for all $Ω≠1$ universe have two different possibilities. It kind of seemed special "stable point". But now I am thinking $Ω=1$ as a local maximum point of possible $Ω$.

I was assuming that you are discussing our universe (mentioning the flatness problem), not a arbitrary FRW model. Then if you drop the inflation which produces matter wherelse should matter density come from?

That is a good point. Hmm well, it's hard to imagine maybe we will not have standard model particles but still, we can have some sort of radiation energy density, which can determine the fate of the universe?

 

[PeterDonis]

for all Ω≠1 universe have two different possibilities.

What are you referring to here?

 

[Arman777]

What are you referring to here?

$Ω<1$ a universe with hyperbolic spatial geometry
For $Ω>1$ a universe with spherical spatial geometry

 

[PeterDonis]

Ω<1a universe with hyperbolic spatial geometry
Ω>1 a universe with spherical spatial geometry

Ok. But why are these not "stable"?

 

[Arman777]

Ok. But why are these not "stable"?

They are "stable" in their own type of spatial geometry.

The first I said stable was here,

I don't think so. One of the crucial points in the inflation theory is that it solves flatness problem. Without the inflation Even there's CC I think the universe cannot be stable.

By that I mean this, I'll quote from a book

"The flatness problem states that such finely tuned initial conditions seem extremely unlikely. Almost all initial conditions lead to either closed universe that recollapses after immediately, or to an open Universe that very quickly enters the curvature-dominated regime and cools down to below 3K within in seconds. For this reason, the flatness problem also phrased as an age problem- how did our Universe get to be so old ?"

In this case by saying "cannot be stable" I was referring to this part, Depending on the initial conditions the universe can evolve in some direction.For example (quoting again)

"In the nucleosynthesis, when the universe was around 1s old we require that for a flat universe the density should be $\left|Ω_{nuc}-1\right|≤10^{-16}$

It's such a low number and that is why we need a tuning.

(Andrew Liddle, Cosmological Inflation and Large-Scale Structure page 37)

 

[Arman777]

I was assuming that you are discussing our universe (mentioning the flatness problem), not a arbitrary FRW model.

Well kind of yes, by mentioning flatness problem I was actually referring to this

"The flatness problem states that such finely tuned initial conditions seem extremely unlikely. Almost all initial conditions lead to either closed universe that recollapses after immediately or to an open Universe that very quickly enters the curvature-dominated regime and cools down to below 3K within in seconds. For this reason, the flatness problem also phrased as an age problem- how did our Universe get to be so old ?"
as I said in my previous post.

In this case, I was just trying to mention that without the inflation it's hard to say something about the universe spatial geometry and hence about its future. But you are right I think, in any case, we wouldn't have matter density (since we can't make an experiment for other possibilities) and the universe would have been evolved in de Sitter or Milne Model as you referred.

But now I am also thinking where the CC came from? Will it be there even there would be no inflation?

 

[timmdeeg]

But now I am also thinking where the CC came from? Will it be there even there would be no inflation?

We are quite sure that there exists repelling gravity which is usally called dark energy. But according to the data the latter could be also a CC. We don’t know the nature of this kind of gravity. And as was pointed out by others the inflation is independent of that. CC or dark energy to exist does not require inflation.

 

[Arman777]

We are quite sure that there exists repelling gravity which is usally called dark energy. But according to the data the latter could be also a CC. We don’t know the nature of this kind of gravity. And as was pointed out by others the inflation is independent of that. CC or dark energy to exist does not require inflation.

Is there any other dark energy theories other than CC? Is it a good idea to treat the CC a kind of repelling gravity?

Inflation cannot be caused by CC but I am not sure. If CC is there inflation happens or not then CC becomes a natural instinct property of the space-time and nothing else.

In that case, CC never can be zero. Since its a property of ST.

 

[timmdeeg]

Is there any other dark energy theories other then CC ? Is it a good idea to treat the CC a kind of repelling gravity ?.

I woudn’t call CC a dark energy theory. My advise is to google DE to see the difference. The observed accelerated expansion of our universe is due to something which is sometimes called a bit sloppy “repelling gravity”. You could have look to the 2. Friedmann equation and see what happens to the sign of the second derivative of the scale factor in case $\Lambda$ dominates $(\rho+3p)$.

Inflation cannot be caused by CC but I am not sure. If CC is there inflation happens or not then CC becomes a natural instic properity of the space-time and nothing else.

In that case CC never can be zero. Since its a properity of ST.

Inflation is independent of CC, please see my previous post. What is ST?

 

[PeterDonis]

Inflation cannot be caused by CC but I am not sure.

Inflation itself could be caused by a CC, but the value of the CC would have to be much, much larger than the one we actually measure.

What cannot be caused by a CC is the end of inflation, where the energy stored in the inflaton field gets transferred to the Standard Model fields. The energy density of a CC is constant--that's what "cosmological constant" means. So it can't get transferred to anything else.

So whatever caused inflation, it has to be something that can give up energy to something else; the simplest assumption is a scalar field. According to our best current model, during inflation, the energy density of this field was so large compared to the CC (which had the same value as it does today) that the effect of the CC on the dynamics of the universe was negligible, since both the energy density of the scalar field during inflation and the CC had constant values.

Once inflation ended, and all of that energy got transferred to the Standard Model fields, the energy density in those fields--what we usually call "matter" and "radiation"--started to decrease as the universe expanded. A few billion years ago, the energy density in matter and radiation became smaller than the energy density of the CC; that's when the CC started to be the major factor determining the dynamics of the universe.

In that case CC never can be zero. Since its a properity of ST.

What are you referring to here?

 

[Arman777]

Inflation is independent of CC

Yes, I am aware of that. As I said

If CC is there, inflation happens or not, then CC becomes a natural instinct property of the space-time and nothing else.

In that case, CC never can be zero. Since its a property of ST.

What are you referring to here?

ST means space-time.

Since CC was there even in the period of cosmic inflation then we can conclude that CC was an instinct property of the space-time. Which indeed it is. So in this sense, we can say that even there's nothing (no matter and no radiation) we would have only the cosmological constant.

If the universe was created without inflation, it would be the "de Sitter" universe. That's the only answer then.

 

[nearc]

I was assuming that you are discussing our universe (mentioning the flatness problem), not a arbitrary FRW model. Then if you drop the inflation which produces matter wherelse should matter density come from?

for my own clarity, are you saying inflation is required to produce matter or inflation affects the production of matter?

 

[timmdeeg]

for my own clarity, are you saying inflation is required to produce matter or inflation affects the production of matter?

According to the inflationary theories matter is produced at the end of inflation, see Reheating. So inflation is required and affects the production of matter.

 

[nearc]

According to the inflationary theories matter is produced at the end of inflation, see Reheating. So inflation is required and affects the production of matter.

unless I'm very confused [which is often] i thought matter forms when the temperature drops. there might also be some need for expansion or even complicated cooling/heating but ultimately once things are cool enough and there is enough room matter can form? we tie matter formation into inflation as a nice gift wrapped package, but if there were some other way that allows the universe to cool and spread out matter should still form?

 

[bapowell]

unless I'm very confused [which is often] i thought matter forms when the temperature drops. there might also be some need for expansion or even complicated cooling/heating but ultimately once things are cool enough and there is enough room matter can form? we tie matter formation into inflation as a nice gift wrapped package, but if there were some other way that allows the universe to cool and spread out matter should still form?

By "matter forms when the temperature drops" are you referring to the broken symmetries that confer mass to the various elementary particles, or are you thinking about something more generic?

We don't *need* inflation to create matter, since that would be a circular argument (i.e. what created the inflaton?) The novelty of reheating is that inflation effectively erases the energy density in the inflated region, and without it we get a cold, empty universe after inflation.

Also, I'll mention that the universe cools as it expands, whether inflation happened or not.

 

[nearc]

By "matter forms when the temperature drops" are you referring to the broken symmetries that confer mass to the various elementary particles, or are you thinking about something more generic?

We don't *need* inflation to create matter, since that would be a circular argument (i.e. what created the inflaton?) The novelty of reheating is that inflation effectively erases the energy density in the inflated region, and without it we get a cold, empty universe after inflation.

Also, I'll mention that the universe cools as it expands, whether inflation happened or not.

that's what i thought thanks for the clarification. i was tempted to use the analogy about how babies are produced during sex but babies can also be produced without sex, however, in that analogy inflation would be intercourse so there are some obvious crass images plus the very short duration of inflation might hit too close to home for some.

 

[JMz]

It has been pointed out that we are in the midst of a new BB, due to the cc. (That does not mean that the previous BB was related in any way to the cc.)

BTW, there is no a priori reason that the cc (vacuum energy density) should be positive. We do not currently know of any reason it could not have been negative, in which case the expansion would eventually reverse regardless of how low the mass density was.

 

[timmdeeg]

It has been pointed out that we are in the midst of a new BB, due to the cc.

By whom?

BTW, there is no a priori reason that the cc (vacuum energy density) should be positive. We do not currently know of any reason it could not have been negative, in which case the expansion would eventually reverse regardless of how low the mass density was.

We do currently have a reason to believe that the CC is positive. Otherwise we couldn't explain why we observe that the universe expands accelerated.