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