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A Steady State Universe


Carrock

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Fred Hoyle's steady state universe is overdue for revival. I'll try to have something up for Monday.

So many crackpots try and defend that idea, it is a bit cliched. We need someone to revive phlogiston.

 

I can't revive every idea but if dephlogisticated air was good enough for Priestley it's good enough for me...

 

Monday was rather optimistic....

A brief preemptive defense...

 

This post

....is pretty conceptual, which a skeptic might take as a euphemism for "hand-waving".

Steady state cosmology, proposed by Sir James Jeans and later revised by Fred Hoyle, Thomas Gold, Hermann Bondi and others, postulated an eternal, exponentially expanding universe with matter creation such that the average matter density was always constant.

 

This theory was effectively refuted observationally by the discovery of cosmic microwave background radiation (CMBR) in 1965.

 

There was also a serious problem with this theory which did not affect its verifiable predictions but dealt a fatal blow to the 'steady state' description:-

 

If it is assumed that at some past time the universe had a countably infinite ( ie aleph-null ) volume and number of discrete particles, and expansion continued for countably infinite time, the volume of space and the number of particles in it become uncountably infinite.

That is, the volume and number of particles increases by the factor n^aleph-null, where n>1.

Since n^aleph-null is equal to aleph-one, the volume of space and the number of particles in it would become equal to the uncountable ( or non-denumerable) infinity aleph-one, which is physically impossible.

At least, I am not aware of any way it could be possible.

 

A detailed and rigorous analysis of the problem is presented by Richard Schlegel in

Philosophy of Science Vol. 32, No. 1 (Jan., 1965), pp. 21-31

 

Before observational refutation, Steady state cosmology could only be kept viable by assuming exponential inflation started at an indefinitely distant but finite time in the past and will end at an indefinitely distant but finite future time.

ie, more formally, exponential inflation must be past-incomplete and future-incomplete.

 

 

The same problem occurs with a newer theory of an eternal, exponentially expanding universe ie eternal inflation which also predicts exponentially increasing space and number of particles.

Such future-incomplete expansion is often described by cosmologists as 'eternal to the future', a convention which I will adopt.

 

 

Cosmology is a science where many competing theories can survive because confirming or refuting them is difficult or impossible.

 

I have a subjective preference for theories which are past- and future- complete and do not require the universe to be finite.

 

 

One possibility which has been somewhat neglected is an eternal steady state static universe with finite inflation and a concept originated by Dr. Schuetz:

I will conclude this paper with an idea of my old assistant, Dr. Schuetz.

 

We assume that the whole universe is, and rests for ever, in thermal equilibrium. The probability that one (only one) part of the universe is in a certain state, is the smaller the further this state is from thermal equilibrium; but this probability is greater, the greater is the universe itself. If we assume the universe great enough, we can make the probability of one relatively small part being in any given state (however far from the state of thermal equilibrium), as great as we please. We can also make the probability great that, though the whole universe is in thermal equilibrium, our world is in its present state. It may be said that the world is so far from thermal equilibrium that we cannot imagine the improbability of such a state. But can we imagine, on the other side, how small a part of the whole universe this world is? Assuming the universe great enough, the probability that such a small part of it as our world should be in its present state, is no longer small.

 

The specific aspect which I feel has been neglected is that in an eternal universe no eternal process ( not necessarily inflationary ) which requires the creation of space or discrete particles can ever be initiated.

 

 

My steady state 'update' is not up to the old steady state theory

...alone among all cosmologies, the steady-state model makes such definite predictions that it can be disproved even with the limited observational evidence at our disposal.

in falsifiability, but it is incompatible with some respected theories and may soon make the trip to 'Speculations'. >:D

 

 

I assume an eternal ( ie past and future complete ), flat, static, spatially infinite universe which, on a large scale, has asymptotically zero energy and maximum entropy ie Minkowski space.

I will follow precedent and call 'local' universes like ours 'pocket universes'.

 

As eternal or finite inflation theories are the most consistent with the observed CMBR, I will use finite inflation in my theory.

It is then necessary that there be a nonzero possibility of inflation and it is convenient and perhaps necessary to assume that the probability of producing Boltzmann Brains ( an awkward prediction of many theories ) is much lower than the probability of inflation.

In Can the universe afford inflation? Andreas Albrecht and Lorenzo Sorbo propose that this is a viable assumption.

 

 

There is a ( small ) possibility that ongoing observations of the CMBR will support this theory.

Its main value, if any, is that some well regarded theories' predictions are incompatible with this theory.

Therefor, in this post, rather than make predictions consistent with other theories I will only consider predictions of theories which are inconsistent with this theory.

 

 

The most important constraint of this eternal universe theory, which does not apply to most theories, is that to avoid slow, exponential inflation of the universe it is necessary for everything created by an instance of inflation to disappear completely within finite time.

 

That is:-

 

Within finite time, each instance of inflation must end and all created space, particles and other entities eg singularities must disappear. This may take a very long time - eg the half-life of the proton is greater than 10^33 years.

 

From this it follows that the pocket universe we live in ( and everything created by inflation ) cannot expand eternally to the future, but there need not be any presently detectable way for it to disappear. All models where quintessence, cosmological constant etc cause such expansion are not viable.

As the expansion of space during inflation is finite, after sufficient time has elapsed, all created space must eventually be separated by time-like intervals. This should lead to the complete disappearance of everything created by the inflation episode.

 

If, as is certainly plausible, new instances of inflation can start within an inflation field or pocket universe, finite inflation requires on average less than one in each new instance of inflation. ( Otherwise inflation would be eternal to the future.)

 

An adaptation of reasoning regarded as dubious by Alan H. Guth:

If finite inflation is assumed to have an exponential phase, it is likely our universe was created around the time of peak creation of universes when inflation was about to end; there may possibly be some trace of this in the microwave background.

 

If it is possible for intelligent life to initiate inflation, this sets a further constraint on the probability of any single inflation episode producing intelligent life.

If on average each instance of intelligent life creates x new inflation episodes, then all inflation episodes must on average produce less than 1/x instances of intelligent life.

if this is the case, the total duration of inflation is further limited and there is a slightly better chance of observing transients dating back to the inception of inflation.

 

 

I suggest one other constraint for finite inflation in an eternal universe, which is that its finiteness must not depend on carefully selected parameters. In an eternal universe the probability of eternal inflation must be 0.

 

 

Finally there are so many extant theories I can only hope that I am not repeating one of the more obscure ones......

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There is one key factor you missed. In the steady state universe the temperature is constant. The matter creation maintains the same energy density so according to the ideal gas laws the eternal steady state universe would not show a change in temperature. This is one of the why the CMB disproved the steady state model. The temperature of the CMB is roughly 3000 kelvin today it 2.73 kelvin which shows that the average energy density is decreasing due to expansion with a finite amount of mass energy per volume.

Edited by Mordred
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Mordred, michel123456, swansont et ( I hope ) al : Thank you for responding to my post.

 

There is one key factor you missed. In the steady state universe the temperature is constant. The matter creation maintains the same energy density so according to the ideal gas laws the eternal steady state universe would not show a change in temperature. This is one of the why the CMB disproved the steady state model. The temperature of the CMB is roughly 3000 kelvin today it 2.73 kelvin which shows that the average energy density is decreasing due to expansion with a finite amount of mass energy per volume.

The "Steady State Universe" I referred to is

an eternal ( ie past and future complete ), flat, static, spatially infinite universe which, on a large scale, has asymptotically zero energy and maximum entropy ie Minkowski space.

and also asymptotically zero temperature.

 

In my theory, our observable ( pocket) universe is a result of finite inflation from this steady state universe much as described in eg

Eternal inflation and its implications:

 

it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region.

Except possibly for subtle CMBR variations my theory does not require any variation in the observable universe from predictions in other inflation theories (but is incompatible with theories requiring future-incomplete eternal expansion).

 

Therefor the posts about the CMBR background are not really relevant to this theory.

 

For brevity and laziness, there are a lot of implicit assumptions in my original post; some of them 99% of cosmologists would agree with, others not. :(

 

I'd be happy to defend or abandon assumptions anyone on the forum finds dubious.

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That is not evidence.

the very fact that there is a CMB is proof of a hot dense past. The measured elements hydrogen and lithium with few other elements show that the universe came from a much hotter and denser state. More complex elements could not form as the temperatures were too high. The condition is called thermal equilibrium. We have mountains of data from WMAP and PLANCK that support this with direct measurements. They did measure the temperature variations when they mapped the CMB. If direct measurements isn't proof then what is?

Mordred, michel123456, swansont et ( I hope ) al : Thank you for responding to my post.

 

 

The "Steady State Universe" I referred to is

and also asymptotically zero temperature.

 

In my theory, our observable ( pocket) universe is a result of finite inflation from this steady state universe much as described in eg

Eternal inflation and its implications:

 

 

Except possibly for subtle CMBR variations my theory does not require any variation in the observable universe from predictions in other inflation theories (but is incompatible with theories requiring future-incomplete eternal expansion).

 

Therefor the posts about the CMBR background are not really relevant to this theory.

 

For brevity and laziness, there are a lot of implicit assumptions in my original post; some of them 99% of cosmologists would agree with, others not. :(

 

I'd be happy to defend or abandon assumptions anyone on the forum finds dubious.

Mordred, michel123456, swansont et ( I hope ) al : Thank you for responding to my post.

 

 

The "Steady State Universe" I referred to is

and also asymptotically zero temperature.

 

In my theory, our observable ( pocket) universe is a result of finite inflation from this steady state universe much as described in eg

Eternal inflation and its implications:

 

 

Except possibly for subtle CMBR variations my theory does not require any variation in the observable universe from predictions in other inflation theories (but is incompatible with theories requiring future-incomplete eternal expansion).

 

Therefor the posts about the CMBR background are not really relevant to this theory.

 

For brevity and laziness, there are a lot of implicit assumptions in my original post; some of them 99% of cosmologists would agree with, others not. :(

 

I'd be happy to defend or abandon assumptions anyone on the forum finds dubious.

the paper you just posted has nothing to do with the steady state universe. The last paper is in support of chaotic eternal inflation. Which is a big bang theory model. The steady state universe always existed no big bang. Please take the time to at least understand the models your supporting. In the steady state universe there is no big bang nor can there be a CMB. That is what steady state means... In the last paper you posted Guth states the number of particles at [latex]10^90[/latex]. Hoyles steady state model requires new matter to form as the universe expands.

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the very fact that there is a CMB is proof of a hot dense past. The measured elements hydrogen and lithium with few other elements show that the universe came from a much hotter and denser state. More complex elements could not form as the temperatures were too high. The condition is called thermal equilibrium. We have mountains of data from WMAP and PLANCK that support this with direct measurements. They did measure the temperature variations when they mapped the CMB. If direct measurements isn't proof then what is?

 

 

the paper you just posted has nothing to do with the steady state universe. The last paper is in support of chaotic eternal inflation. Which is a big bang theory model. The steady state universe always existed no big bang. Please take the time to at least understand the models your supporting. In the steady state universe there is no big bang nor can there be a CMB. That is what steady state means... In the last paper you posted Guth states the number of particles at [latex]10^90[/latex]. Hoyles steady state model requires new matter to form as the universe expands.

Are you saying a Steady State would have no CMB of any kind? Or not the one we observe?

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Correct the steady state universe has no temperature variations new matter forms as the universe expands. So the average energy density is constant. This is what Hoyle originally proposed to counter the big bang model. The CMB is a result of a hot dense past. In the steady state universe there is no hot dense past. Conditions in the past would be identical to conditions now and in the future. Hence the name "Steady state" The ideal gas laws are fundamental in cosmology. Every model must use the ideal gas laws. There is a big difference between the steady state universe and chaotic eternal inflation. The two models are direct opposites.

 

Chaotic eternal inflation is still a valid model it is among over 70 other competing inflation models that are all equally valid. Including Higgs inflation, slow roll approximation, Natural inflation, Hill inflation etc. All inflationary models is not a "Steady State Universe" The steady state universe has been proven wrong in favor of inflation due to observational evidence.

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At the risk of seeming smug, have a look at my post-count and status as a resident expert then think about why I asked the why it goes dark at night and why I linked it to a steady state universe/

 

You are answering the wrong question.

Why does it go dark: ever?

Edited by John Cuthber
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If your referring to Olbers paradox (which you probably are) the universe is

not flooded with light from the stars as both the steady state model and the inflation models are expanding. The steady state universe is an expanding universe. The difference is that new matter forms causing the universe to expand. Where in inflation the number of particles is constant

Working from phone so can't see the posters stats lol

Edited by Mordred
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At the risk of seeming smug, have a look at my post-count and status as a resident expert then think about why I asked the why it goes dark at night and why I linked it to a steady state universe/

 

You are answering the wrong question.

Why does it go dark: ever?

I think Fred Hoyle had that, Olber's Paradox, covered in his model of an expanding steady state Universe.

 

So we have no infinite radiation...but instead a more limited but steady amount, depending on mass/energy density maintained by creation, and on the expansion rate...

 

so, why could that not fit the profile of the CMB?

Edited by J.C.MacSwell
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If your referring to Olbers paradox (which you probably are) the universe is

not flooded with light from the stars as both the steady state model and the inflation models are expanding. The steady state universe is an expanding universe.

 

I don't think so expansion is required to solve Olbers' paradox.

 

First of all we have large distances between stars (we can hypothesize that neutral gases were created where they're now)

Photons illuminating surface obey inverse-square law, so the larger distance, the smaller quantity of photons per area unit arriving.

 

[math]P=\frac{P_0}{4 \pi r^2}[/math]

 

Now repeat it for the all stars in the galaxy and universe, and sum powers together.

 

[math]\sum_{i=0}^{i<j}\frac{P_0(i)}{4 \pi r(i)^2}[/math]

 

The one that has the smallest distance (our Sun in our current location), has the largest influence on result from this equation.

Which is 3.661*10^21 photons with average 532 nm per second per m^2 of Earth at noon.

960000 light years from the Sun it'll be average 1 photon per m^2 per second.

(Notice that this easy equation also gives maximum limit of stars emitting light in radius of 1 mln ly from us.

If there would be 3.661*10^21 stars (with power equivalent to the Sun) at distance 1 mln ly from us, they would sum to the current max power of the Sun, and we would have day all day long)

 

Secondly, stars don't exist forever. They're forming, living and dying, typically running out of fuel to fuse further (so I should rather say "not emitting light anymore", than dying)

Something that Olbers didn't realize.

 

Thirdly, stars don't exist at the same time. Only fraction of gas existing in the Universe is emitting photons from fusion. It must collapse enough to form new star.

 

We can hypothesize that free protons and free electrons (violating current conservation theories obviously, which also does BB) are appearing from nowhere everywhere in space between existing galaxies.

Before they would become new star it would take billions of years in the meantime. Before that we wouldn't even know about their existence.

Star equivalent to the Sun would need 5.761*10^56 Hydrogen and 4.907*10^55 Helium-4 at the beginning.

If rate of production would be 1 bln per second, it would take 1.82*10^31 billion years to make such amount of "fresh neutral Hydrogen gas".

Edited by Sensei
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I assume an eternal ( ie past and future complete ), flat, static, spatially infinite universe which, on a large scale, has asymptotically zero energy and maximum entropy ie Minkowski space [ and by implication has asymptotically zero temperature ].

the paper you just posted has nothing to do with the steady state universe.

The topic title is "A Steady State Universe". Unlike Steady state cosmology, my version has certain values set such that it is past and future complete.

The last paper is in support of chaotic eternal inflation.

I presume you're referring to

 

eternal inflation

For eternal inflation to set in, all one needs is that the probability for the field to increase in a given Hubble-sized volume during a Hubble time interval is larger than 1/20.

I could provide a similar quote from most papers on inflation.

 

Is the value of such inflation theories a function of how many people have demonstrated that with certain assumptions, they predict eternal inflation?

Which is a big bang theory model. The steady state universe always existed no big bang. Please take the time to at least understand the models your supporting. In the steady state universe there is no big bang nor can there be a CMB. That is what steady state means... In the last paper you posted Guth states the number of particles at [latex]10^90[/latex]. Hoyles steady state model requires new matter to form as the universe expands.

I didn't know, let alone understand any of the models you cited. There was one which I managed to work out by searching for "1090". Perhaps you will tell me if I got it right.

 

Again in eternal inflation

First of all, we know that the universe is incredibly large: the visible part of the universe contains about 1090 particles.

I presume you are stating that there are no particles ( and no space ) anywhere except in the visible part of the universe and no more will ever be created.

This seems rather improbable but would certainly make inflation future complete.

 

Correct the steady state universe has no temperature variations new matter forms as the universe expands. So the average energy density is constant. This is what Hoyle originally proposed to counter the big bang model. The CMB is a result of a hot dense past. In the steady state universe there is no hot dense past. Conditions in the past would be identical to conditions now and in the future. Hence the name "Steady state" The ideal gas laws are fundamental in cosmology. Every model must use the ideal gas laws. There is a big difference between the steady state universe and chaotic eternal inflation. The two models are direct opposites.

 

Chaotic eternal inflation is still a valid model it is among over 70 other competing inflation models that are all equally valid. Including Higgs inflation, slow roll approximation, Natural inflation, Hill inflation etc. All inflationary models is not a "Steady State Universe" The steady state universe has been proven wrong in favor of inflation due to observational evidence.

I wonder if you actually read my original post.

 

I gave two important reasons that the Hoyle steady state universe was untenable; you state the ( Hoyle ) steady state universe has been proven wrong ( which I agree with ) as inflation has been observationally proved(!!!!)

 

A brief (over?)simplified resume of my theory:

 

Finite inflation is initiated in flat, past and future complete static Minkowski space.

Most models of inflation are past incomplete and are consistent with this or a similar origin.

Only finite inflation is permitted as no future incomplete processes are possible in a future complete universe.

Therefor the inflation episode we're living in will end completely in less than a very long but finite time.

Over long enough time and distance, this future complete static Minkowski space is unchanging, exactly as the BGH steady state universe was unchanging.

A property of the static Minkowski space I use is that its temperature is asymptotically zero degrees so Olber's paradox is no a problem.

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in a sense the universe is still inflating just at a slower rate the process that caused inflation and is causing expansion may or may not be one and the same. If you didn't understand the inflation models models I posted then how can you say most models have a finite inflation? They do in the sense of a slow roll exit from inflation, that was one of the key problems with false vacuum inflation (Allen Guth's original inflation) once inflation starts there was no way to stop it, some of the earlier inflation models still suffer this problem including chaotic eternal inflation, Google Runaway inflation for more details. There is no reason to believe the universe will become static in the future a static universe is one that will become eternal and requires a highly fine tuned set of conditions which is inherently unstable, The critical density must be exactly zero with no possible fluctuation, even the smallest fluctuation will cause a further expansion or a collapse. The wikidot link in my signature has numerous articles you might read over. However this may interest you

 

http://arxiv.org/abs/1303.3787

 

Encyclopedia Inflationaris there is over 70 reviewed and examined models for inflation, good luck with yours, there is very specific standards to obtain to make a workable inflation model the standards are in the above article. (in order to match observational evidence)

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