Were There Any Proposed Non-Expanding Cosmological Models Without Lambda?

[AWA]

This isn't true, as the early universe starts off with very high temperatures and cools, resulting in lots of conversion of energy between radiation and matter. If you want to get the right answers for BBN and the CMB, you have to take these factors into account.

What is not true?. I have in fron of me a couple of cosmology books (Schutz and Ryder) that say in cosmology and GR the perfect fluid assumption is used and considered valid, and further that perfect fluids are considered adiabatic, now if textbooks are also wrong...

If it has a non-zero temperature, however, there will always be fluctuations around the mean density, which means that it won't stay static for long.

Well of course there will be local fluctuations, but we are talking about idealized cosmological solutions that globally consider the universe as isotropic and homogenous and therefore those fluctuations wouldn't be a problem in order to remain static since they would cancel out. Otherwise you'd be talking about an inhomogenous solution, there you would be right that it wouldn't be static for long.

 

[AWA]

That comment was perfectly sensible to me. Why did it confuse you? A homogeneous universe is inherently unstable, in that it becomes more and more inhomogeneous with time.

Then why physicists rejected Einstein model due to instability? In the end it was an empirical rejection because of the redshift and other things, but at first it was rejected because it was unstable, or so they say in many books.

If our universe is becoming more and more inhomogenous, logic says that eventually it'll become inhomogenous, that is against the main assumption of our standard model.

 

[Chalnoth]

What is not true?. I have in fron of me a couple of cosmology books (Schutz and Ryder) that say in cosmology and GR the perfect fluid assumption is used and considered valid, and further that perfect fluids are considered adiabatic, now if textbooks are also wrong...

What isn't true is that these fluids don't interact and change with temperature. They do interact, and their behavior changes quite a lot with temperature. A perfect fluid, after all, is merely defined as a fluid which can be fully described by its energy density and pressure, and dealing with these interactions doesn't break that assumption.

Well of course there will be local fluctuations, but we are talking about idealized cosmological solutions that globally consider the universe as isotropic and homogenous and therefore those fluctuations wouldn't be a problem in order to remain static since they would cancel out. Otherwise you'd be talking about an inhomogenous solution, there you would be right that it wouldn't be static for long.

No, temperature fluctuations don't cancel out. As long as you have non-zero temperature, the fluctuations will be random, and you will get some deviation from the average density on all scales.

Of course, the deviations from the average density will be smaller on larger scales, but you only need the deviation to be non-zero for the system to start collapsing/expanding.

I think you're thinking in terms of classical thermodynamics, where a gas remains essentially uniform after small perturbations. But this is only the case because it's in a stable configuration, one that tends to go back to the equilibrium configuration after being perturbed. This isn't the case for gravitational systems.

 

[AWA]

I think you're thinking in terms of classical thermodynamics, where a gas remains essentially uniform after small perturbations. But this is only the case because it's in a stable configuration, one that tends to go back to the equilibrium configuration after being perturbed. This isn't the case for gravitational systems.

Be that as it may, I've got the feeling that here we face some arbitrariness towards assumptions like homogeneity and the ideal gas or fluid, so that whenever it's convenient they hold with all the consequences and when it's not convenient they don't hold (and I don't mean the local case as you remark this happens at all scales) and it seems doubtful that this has anything to do with gravitation or GR.
This is great as an argumentative tool but I'm not sure it makes up for the apparent lack of intellectual honesty.

 

[Chalnoth]

Be that as it may, I've got the feeling that here we face some arbitrariness towards assumptions like homogeneity and the ideal gas or fluid, so that whenever it's convenient they hold with all the consequences and when it's not convenient they don't hold (and I don't mean the local case as you remark this happens at all scales) and it seems doubtful that this has anything to do with gravitation or GR.
This is great as an argumentative tool but I'm not sure it makes up for the apparent lack of intellectual honesty.

It's merely a matter of being aware of the realistic limits of our assumptions. Homogeneity, for instance, is never expected to be exact, but only approximate. Since it is only expected to be approximate, it is important to recognize when even tiny deviations from the precise assumption lead to dramatically different behavior.

With a homogeneous, static gas balanced by a cosmological constant, for instance, you can prepare it in a homogeneous state just fine. But it won't stay homogeneous if there is any non-zero temperature. Because it won't stay homogeneous, it is necessary consider what happens when the assumption of homogeneity breaks down, and in this case you'll first get structure formation, but in addition to that you'll end up with the universe as a whole either collapsing or expanding (I think collapse is the more likely, because some of the energy density of the gas will become photons, which have positive pressure).

 

[yogi]

I was wondering if historically there was ever proposed some non-expanding cosmological model without the lambda term, I've read somewhere it's not possible with the assumption of isotropy and homogeneity so I am only interested in terms of the history of cosmology.

As to your original question, Harrison says: "The last static steady state universe was conceived at the university of Chicago in 1918 an elaborated in the 1920s by Astronomer William MacMillan"

And you are right about Eddington - although he received a copy of the 1915 publication early on - the War would most likely have prevented much in the way of communication - so I can't find where I read who influenced Einstein with regard to problem of potential G collapse - but there was almost a 2 year gap between the publication of the first version and the 1917 version - so plenty of time for inputs -

 

[AWA]

As to your original question, Harrison says: "The last static steady state universe was conceived at the university of Chicago in 1918 an elaborated in the 1920s by Astronomer William MacMillan"

And you are right about Eddington - although he received a copy of the 1915 publication early on - the War would most likely have prevented much in the way of communication - so I can't find where I read who influenced Einstein with regard to problem of potential G collapse - but there was almost a 2 year gap between the publication of the first version and the 1917 version - so plenty of time for inputs -

Thanks yogi, I've read in an article of 1930 by de sitter that there was even another static solution in the famous book by mathematician Levi-Civita: The absolute differential calculus from 1924 but I haven't found this book yet.