Why is inflation thought necessary in std. cosm.?

[marcus]

Leaving for the beach today
so I won't be contributing any thoughts
but posters named Nacho and Rudi
wrote some things recently that started me
wondering why (in standard cosmology, not "astro.alt"!)
people find inflation scenarios compelling

the usual answer is, even tho we don't know how it works
or when exactly it happened, it helps us solve
two problems:

"horizon" problem---how in short time could things have
arrived at nearly same temp on both sides of sky?

"flatness" problem----why is space so incredibly flat
near perfect as far as we can tell?


but if the divergence at time zero is controlled by
quantum geometry maybe inflation is not the only way
to address these probs?

 

[meteor]

How can quantum geometry solve the horizon problem without inflation?
Also, what model of inflation do you want to discuss? I know at least four models:
-The old inflation, proposed by Guth in 1981.this model has so many problems that the same guth renounced to it in a paper
-The new inflationary theory, proposed by Linde in 1982.This model introduces the concept of inflaton, that is a scalar field
-The chaotic inflation, proposed by Linde in 1983. In this model the Universe starts in a cold state
-The self-reproducing inflationary universe, also by Linde in 1986.
Says that ours is one of many inflationary universes that sprout from an eternal cosmic tree

 

[Nacho]

but if the divergence at time zero is controlled by
quantum geometry maybe inflation is not the only way
to address these probs?

I **mostly** understand the idea behind Inflation, but I don't understand what you've said there .. that is new to me (but I mostly read popular accounts). Could you expound on that some?

Heh, a quick one here! Who of us remembers the original article in Scientific American that Guth wrote, right after he formulated Inflation? I do! I was around then, reading SCIAM! I knew nothing of it, and just considered that "another one of those articles", until 5-10 years later when it popularly took off.

BTW, my question on the matter/antimatter annihilation had something to do with Inflation. The part about it that I cannot comprehend (mental block) is the repulsive force that gravitation was supposed to undergo. It was a feable attempt to find something else that drove inflation.

 

[marcus]

Originally posted by Nacho

The part about it that I cannot comprehend (mental block) is the repulsive force that gravitation was supposed to undergo. It was a feable attempt to find something else that drove inflation.

This is an area where people use words differently and have different scenarios in mind, so please be patient if you discover
I have slightly different semantics and premises.

what defines the terms of discussion for me is a 2003 article "Inflation and the Cosmic Microwave Background" by Lineweaver
http://www.arxiv.org/astro-ph/0305179

He says on page 3: "Inflation can be described simply as any period of the Universe's evolution in which the size of the Universe is accelerating."

What is meant by "size" is the scale factor a(t) in the Friedmann equation---the basic equation in cosmology. Space of infinite extent can expand of contract if the scale factor is changing. Inflation means its second derivative is positive.

In Figure 3 he shows what he calls Friedmann oscillations from a "Lambda dominated" era to a "radiation dominated" to a "matter dominated" and then again to a new "lambda" era. We are now entering a period of inflation (expansion is accelerating, Lambda is already 73 percent of the total energy density and its share is on the rise).

In the caption to Figure 3 he says: "the inflationary period can be described by a universe dominated by a large cosmological constant (energy density of a scalar field)"

Basically I'm using Lineweaver as my compass here. He is a major respected mainstream figure. If you want to attack mainstream assumptions, then attack his. If you want to understand the mainstream picture, study his. If you want to see how time might upset the mainstream picture, his 2003 summary of the model is not a bad one to work with. He also references and quotes people like Ned Wright and Alan Guth who represent mainstream thinking too. but since everybody uses words slightly differently, at least in their nuances, I find it helpful to orient myself using Lineweaver's picture.

The mechanism of infl. postulated for the first picosecond (to solve flatness and horizon problems) is the same mechanism we now see causing inflation (accelerated recession measured using Type Ia supernovae)

Nacho, you have asked about the "repulsive force". Several people here can give a simple explanation of that---eg Hurkyl and PF mentors and so on. I will try and maybe others can fill in the gaps. It is totally a Friedmann equation thing, in my view.
But the Friedmann equation is one of the simplest differential equations in Western Civilization (like the harmonic oscillator or the pendulum) so since it describes the universe, hey it is kind of basic culture rather than obscure esoterica and I will write it down
in the next post.

 

[marcus]

"repulsive" force that accelerates expansion

there are two F. equations and one of them is

a_tt/a = (-4pi/3) (rho + 3p)

What? well a(t) is the scale factor in the metric.
The metric of spacetime is a formula for calculating distances between points---its non-constancy is the basis for thinking of spacetime as curved----and in GR the metric is a dynamic changing thing governed by the energy density (rho) in space.

a_t is shorthand for the time-derivative da/dt

if a_t is positive then space is expanding

dividing a_t(t) by a(t) gives the *percentagewise* expansion rate
a_t(t)/a(t) which is the definition of the Hubble parameter H(t)

they never tell you this! a lot of expertise is just redefining things!
they use a special time zero to refer not to the beginning of the current expansion phase but to the present and H(0), also written H₀ is the current value of a_t(t)/a(t) at this very instant-----sorry about the redefiniitons---a nervous tic widely shared by scientists of all description.

RHO is the average energy density in space and 4% is estimated to be ordinary visible matter, 73% is the dark energy or cosmological constant and the rest is dark matter and radiation.

Now I have to stop and ask why grown men and women can believe such obvious loony nonsense and it seems to me the answer is straightforward---Western Civ has a long tradition of taking the best mathematical model you can find (and after testing it however you can think to test it, as a check) just going with the mother. Go with it to the edge of its applicability and draw all the conclusions and predictionns you can and eventually it will break down and you get another. the tradition is to drive mathematical models as hard as you can.

So why this crazy conclusion that 73% of universe is something we never heard of and can't imagine what it is? That is easy.
the two friedmann eqs. are what the 1916 Einst. eq. of GR turn into if you assume a kind of average uniformity. Assuming things look much the same througout let's the equations be simplified
down to simple one-liners. The universe looks spatially flat and the F. eqn REQUIRES that rho be such and such in order to have flatness. The 4% is all we can see and the dark matter is all we can infer from the stability of clusters so there is this huge gaping 73% left over.

And also that much turns out by amazing coincidence to be just the right amount to explain the measured acceleration (from the Type Ia supernovas).

The luck of the differential-equation-model approach is that *often* you get these entirely unexpected coincidences that prove that somehow even tho it seemed crazy to take GR and the friedmann equation seriously and postulate that crazy 73%----even tho---it turns out to agree with supernova data that no one was expecting.

So now the big unanswered question is why this dark energy
causes expansion.

The answer to that is in the pressure term----3p in the Friedmann equation.

a_tt/a = (-4pi/3) (rho + 3p)

Remember F. got the equation by boiling 1916 Einstein down using uniformity. If you believe GR (and perihelion of mercury and gravitational lensing and black holes powering quasars etc) then you probably believe F. eqn derived from it. And it has this pressure term (original Einst did too but was too complicated to see immediately).

To have inflation, i.e. acceleration, the RHS of that eqn MUST BE POSITIVE. And because of the minus sign of -4pi, the only way to have that is if (rho + 3p) is NEGATIVE.

So if you are Alan Guth and want to think of accelerating expansion you have to come up with a way to make rho+3p negative. Thats all there is to it.

And rho is energy density and can only be positive. So you try to think of something with negative pressure that can overwhelm the positivity of rho (the energy of all the matter and light and everything and even its OWN energy the energy of the vacuum) overwhelm the positivity of rho and make the total come out negative.

So I will give the usual explanation with the piston in the cylinder of how vacuum energy has negative pressure.

Einstein had already thought of that piston and the negative pressure back in 1916 which is why he put the Lambda (the constant vacuum energy) into the equation----the dude obviously had a good imagination: we only started needing that Lambda when the supernova data came in around 1998 so it was a sleeper for 80 years.

Now for that damned piston.

 

[marcus]

the innocent-looking assumption that the vacuum has an energy density (constant through space and time or slowly changing will work OK too) brings with it a logical consequence of negative pressure

you take a pump cylinder full of vacuum
and so as you can study it properly you go into nothingness where there is not even vacuum around you

and you pull out the piston a little ways
and now there is more volume of vacuum
so, because vacuum has constant energy density
there is more energy

therefore by conservation that new energy came
from work you did by pulling out the piston
therefore a force was resisting your pulling it out
so vacuum energy gives the vacuum a negative pressure

Clearly Einstein was good at following things out logically even
to the point of absurd conclusions, maybe he even enjoyed
doing this.

So he put a vacuum energy density constant Lamda in the
original equations and the boiled down simplified Friedman
version inherited that so if you look at (rho + 3p) carefully
it includes a Lambda contribution making up 73% of rho.

And ordinary matter and radiation contribute negligible pressure
(the pressure of ordinary matter only counts for something in the cores of stars where the pressure gets to be significant and then it does really affect the gravity but in cosmology you just count the pressure of ordinary stuff as zero)

but for vacuum energy the pressure term p is actually equal to minus rho!
p = -rho
So 3p = -3 rho
So 3p overwhelms and swamps rho
And (rho + 3p) gets to be negative
so that the RHS of the F. eqn. gets to be positive
so that a(t) accelerates
and H(t) is increasing (instead of decreasing, a widespread earlier view)

One little detail. Anyone who is used to doing dimensional analysis----comparing the UNITS of quantities in an equation----should maybe check that energy density (energy per unit vol) has the same units as pressure ( force per unit area). That this is so allows one to write (rho + 3p) and have it make sense
because it is only apples rather than apples-and-oranges.

And the units being the same came in quietly when we were discussing the cylinder full of vacuum and saying

pressure = - energy density

because that equality would not make sense unless the units on both sides were the same.

 

[marcus]

Originally posted by meteor
How can quantum geometry solve the horizon problem without inflation?

In this context time zero means the beginning of the expansion. The time of the singularity where the GR equations cannot go and calculation becomes impossible because of divergence in the model.

When GR is quantized the divergence goes away (Bojowald has written a half dozen papers about various aspects of this over the past year or so) and the model extrapolates back in time past zero.

So you and I are asking the same question. Does this new picture, where the universe existed before time zero, solve the horizon problem without the need for inflation?

I am not telling you it does or does not. I want to know too.
I think we should ask "What is the horizon problem?"

Does the horizon problem arise from having no universe before time zero?

Inflation is not physically necessary from known laws. It is just a scenario postulated to solve certain problems. People like it because it predicts flatness and uniform CMB temperature (i.e. solves "horizon" problem).

Now we should ask if the new picture, with no time zero singularity, still has these problems which inflation scenario was designed to solve.

I feel open-minded about it. Quite possibly someone here at PF understands the horizon problem and can say whether or not it arises from having no universe before time zero.

Would you like URLs for a half dozen or so Bojowald papers? You could see what the various assumptions and models are. Quantizing the Friedmann equations turns out to be easier than quantizing the whole GR theory----because of the simplifying assumptions (eg homogeneity) some of what is still troublesome in the full version can be managed in the version needed for quantum cosmology.

 

[Tyger]

There are serious difficulties

with all the scenarios listed, and quite a few not listed in this thread. Inflation was thought of to eliminate some of the problems with Big Bang but it has its own. For one thing, during the inflationary period the laws of nature are completely scale invariant. Why, at the end of that period did scale invariance suddenly become a broken symmetry all over the Universe?

The Dark Eneergy/Lambda hypothesis has its own problems. Energy is generally localizeable, so where is the Dark Energy? And we don't really know of anything that has a net negative energy, this seems to be another important broken symmetry in the world.

I've mentiioned before that I adhered to the Dirac Large Number Hypothesis as a basis for building cosmological models, solely for the reason that it has some experimental basis. When you incorporate the assumption (and it really is just an assumption) that the large number relationships apply throughout the history of the Universe you are lead naturaly, one might almost say forced, to the conclusion that on the large scale the Universe operates as a fed back system, and this eliminates the horizon, isotropy and homogeneity problems in one fell swoop. Something else you get is that Gravity must have "more parts" than just the familiar R^−2 Newtonian term, otherwise the feedback would be inefective for maintainng the relationships. Whether these other parts will solve other aspects of large scale dynamics such as galactic rotation curves would need to be seen.

And these is another problem not addresed by ANY of the scenarios mentioned including the LNH, and that is the origin and source of the matter in the world.

 

[Tyger]

Clearly Einstein was good at following things out logically even
to the point of absurd conclusions, maybe he even enjoyed
doing this.

Einstein was employed as a clerk at the Swiss patent office, which is where he honed many of his reasoning skills. And the notion that you should follow a line of reasoning out to find ALL of its conclusions is a very good one, but many people only follow it to the point where they find the answer they were looking for.

 

[marcus]

Tyger what about the horizon problem?

I think it is a problem that plagues models with an abrupt origin.

If the model will run back over time zero without breaking then I think the horizon problem (the sameness of temperature in all directions) goes away.

Because the contracting phase before us already had a chance to come into equilibrium.


It is only when one denies that there was anything before time zero that one must explain how widely separated regions managed to come into thermal equilibrium with each other before light had a chance to travel back and forth between them.

this is my hunch.
I am hoping people who have read some about the horizon problem will comment.

here are some papers, no particular recommendations

(Isotropic L. Q. cosmology)
http://www.arxiv.org/gr-qc/0202077

(Isotropic L. Q. cosmology with matter)
http://www.arxiv.org/gr-qc/0207038

(Homogeneous L. Q. cosmology)
http://www.arxiv.org/gr-qc/0303073

(Initial conditions for a universe)
http://www.arxiv.org/gr-qc/0305069

(Cosmological applications of L. Q. gravity)
http://www.arxiv.org/gr-qc/0306008

you can see the preprint dates range from Feb 2002 to
June 2003, it is not a complete list but does give some
idea of the work going on around removing the time-zero obstacle
by quantizing the equation that govern the evolution of space

I am not interesting in arguing that the Einstein equation or the quantum versions derived from it are RIGHT for describing the evolution/shape of space. But that model gave us inflation scenarios in the first place because of a problem which the model had. I am curious to see the model pushed as far as it can go and to learn whether, in the end, it will require an inflation scenario in the first picosecond after time zero or not. Maybe it will not. Who understands the horizon problem well enough to say what the issues are?


or, mutatis mutandis, the flatness problem

 

[Tyger]

Originally posted by marcus
Tyger what about the horizon problem?

I think it is a problem that plagues models with an abrupt origin.

If the model will run back over time zero without breaking then I think the horizon problem (the sameness of temperature in all directions) goes away.

Because the contracting phase before us already had a chance to come into equilibrium.

If the horizon were sufficiently far enough away from us it would be hard to know if it were there. That's one problem, we don't have enough data to tell if we live in a Universe with a horizon/boundary or not. We just assume homogeneity/isotropy and go from there. And if the Universe had a point of origin and we lived close to it we might never know.

It is only when one denies that there was anything before time zero that one must explain how widely separated regions managed to come into thermal equilibrium with each other before light had a chance to travel back and forth between them.

this is my hunch.

Here I think we also have to include the possibility that some kind of signals, not that carry energy, but that determine the rates of changes, may propagate faster than light.

I'm not sure that it's neccesary that there be anything before time zero. I take a very mathematical view and the notion may be meaningless. Some functions aren't defined for the upper half of the complex plane, so to speak.

I am hoping people who have read some about the horizon problem will comment.

here are some papers, no particular recommendations

(Isotropic L. Q. cosmology)
http://www.arxiv.org/gr-qc/0202077

(Isotropic L. Q. cosmology with matter)
http://www.arxiv.org/gr-qc/0207038

(Homogeneous L. Q. cosmology)
http://www.arxiv.org/gr-qc/0303073

(Initial conditions for a universe)
http://www.arxiv.org/gr-qc/0305069

(Cosmological applications of L. Q. gravity)
http://www.arxiv.org/gr-qc/0306008

you can see the preprint dates range from Feb 2002 to
June 2003, it is not a complete list but does give some
idea of the work going on around removing the time-zero obstacle
by quantizing the equation that govern the evolution of space

I am not interesting in arguing that the Einstein equation or the quantum versions derived from it are RIGHT for describing the evolution/shape of space. But that model gave us inflation scenarios in the first place because of a problem which the model had. I am curious to see the model pushed as far as it can go and to learn whether, in the end, it will require an inflation scenario in the first picosecond after time zero or not. Maybe it will not. Who understands the horizon problem well enough to say what the issues are?


or, mutatis mutandis, the flatness problem

 

[thermonuclear]

Hi!

both of this problems, "flatness" and "horizon", are clearly solved by inflation in an elegant way, OK. Therefore, it seams to be beyond any doubt, that any theory which aspires to replace inflation should be able to deal with both.

But, what about the creation of matter? Inflation explains the accumulation of energy, taken from the gravitational field, in the vacuum energy due to it's false vacuum properties during the inflationary period. Matter appeared afterwards by a transfer of this energy to the matter fields during reheating. So, any theory which claims to replace inflation, should be able also to explain the colossal amount of matter in the visible universe (e.g. starting from a small big-bang energy as in the models of Vilenkin and Linde).

So, what about that point?

Regards.

 

[marcus]

when the equations are quantized and the singularity at time zero goes away what appears is our universe with matter prior to time zero in a collapsing mode

so there is no problem explaining the emergence of matter since it was already there

so inflation is not needed to explain the appearance of matter it would seem

you may wish to look at the online article LQ cosmology with matter (link in previous post) and also
"homogeneous LQ Cosmology" which has pictures on page 16 of time evolution thru zero----transition from contracting phase to expanding phase

also "Isotropic LQ Cosmology" where Bojowald describes the transition from contraction to expansion as a "bounce" see page 25. The link to the online article is also in the previous post.

This LQ Cosmology work is very new and in progress, since 2001, and based on the surprising discovery that the singularity in GR goes away when the Friedmann equations or their like are quantized using Ashtekar's variables.

So I am beginning to notice that inflation seems to accomplish a lot of stuff in the first picosecond that would maybe not need to be accomplished, if there is no singularity after all.

Originally posted by thermonuclear
Hi!

both of this problems, "flatness" and "horizon", are clearly solved by inflation in an elegant way, OK. Therefore, it seams to be beyond any doubt, that any theory which aspires to replace inflation should be able to deal with both.

But, what about the creation of matter? Inflation explains the accumulation of energy, taken from the gravitational field, in the vacuum energy due to it's false vacuum properties during the inflationary period. Matter appeared afterwards by a transfer of this energy to the matter fields during reheating. So, any theory which claims to replace inflation, should be able also to explain the colossal amount of matter in the visible universe (e.g. starting from a small big-bang energy as in the models of Vilenkin and Linde).

So, what about that point?

Regards.

 

[marcus]

Originally posted by Tyger

Hello Tyger, the "horizon problem" that I was talking about is
defined in Lineweaver's survey of cosmology

http://www.arxiv.org/astro-ph/0305179

it is not about whether or not the U has a horizon or a boundary, I think

but rather it is about why the CMB is much the same temp
as if different sides of the sky had been in causal contact (in each other's lightcones) and come to thermal equilibrium

but in a simple expansion model there would not have been time
for equilibrium to be reached.

Lineweaver explains well and in detail with several diagrams

unfortunately must go, but will get back to this
I want to understand your ideas on the subject, which right
now I do not

 

[meteor]

I don't know why inflation solves the horizon problem
Imagine that the universe appeared at time zero been almost perfectally homogeneous and isothermal. Then starts to expand and the expansion is equal in all directions.The fact that the expansion is equal in all directions allows to the isothermality to persist. Then arrive a moment (300000 years after Big Bang) that the density of matter is enough low to permit light to travel free.At that moment the light has a characteristic spectrum of a blackbody at 3000 K. The expansion of the space is the same in all directions, and this expansion produce that the photons lose energy and now they are observed with a spectrum of a blackbody at 2.7 k. Why do you need inflation?

 

[Nacho]

Then arrive a moment (300000 years after Big Bang) that the density of matter is enough low to permit light to travel free.At that moment the light has a characteristic spectrum of a blackbody at 3000 K. The expansion of the space is the same in all directions, and this expansion produce that the photons lose energy and now they are observed with a spectrum of a blackbody at 2.7 k. Why do you need inflation?

Heh big guys, take a rest .. I can take this question .. ;) (I'm just kidding! I'll probably mess it up!)

Unless the Universe is closed/finite & unbounded (curved back in on itself), or infinite, those photons would have passed us by, a long time ago, and they wouldn't be around to measure. Think about it .. The Universe expanding at a pace less than the speed of light. At the time that CMBR was emitted, 300000 years after the BB, the Universe would have to have been less than 300000 LY across. Depending on how close to the speed of light expansion was, it is very probable that light transverse the 300000 LY and the extra distance because of continued expansion, and catch up to the expansion. Where would it go then (I seriously have no idea)? -- unless the Universe is closed & unbounded -- curved back in on itself, or infinite. Then we could be seeing that CMBR in its upteen-millionth pass around the Universe, or from the infinite reaches of the Universe (I really don't believe in infinities in physical processes .. infinities are a product of the mind of mathematicians).

I think either the Universe has to be closed & unbounded, and/or big enough that the CMBR could not have transversed the Universe yet. And you need inflation for that.

 

[meteor]

I think either the Universe has to be closed & unbounded, and/or big enough that the CMBR could not have transversed the Universe yet. And you need inflation for that.

I can't see why do you need inflation. If the Universe started finite but with a radius superior to 13.7 billion yl, then the CMB would still be reaching the earth, even without inflation

 

[Nacho]

I can't see why do you need inflation. If the Universe started finite but with a radius superior to 13.7 billion yl, then the CMB would still be reaching the earth, even without inflation

So, no BB, or are you speculating a BB over a volume with a radius of at least 13 billion years? For the BB to proceed like it has, with multiple spikes in the CMBR, there would had to bee a high density of matter at that time. That's a pretty high density. Where did all of it go? Maybe some of it the missing mass? There are probably other good reasons why we need such a concentration of matter/energy at a moment after creation, that the compactness of the BB provides.

Ya know, even though space/time and matter/energy are woven together sooo much, we (I) tend to think of the creation of them separately. I tend to see it as Inflation creating space, and creating matter/energy at the same time, but separately. And expansion creating more space, but not more matter/energy. I think this is the prevailing thought. And then you have the steady state theorist, but not too many anymore. I tend to think both are correct. That is, as the Universe expands, it creates matter (really energy) as a process of expansion. I mean, we (I) tend to think of the false vacumn as a state of space. I think it hard to believe that as the Universe expands, the false vacumn is, for lack of better word, "diluted" in the process. I see it natural as the Universe creating its own energy (false vacumn) as it goes, as a product of expansion, and the state of the false vacumn per unit volumn staying roughly constant.

In that sense, maybe both of these competing theories are correct.

 

[Tyger]

Originally posted by marcus
Hello Tyger, the "horizon problem" that I was talking about is
defined in Lineweaver's survey of cosmology

http://www.arxiv.org/astro-ph/0305179

it is not about whether or not the U has a horizon or a boundary, I think

but rather it is about why the CMB is much the same temp
as if different sides of the sky had been in causal contact (in each other's lightcones) and come to thermal equilibrium

but in a simple expansion model there would not have been time
for equilibrium to be reached.

Lineweaver explains well and in detail with several diagrams

unfortunately must go, but will get back to this
I want to understand your ideas on the subject, which right
now I do not

Actually it's called the horizon problem because it was beleived that if the universe had a horizon it would result in anisotropy of the microwave background. Also the universe may have had multiple regions where expansion was occurring at different rates.