# How General R disobeys the (Special R) speed limit

#### marcus

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its routine in mainstream cosmology that much of space expands away from us faster than the speed of light

A poster (DrChinese) back in PF Astro "Archive" was inquiring about this---it was in the "Superluminal Recession Speeds". If you want, we could carry on the discussion out here rather than back in Astro Archive.

The paper we were discussing was Davis and Lineweaver
"Superluminal Recession Velocities"
http://arxiv.org/astro-ph/0011070 [Broken]

A more recent and complete discussion is in Lineweaver's
"Inflation and the CMB"
http://arxiv.org/astro-ph/0305179 [Broken]

To get an idea of the magnitudes, the CMB has redshift 1100
and the highest observed redshift of a quasar is 6.4
A great many objects have z > 2. How many? I dont know but the volume in which objects have redshift 2 or greater is more than 95 percent of the volume of the observable universe.

I'll check that with Wright's "cosmocalculator" and be back.

http://www.astro.ucla.edu/~wright/CosmoCalc.html

It is very handy, you just type in a value for z and select the "flat" button----it uses the most recent values of the hubble parameter and for dark energy, to calculate the distance and light travel time and so forth, from the redshift z you put in.

You might want to translate some observed redshift like z = 3 into a recession speed----how fast was the object receding at the time the light was emitted and how fast is it currently receding?
If so ask about it (several people around here can explain) or if you know you might want to explain how its calculated yourself.

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#### marcus

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Originally posted by marcus
its routine in mainstream cosmology that much of space expands away from us faster than the speed of light...
If you enter z = 2 into the cosmocalculator it tells you that
the volume with redshift 2 or LESS is 604 units

The whole observable volume out to unlimited redshift is 12,000 units

(the units are cubic Gigaparsecs but it doesnt matter what they are)

So the redshift z = 2 or less constitutes 5 percent of the total observable

That's why I was saying z>2 objects occupy 95 percent of the volume

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bogus

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#### marcus

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Oh I see, "c^3" means "bogus".

Hang in there. Whatever is bothering you may turn out to be not so strange after all

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#### DrChinese

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Yes, great, let's pick this up here.

I was having trouble - as I am sure others do - comprehending how a high z can result from an expansion of the universe, and that high z indicates objects moving away from us faster than c.

The referenced article was very good. However I still did not follow completely. I got the impression they were saying that high z objects emitted their light which we are now seeing near the Big Bang. But I am not sure I read that correctly.

Can anyone help me though the thinking? Thanks.

#### marcus

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Originally posted by DrChinese
Yes, great, let's pick this up here.

I was having trouble - as I am sure others do - comprehending how a high z can result from an expansion of the universe, and that high z indicates objects moving away from us faster than c.
DrC, it will be easier for me if you are willing to trust Ned Wright---
he has good credentials and I havent detected any difference between what he says and other working observatonal cosmologists

credentials: one of principal investigators of WMAP
teaches the graduate cosmology course at UCLA
his notes for UCLA course Astro 275 Spring 2003
(cosmology) are available on line at his website
which also has an undergrad level tutorial and FAQ.

his cosmocalculator is really handy and uses the latest most accurate parameters (you can also customize it if you have
some value of the Hubble parameter you like better etc.)

Anyway you asked for starters about the relation between z and the time the light was emitted----that is something it is good to get used to using the calculator for.

Plug in z = 2 and press the "flat" button and it tells you how long ago the light was emitted.

In Davis/Lineweaver, the article you read, they say things like
for any z >3 the galaxy that emitted that light was receding at greater than c.

This is the crux---we have to discuss that and see if you believe it. I do and it agrees with other cosmologists say but I dont need to convince you---we can see.

The all-important thing that Davis/Lineweaver say in that article you read is this: there are two kinds of velocity!

There is local motion (in a local coordinate patch where SR applies and where no relative velocity can exceed c) but when we talk about the expansion of space we are not talking about that.

There is RECESSION velocity that is the rate of change of the distance between two stationary objects. Imagine two galaxies both at rest with respect to the microwave background---or if moving only moving at a piddling speed: essentially at rest.

I guess the Milkyway galaxy is going some 250 km/sec relative to CMB but that is just local motion at a small fraction of c and I'm ignoring it and assuming both galaxies are at rest.

The recession speed comes about because the physical metric has a scalefactor
a(t) in it and this scalefactor keeps increasing
because the metric is a solution of the GR equation.

That is the speed that the Hubble law talks about, that is proportional to the current distance between two stationary objects

vrecession = H D

the best graphic picture of this is Lineweaver's figure 1
It shows the Hubble sphere-----the Hubble radius is the distance that if you go out that far (at the present moment) then the galaxies are receding at the speed of light.

Because of proportionality if you go out twice the Hubble radius they are receding at twice the speed of light,

three times, then three times the speed of light

That is still in our observable universe because for one thing we saw those guys when they were closer to us

Figure 1 does show a cosmological horizon or "event horizon" which is the absolute limit of what we can see or will ever be able to see. But it is out beyond the Hubble sphere, which is not a horizon of any sort (as they say explicitly).

The Lineweaver article "Inflation and the CMB" is from this year and is updated from the Davis/Lineweaver article you read---pictures are a bit better drawn. So have a look at Figure 1 and see what you think

One place to find it is
http://arxiv.org/astro-ph/0305179 [Broken]

Another is at a Caltech site that has the figures separate so you dont have to download the whole article. This is just figure 1, with no explanation:

http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure1.jpg

this is the full article at the Caltech site, so it shows the figure with its caption and some explanatory stuff
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver_contents.html

Here is Ned Wright's COSMOCALCULATOR.

http://www.astro.ucla.edu/~wright/CosmoCalc.html

Despite the comicbook name I really think this is the single most important tool to get accustomed to using----real eyeopener to get to translate whatever z you want into light traveltime and present distance and so on.

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#### marcus

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Notice in figure 1 that at scalefactor a = 0.4
or equivalently at time 4 billion years from start (or 10 billion years before present)

as you can read marked on the left hand (the a = 0.4 is marked on the righthand side)

what important thing happens?

at that moment the past lightcone crosses OUTSIDE the Hubble sphere

a galaxy on our past lightcone was emitting light which is now coming in---it is visible now

a galaxy outside the Hubble sphere and on our past lightcone was emitting light (now reaching us) as it was receding at greater than c (because it was outside the Hubble sphere)

this is an amazing aspect of standard GR cosmology which in that Davis/Lineweaver article they were trying to explain by the swimmer analogy. Few people seem to have assimilated it and I'm curious to find out how you do with it

Whoa there. GR doesn't disobey SR. Space itself can expand at any rate it wants. It is what is called a Global theory. SR is a localized theory and it states that no information may travel faster than light. Space expanding is hardly something that constitutes useful information about something, after all, it is just space.

#### marcus

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Whoa there. GR doesn't disobey SR. Space itself can expand at any rate it wants. It is what is called a Global theory. SR is a localized theory and it states that no information may travel faster than light. Space expanding is hardly something that constitutes useful information about something, after all, it is just space.
This is an excellent way to put it!
the expansion of space can be happening at speeds which are several times the speed of light
and yet no information is traveling faster than light
nothing can ever PASS you going faster than light

(that would be breaking the rules in your local frame)

but things can be and typically are RECEDING faster than light
(and the surprising thing is that some of that stuff receding >c
is part of our observable universe---something people often do not understand)

Anyway, like Davis/Lineweaver say, there are two kinds of velocity
only one of which is governed by the speed limit
and your description of the difference based on speed info travels is a good way to make the distinction

Right. The things that are apparantly receeding from us at superluminal velocities are in fact not themselves moving that fast. Rather, the space between us is expanding, and so it is the metric that we use to define the distance that is getting ever larger.

#### marcus

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Right. The things that are apparantly receeding from us at superluminal velocities are in fact not themselves moving that fast. Rather, the space between us is expanding, and so it is the metric that we use to define the distance that is getting ever larger.
A nice extra feature is that we can readily calculate how fast objects we now see were receding when they emitted the light now arriving here

Sky and Telescope published a program to do the calculation and a neat lady astronomer has it as a utility at her website

http://www.earth.uni.edu/smm.html [Broken]

She teaches Astro at Univ. of N. Iowa and is an observational astronomer who publishes a lot and specializes in variable stars
(Cepheid etc.) Her name is Dr. Siobahn Morgan. She likes Sci Fi and has excellent taste in superhero comic books and maintains a Dr. Who website. A very attractive single woman in my judgement and a good astronomer.

Here is the calculator. Be sure that you put 0.73 for lambda and 0.27 for omega. Keep the Hubble parameter 70. Then it will give mainstream cosmology answers similar to Ned Wright's cosmocalc.
But it give additional info that Wright's doesnt! The woman is cool.

For example, a quasar with redshift z = 6.4 was recently observed.
How fast was this quasar receding from Milky W. when it emitted the light we now see?????
Ahah! you simply put 6.4 in the box and press the "calculate" button and it will tell you what multiple of speed of light he was going away from us when he sent off the light

and of course will also tell how long ago it was and how far away he was then and how far away he is now. but the novelty is that her calculator also tells his recession speed

As a public service she has a whole bunch of Java applets for astronomy on line here:
http://www.earth.uni.edu/~morgan/ajjar/ [Broken]

The cosmology calculator is the last link on that list of Javaapplets:
http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html [Broken]

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#### DrChinese

Gold Member
Originally posted by marcus
DrC, it will be easier for me if you are willing to trust Ned Wright---
he has good credentials and I havent detected any difference between what he says and other working observatonal cosmologists

...

In Davis/Lineweaver, the article you read, they say things like
for any z >3 the galaxy that emitted that light was receding at greater than c.

This is the crux---we have to discuss that and see if you believe it. I do and it agrees with other cosmologists say but I dont need to convince you---we can see.

The all-important thing that Davis/Lineweaver say in that article you read is this: there are two kinds of velocity!

There is local motion (in a local coordinate patch where SR applies and where no relative velocity can exceed c) but when we talk about the expansion of space we are not talking about that.

There is RECESSION velocity that is the rate of change of the distance between two stationary objects. Imagine two galaxies both at rest with respect to the microwave background---or if moving only moving at a piddling speed: essentially at rest.

I guess the Milkyway galaxy is going some 250 km/sec relative to CMB but that is just local motion at a small fraction of c and I'm ignoring it and assuming both galaxies are at rest.

The recession speed comes about because the physical metric has a scalefactor
a(t) in it and this scalefactor keeps increasing
because the metric is a solution of the GR equation.

That is the speed that the Hubble law talks about, that is proportional to the current distance between two stationary objects

vrecession = H D

the best graphic picture of this is Lineweaver's figure 1
It shows the Hubble sphere-----the Hubble radius is the distance that if you go out that far (at the present moment) then the galaxies are receding at the speed of light.

Because of proportionality if you go out twice the Hubble radius they are receding at twice the speed of light,

three times, then three times the speed of light

...

Here is Ned Wright's COSMOCALCULATOR.

http://www.astro.ucla.edu/~wright/CosmoCalc.html

Despite the comicbook name I really think this is the single most important tool to get accustomed to using----real eyeopener to get to translate whatever z you want into light traveltime and present distance and so on.
Well, it's certainly not about me believing or disbelieving someone. I guess I had never realized that this side of GR had existed. I certainly wasn't aware that the concept of galaxies moving apart faster than c was something that is generally accepted. (Musta been asleep on that one.)

At any rate, I had already been to the calculator and realized that it would give the kind of results you indicated. However, that presupposed that which I was trying to understand so it didn't help much. But we can use it as a discussion point. I am assuming that there must be any number of people as confused on this issue as I am. So perhaps we can walk through it a bit at a time, as you have already (and generously) taken the time to do.

I think we have something as follows:

a. There are a number of possible space-time metrics which satisfy GR.
b. The discovery of actual high z values from the relatively early universe indicate that certain of these metrics are supported, and therefore others must be discarded as describing our universe.
c. In the high z scenarios we are able we witness, the additional "velocity" component - which gives rise to recession >c - is a function of the expansion of the spacetime metric.

I hope this is accurate. If so I would ask as follows:

1. Presumably it would not be possible for any objects to move towards each other faster than the speed of light - only away from each other in this fashion.
2. I would also assume that this would throw a wrench into our understanding of relativistic QM and our need to integrate QM and GR. But perhaps not.
3. The Hubble constant is not, as I understand it, a fundamental value itself but more an outgrowth of our understanding of cosmology.
4. For the life of me, it seems as if there is an ether after all!

#### DrChinese

Gold Member
I am reading the other Lineweaver article (Inflation and the CMB). I can see this has a lot of explanation that the other one does not have. Up through the first 3 pages, I am familiar with the concepts but I have 31 more pages to go...

#### Mentat

Right. The things that are apparantly receeding from us at superluminal velocities are in fact not themselves moving that fast. Rather, the space between us is expanding, and so it is the metric that we use to define the distance that is getting ever larger.
Thanks for making that point, Brad. You have probably done a better job than I would have, since I often get into the analogies (like the "balloon analogy") to explain the phenomenon and then the thread gets side-tracked.

#### marcus

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Dearly Missed
DrChinese, Mentat, Brad, thank for keeping this thread alive! I got distracted and didnt check here for several days. Mentat and Brad exactly right about metric distances increasing being different from stuff moving through space. Stuff can be sitting still and yet be getting farther apart---metric is dynamic (a solution to some equations that include matter density etc).

DrC your comments and questions are clearsighted (plainspoken too ) and I wish I had noticed what was going down at this thread, would have replied earlier.

Originally posted by DrChinese

I think we have something as follows:

a. There are a number of possible space-time metrics which satisfy GR.

yes

b. The discovery of actual high z values from the relatively early universe indicate that certain of these metrics are supported, and therefore others must be discarded as describing our universe.

c. In the high z scenarios we are able we witness, the additional "velocity" component - which gives rise to recession >c - is a function of the expansion of the spacetime metric.

yes and it is probably simpler than you imagine, Friedmann got simpler equations boiled down from Einstein by assuming a sort of uniform largescale sameness, and when the Friedmann equations are combined with the observed largescale spatial flatness the metric turns out to be incredibly simple---the spatial part of the metric is just an ordinary euclidean distance with a timedependent scalefactor a(t) multiplying it so that distances between regions increase in exact proportion as this function a(t) is increasing----and it is just an ordinary real function of one real variable right out of first year calculus. so there is hope for us. like, you can graph a(t)----Lineweaver does this at Figure 14. He calls it R(t)----there are these two mainstream notations for the same thing, a(t) and R(t). Both are loosely referred to as the "size" of the universe and usually normalized so that they equal one at the present time, also, since universe is quite possibly infinte saying "size" doesnt sound quite right so people sometimes say "average distance between galaxies" but the mathematical reality is that it is the scalefactor of the metric, normalized to equal one at the present time.

I hope this is accurate. If so I would ask as follows:

1. Presumably it would not be possible for any objects to move towards each other faster than the speed of light - only away from each other in this fashion.

interesting thought! but if cosmos ever starts to contract then a(t) will start to go back down to zero and things will rush towards us the same way they now rush away. Friedmann equation allows contracting U as one solution but we happen to be in an expanding case.Distances could be decreasing, they just happen to be increasing.

2. I would also assume that this would throw a wrench into our understanding of relativistic QM and our need to integrate QM and GR. But perhaps not.
3. The Hubble constant is not, as I understand it, a fundamental value itself but more an outgrowth of our understanding of cosmology.

the Hubble parameter is defined by a(t). You see that a(t) is the basic thing in cosmology. It is defined as the slope of a, then divided by a-----or the timederivative of a(t), divided by a(t)----in freshman calculus terms H(t) equals a'(t)/a(t)

so if a is growing then its derivative a'(t) is positive and you divide by a(t) to sort of normalize it or get a percentagewise increase rate handle on it, it just turns out to be a convenient
handle on a(t)'s growth that you can work with and relate to observational measurements etc.

4. For the life of me, it seems as if there is an ether after all!

yes of course! we still have much to learn about what space itself is! and many pratfalls by the "experts" still to come, if would not surprise me in the least if there turned out to be ether, and elusive loop soup perhaps, or a giant polymer. what color is it I wonder

It is mutual. Your responses help me get understanding of the subject matter as well.

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#### DrChinese

Gold Member
Originally posted by marcus
DrChinese, Mentat, Brad, thank for keeping this thread alive! I got distracted and didnt check here for several days. Mentat and Brad exactly right about metric distances increasing being different from stuff moving through space. Stuff can be sitting still and yet be getting farther apart---metric is dynamic (a solution to some equations that include matter density etc).

DrC your comments and questions are clearsighted (plainspoken too ) and I wish I had noticed what was going down at this thread, would have replied earlier.
Ok, I have been working on the Lineweaver reference. You are right, it is quite thorough. I have seen most of the material previously in one form or another, but here it is spliced into a coherent story. I am still only about 2/3 complete, so I probably shouldn't post yet but... what the hey.

Clearly, the idea of inflation was to solve some fundamental problems in the very early universe (at least in our picture of it). I have always mentally separated the inflationary period from the GR model (i.e. the era following the first Nth of a second). If inflation is to be taken seriously, then it must be considered "real". If it is real and the universe expanded during the very early universe, then it must also be possible that expansion is going on today. And therefore is every bit as real.

It shouldn't surprise me that we could actually detect relatively early star clusters either. I guess what surprises me is that the math works out that the universe could have been expanding as much as it has. So as I read the numbers, we are in a 13.5 billion year old universe with a "diameter" of about 47 billion LY. I am still trying to put it all together, but a few thoughts come to mind.

1. We talk about the idea that inflation solves the horizon problem (section 4.3, p. 12 of the Lineweaver article). It is stated that there would have been time enough for thermal equilibrium to have been achieved. This provided the needed causal contact required to explain the homogeneity of the observed universe. But can we really say that such a universe, as hot as it was, could really have achieved equilibrium in such dynamic circumstances? Any kind of damping or delay would seem to prevent this from happening.

2. Presumably, inflation (expansion of the universe) is not 0 today. Possibly there is a universal factor of the current inflation of the universe; i.e. it changes in all of space in the same way at the same time. Oops! That doesn't seem reasonable unless there is an absolute time (so it can be synchronized) or the universe is still causally connected on some level (which it may be). Alternately, the expansion is driven by some local factor - similar to gravity itself, which is dominated by large nearby objects.

#### ranyart

Originally posted by DrChinese
Ok, I have been working on the Lineweaver reference. You are right, it is quite thorough. I have seen most of the material previously in one form or another, but here it is spliced into a coherent story. I am still only about 2/3 complete, so I probably shouldn't post yet but... what the hey.

Clearly, the idea of inflation was to solve some fundamental problems in the very early universe (at least in our picture of it). I have always mentally separated the inflationary period from the GR model (i.e. the era following the first Nth of a second). If inflation is to be taken seriously, then it must be considered "real". If it is real and the universe expanded during the very early universe, then it must also be possible that expansion is going on today. And therefore is every bit as real.

It shouldn't surprise me that we could actually detect relatively early star clusters either. I guess what surprises me is that the math works out that the universe could have been expanding as much as it has. So as I read the numbers, we are in a 13.5 billion year old universe with a "diameter" of about 47 billion LY. I am still trying to put it all together, but a few thoughts come to mind.

1. We talk about the idea that inflation solves the horizon problem (section 4.3, p. 12 of the Lineweaver article). It is stated that there would have been time enough for thermal equilibrium to have been achieved. This provided the needed causal contact required to explain the homogeneity of the observed universe. But can we really say that such a universe, as hot as it was, could really have achieved equilibrium in such dynamic circumstances? Any kind of damping or delay would seem to prevent this from happening.

2. Presumably, inflation (expansion of the universe) is not 0 today. Possibly there is a universal factor of the current inflation of the universe; i.e. it changes in all of space in the same way at the same time. Oops! That doesn't seem reasonable unless there is an absolute time (so it can be synchronized) or the universe is still causally connected on some level (which it may be). Alternately, the expansion is driven by some local factor - similar to gravity itself, which is dominated by large nearby objects.

Originally posted by DrChinese
Oops! That doesn't seem reasonable unless there is an absolute time (so it can be synchronized)
But there is a case that irons out this, and it has its roots within Human perception. As far as we are aware there is a core Blackhole within our Milky Way,and as observers we are contained within an individual Galaxy. This is our Observational Preference Frame,we cannot geta way from this fact, all of our physical 4-Dimensional Spacetime is CONTAINED within this reference frame we call Galaxy.

Relativity equations can be constrained to within just our Galaxy, Time starts and ends with our galactic Blackhole. The really interesting fact ist that when you derive the Equations outwards, the SPACE of intergalactic medium is Explained by Quantum Field Theory, and its a perception thing, SPACE between Galaxies is reduced to a 2-dimensional field theory, coupled to Vacuum force equations, there is no TIME needed here!

Spacetime seperates from a 4-d state(Galaxy)> to a 3-d field(EM-MEDIUM)>>down to a dynamical force field Gravitational repultion(vacuum expansion).

It does seem hard to expect that our physical Galaxy is surrounded by a 2-dimensional space(not-Time-frame) but this is what contracts(by a defined force, a two dimensional field contracts its inner product-GALAXIES!) while we inside this location, see everything outside our Galaxy as Expanding away from our Prefered frame.

What the equations also show, is if one could go to a far far away location that had a nearly pure vacuum, away from Galaxies, one would indeed see that Galaxies were not receeding, but disolving(contracting, really its a perception thing) at a defined boundery.

#### marcus

Gold Member
Dearly Missed
Originally posted by DrChinese

2. Presumably, inflation (expansion of the universe) is not 0 today. Possibly there is a universal factor of the current inflation of the universe; i.e. it changes in all of space in the same way at the same time. Oops! That doesn't seem reasonable unless there is an absolute time (so it can be synchronized) or the universe is still causally connected on some level (which it may be). Alternately, the expansion is driven by some local factor - similar to gravity itself, which is dominated by large nearby objects.
definition of inflation is accelerated expansion (the rest is just details, whether it is the early episode or the one were now in, and difference of degree---acceleration very gradual now

and there is no problem getting inflation to kick in at roughly the same time (in a sense I will explain) all over the universe---you just have to have a constant Lambda (they think it is 0.6 joules per cubic km) constant thru all space and time and its effect will be waiting to be felt for, like, 10 billion years and then only when matter has thinned out enough that the SLOWING effect of matter no longer dominates----only then will Lambda come into its own and a bout of acceration will start

so it is a timebomb and the clock ticking is the expansion of the universe (reducing the once-dominant density of matter) itself---no other clock is needed

second point is that cosmologists DO have a synchronized clock with a copy in every galaxy everywhere. there is a universal standard time, and the Friedmann model (dominant model they all use) is BUILT using that standard clock

the reason is there is a universal notion of being at rest, called
"at rest with respect to the Hubble flow" or "at rest with respect to the microwave background".

the spatial part of the metric measures distance at the present moment---meaning by this universal clock---and the time part of the metric is time as seen by observers "comoving" with the Hubble flow---another name for the expansion process----or in other words at rest with respect to it

It is a shame the way they indoctrinate us all with "Special" relatitivity till we all believe certain things (like no absolute time, no absolute idea of rest) and then a year or two later in school they contradict much of this and confront us with exceptions to the earlier doctrine.

But thats how it is unfortunately and two people in two separate galaxies will both say the universe is 13.8 billion years old as long as both galaxies are at rest---even tho the distance between the galaxies is increasing

if we could tell all the other galaxies about Cesium atomic clock seconds, and how long a year is, then all the galaxies (to the extent they are not moving significantly wrt CMB, or only a few 100 km/s random scooting around) would agree 13.8 billion, and also that acceleration kicked in again at 10 or 11 or 12 billion or whenever it was

#### marcus

Gold Member
Dearly Missed
Originally posted by DrChinese

1. We talk about the idea that inflation solves the horizon problem (section 4.3, p. 12 of the Lineweaver article). It is stated that there would have been time enough for thermal equilibrium to have been achieved. This provided the needed causal contact required to explain the homogeneity of the observed universe. But can we really say that such a universe, as hot as it was, could really have achieved equilibrium in such dynamic circumstances? Any kind of damping or delay would seem to prevent this from happening.
Im looking at page 14 of Lineweaver and I cant give a decent answer. Somebody thought expansion by factor of exp(60) was enough----and it is only a lower bound estimate---they allow that it could have been much more. I'll say what I can but it wont be entirely satisfactory, and we may get help too.

the early inflation is called a "scenario" instead of a theory because it is very speculative---they dont agree on a clear idea of when or why or how long or what an "inflaton" looks like.

The common estimate of at least 60 "e-foldings" is a number which people came up with JUST TO SOLVE THE HORIZON PROBLEM. The say that inflation blew space up by a factor of exp(60) or e60 or inothere words around 1030 because that number is big enough to explain the uniformity---it means everything came out of a region that people have convinced themselves would have been small enough to be uniform

the scenario is made to order to explain the contemporary scene and in that way it faintly resembles a Kipling "Just So Story" which is OK. I mean, can any of us do better? We have to allow a little of that, as long as they dont call it a theory but just the "inflation scenario"

BTW figure 4 on page 13 has a kind of sloppiness in that Lineweaver didnt have his graphics person redraw the right hand side scale when the "surface of last scattering" line was moved up. The scale in figure 4 is just the same scale that goes with the lower of the two "surface of last scattering" lines---it is really two spacetime diagrams in one and the scale only matches one of the two cases. It is the only carelessness or flaw Ive found in that article.

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