FLRW Metric and ‘Expansion of Space’

We start from Wikipedia’s explanation of ‘Metric Expansion of Space’:

“The metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself changes. It means that the early universe did not expand “into” anything and does not require space to exist “outside” the universe – instead space itself changed, carrying the early universe with it as it grew. This is a completely different kind of expansion than the expansions and explosions seen in daily life. It also seems to be a property of the entire universe as a whole rather than a phenomenon that applies just to one part of the universe or can be observed from “outside” it. Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the Friedmann-Lemaître-Robertson-Walker metric (FLRW Metric) and is a generic property of the universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above), because gravitational attraction binds matter together strongly enough that metric expansion cannot be observed at this time, on a smaller scale.”

In short, according to official sources, ‘Expansion of Space’ stuff is rooted in FLRW metric. It is said that before the discovery of ‘redshift-distance’ relationship in light coming from far off galaxies in 1929 by Edwin Hubble, (F) Friedmann (1922) and (L) Lemaître (1927) already had described ‘Expansion of Space’ in their respective works.

Before presenting the actual points of (F) Friedmann (1922) and (L) Lemaître (1927), let me first share point of view of a famous Internet Physics writer Mr. Victor T. Toth on this topic. Following was his reply dated December 01, 2017 to a question:

Big Bang theorists do not claim that space is “created physically”, whatever that means.

Big Bang theorists do claim that things, on average, recede from each other; that the distance between things is therefore increasing, on average; and that correspondingly, the metric of spacetime evolves as governed by Einstein’s field equations.

None of this implies space being created, “physically” or otherwise. (For starters, space is not a measurable, tangible concept, nor is it a conserved physical quantity. When you measure “space”, what you actually measure is the distance between things, not space itself, which is intangible.)

In above answer, Mr. Victor T. Toth is saying that Big Bang Theorists do not claim that space is expanding or being created or anything like that. But in another recent answer, he is accepting that Big Bang Theorists do say like that and thus he is showing his disagreement with those Theorists:

Not for the first time, allow me to be the contrarian here and challenge my esteemed colleagues who are telling you that space is expanding, by making three (to me) rather important points: (i) What is this “space” that is expanding? How do you measure it? Where are its little markers to which you can attach your measuring tape? And exactly how is this “space” represented in the Friedmann equations? (ii) Speaking of which, if it was space expanding, how come I can derive (see, e.g., books by Weinberg or Mukhanov) the aforementioned Friedmann equations purely in the context of Newtonian physics, with its concept of absolute space and time? (iii) Last but not least, when gravity brings expansion to a halt, how does it do that? Is it somehow acting on “space”, as opposed to acting on matter? (See also Peacock’s Cosmological Physics.)

No, space is not expanding. It’s not even something we could measure if it did. The Friedmann equations contain two entities: matter (represented by its density and pressure) and the gravitational field (represented by one component of the very special, homogeneous and isotropic FLRW metric.)

Galaxies are moving further apart. If you could stretch a measuring tape from the Milky Way to a distant galaxy, the distant galaxy would be zipping alongside that measuring tape at quite a clip (probably several hundred kilometers a second, at the very least.) And when, in a region where matter is denser-than-average, gravity prevails, it stops those galaxies from moving away from one another.

The purpose of presenting quotes of Mr. Victor T. Toth was to show that some big bang cosmologists are already against the idea of Expansion of Space. However here Mr. Victor T. Toth is not representing the dominant opinion of mainstream big bang cosmologists who overwhelmingly think that Space is Expanding and that this notion of Expansion of Space is rooted in the works of (F) Friedmann (1922) and (L) Lemaître (1927).

Therefore, now I will show that both (F) Friedmann (1922) and (L) Lemaître (1927) did not actually talk anything about Expansion of Space and that this notion is deceptively being attributed to them by the mainstream cosmologists. Mr. Victor T. Toth already has given a hint that Friedmann equations contain two entities which are (i) matter and (ii) gravitational field and thus there is nothing like Expansion of Space in the works of Friedmann (1922).

So let us first check the Friedmann’s actual concept of space. The English Translated title of his 1922 paper is “On the Curvature of Space”. He uses terms ‘space’ synonymous to ‘radius of universe’. By the term ‘radius of universe’ his meaning is that mass contents of universe would cause gravitational boundary of universe that a straight line universal journey of a physical object would be a complete circle and would reach back to the original point. ‘Radius of universe’ is radius of this universal ‘straight’ line which is actually circular. Within this meaning of ‘space’, it is physically valid to say that space may expand or contract. Within mathematical model of Friedmann, space is really expanding or contracting according to this meaning. Following are some examples in Friedmann’s paper of usage of term Radius R as curvature of space:

“Here R depends only on x4 and it is proportional to the radius of curvature of space, which may therefore change with time.”

While deriving constant universe model of Einstein within his own general scheme,

Friedmann writes: “whereby R signifies the constant (independent of x4) radius of curvature of space.”

“If we restrict our consideration to positive radii of curvature”.

“Let the radius of curvature equal R0 for t = t0.”

“Positive or negative depending on whether the radius of curvature is increasing or decreasing for t = t0.”

“by choice of the time it can always be arranged such that the radius of curvature increases with increasing time at t = t0.”

It is now clear that yes space is contracting or expanding in Friedmann’s model but it is contracting or expanding within above physically valid meanings of contraction or expansion of space. But Big Bang Cosmologists tell us a whole different and misleading thing and they attribute their own faulty model to Friedmann. They call their own misleading model of ‘expansion of space’ as ‘metric expansion of space’ and wrongfully attribute this faulty physical model to Friedmann.

After checking the actual position of Friedmann (1922), now we come to see the actual position of Lemaître (1927) with regards to the notion of Expansion of Space.

Modern concept of Expansion of Space has actually come from manipulating Equation No.23 of Lemaître (1927) paper. Following is the snapshot of Equation No.23:

This equation can be written as V/C = (R’/R)r

The above form of equation No.23 superficially resembles to Hubble Law which is V = HD

In Equation No.23, V/C is ‘Redshift’ and in Hubble Law, V is ‘Redshift’; thus LHS of both equations are equal.

Moreover, in Equation No.23, r is Distance, so ‘r’ and ‘D’ of RHS of both equations are also equal.

Therefore, if we use the notation of Hubble Law, we can write Equation No.23 as following:

V = (R’/R)D

R means radius of whole Universe … (Radius of ‘whole’ universe itself should have been regarded as ‘cranky idea’ in first place).

Anyhow ‘R’ means radius of whole universe.

What Lemaître stated was like V=(R’/R)D

What standard ‘interpretation’ goes in every official source … books/papers etc. that is V=(S’/S)D

In short Lemaître was saying in his equation No.23 (1927) that redshift (V) is caused by increase of radius of whole universe. While distance of galaxy (D) remains constant.

Actual equation No.23 is not exact this one. If we use notation of Hubble law then equation No.23 becomes like this and superficially does resemble with Hubble law.

But unlike Hubble law where H is constant … here we have distance of galaxy (D) as constant.

R’/R … does it mean H or not?

Whether or not it mean H … it is not constant like H

This is the actual position of Lemaître .

What FLRW metric attributes to him?

FLRW metric makes this thing into V=(S’/S)D where S means ‘Space’.

Here conversion of R into S is a simple manipulation.

Lemaitre here did not say increase of Space or even increase of distance of galaxy… according to equation No.23, distance of galaxy remained the same.

This thing has been ‘interpreted’ in FLRW metric that ‘coordinate’ of galaxy remains the same and space is increasing.

In the end … after all this is a deceptive manipulation. V=(R’/R)D is NOT equal to V=(S’/S)D.

Thus we have seen and confirmed that both Friedmann (1922) and Lemaître (1927) had not coined the term or concept of Expansion of Space and that this concept or notion is only deceptively being attributed to both of them by the so-called FLRW metric.

Position is that without the notion of Expansion of Space, the Standard Model of Cosmology (Lambda-CDM) does not work and this notion itself is unreal, illogical, non-physical as well as deceptive.

For further details, please see my book “A Philosophical Rejection of The Big Bang Theory”.

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larryzb
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Perhaps I missed something here, but with the light from distant galaxies redshifted, these must be moving further away from us here on Earth. Now, this does not mean by default that space is expanding, but galaxies are moving further away from each other. That needs a satisfactory explanation as to its cause.

Magellanic Cloud
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One option is ‘expansion of space’. This option solves problems like why do we appear to be at center and far off galaxies are not moving at speed greater than c because galaxies are not moving just space is expanding at constant rate. This option is unreal, non-physical as well as deceptive. Actual mathematics is saying some other thing. Actual mathematics is not even saying that galaxies are moving. Observed redshift is different from ‘Doppler’s Redshift’. It is called ‘Cosmological Redshift’ Doppler’s Redshift = redshift-SPEED relation. Cosmological Redshift = redshift-DISTANCE relation Doppler’s redshift is the proof of receding of things.… Read more »