“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.)

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.

There is reality in gravity having its effect distinct from electric effects. But it is also fact that effects of electricity and magnetism start well before reaching to so-called singularity only where according to ‘legitimate’ scientists, theory of gravity fails.

Earth-moon system works differently than the known effects of electricity. So Solar system, galactic system and larger structures are likely being operated by gravity rather than electricity or magnetism. But small scale contributions of forces other than gravity also cannot be denied. Stars are made of plasma therefore within stars major contribution of electric or magnetic effects make sense.

More importantly, mainstream point of view that early universe was hot and dense yet only gravity was the major player in the dynamics of such dense and hot environment makes no sense.

Overall electric and magnetic dynamics are more complex and beyond my satisfactory comprehension ability. Mainstream scientists also avoid indulging themselves into the complexities of electric and magnetic effects at larger scales. Mere presumption that these effects just get neutralized is over simplification. Overall I also assume that larger structures are mainly operated by gravity. I just accept possibility of minor contribution of electricity and magnetism at such scales. Plasma stars are localized structures and major contribution of electricity and magnetism within plasma based local structures cannot be denied. It is also possible that some astronomical effects which are presently regarded or understood to be the effects of gravity might actually be the effects of electricity/magnetism.

By 1916, Einstein had successfully presented his Field Equations of Gravity i.e. General Relativity (GR). In year 1917, he attempted to apply his GR equations to describe whole Universe. Following is the link to English Translation of Einstein (1917) paper:

Einstein starts by evaluating compatibility of General Relativity with an infinite Universe and he does evaluate by going into technical details. Basically he was trying to set ‘boundary condition’ for a spatially infinite universe.

At the end he admits that he failed in doing so:

From what has now been said it will be seen that I have not succeeded in formulating boundary conditions for spatial infinity.

Einstein (1917)

Einstein was more interested in ‘boundary condition’. He failed in determining the boundary condition for spatially infinite universe. But he would ‘successfully’ determine the same for a spatially finite universe.

So how did he ‘derive’ the idea of Finite Universe? Well … he did not derive. He just introduced this idea as a commonsense alternative. Only one extra thing i.e. Cosmological Constant was needed and every problem would be solved. So let’s see how actually the idea of Finite Universe was introduced and what problems were solved through cosmological constant:

Nevertheless, there is still a possible way out, without resigning as suggested under (b). For if it were possible to regard the universe as a continuum which is finite (closed) with respect to its spatial dimensions, we should have no need at all of any such boundary conditions. We shall proceed to show that both the general postulate of relativity and the fact of the small stellar velocities are com- patible with the hypothesis of a spatially finite universe; though certainly, in order to carry through this idea, we need a generalizing modification (i.e. Cosmological Constant) of the field equations of gravitation.

Einstein (1917)

“For if it were possible to regard the universe as a continuum which is finite (closed) with respect to its spatial dimensions …” This sentence clearly shows that finite universe idea was not derived from equations. It was annexed to theory as a commonsense alternative where complexities of infinite option remained unsettled.

How boundary condition was determined? “we should have no need at all of any such boundary conditions.” So problem with regards to boundary condition is solved in a spatially finite universe as now such a boundary condition is not even needed.

And … what were the problems whose solution was the ‘cosmological constant’?

The above quoted paragraph shows that there were two problems:

(i) Finite Universe itself and; (ii) Fact of the smaller stellar velocities.

So the problem was associated with the idea of finite universe. If universe is infinite then there was no need of cosmological constant. With finite universe, Einstein feared that it should be collapsed under gravity.

Generally orbiting objects do not collapse under gravity and Einstein was fully aware of this fact. But why do objects orbit? They orbit due to side-way velocity. Einstein knew this fact also as it is clear from following quote out of same paper:

According to the general theory of relativity the metrical character (curvature) of the four-dimensional space-time continuum is defined at every point by the matter at that point and the state of that matter.

Einstein (1917)

But Universe even if finite must have been very big. Einstein was thinking that at cosmic scale matter must be at permanent rest. In following quote, he is saying that at cosmic scales, the relative velocities of stars are very small:

The most important fact that we draw from experience as to the distribution of matter is that the relative velocities of the stars are very small as compared with the velocity of light.

Einstein (1917)

On the basis of ‘fact’ that relative velocities of stars are very small, he then concludes that at cosmic scales, all matter must be at permanent rest:

There is a system of reference relatively to which matter may be looked upon as being permanently at rest.

Einstein (1917)

“Stars are relatively at rest” … and therefore (finite) universe is at “permanent rest” … Einstein reached to this conclusion and need for introducing ‘cosmological constant’ was invoked.

Because in a finite cosmos, only orbit moving stars could prevent gravitational collapse … since stars were at “rest” … there was no orbiting going on … hence an anti-gravity agent “cosmological constant” was needed to prevent gravitational collapse.

We have seen that basic idea of Einstein was that since stars are relatively at rest therefore finite universe must be at permanent rest. In year 1917, Einstein was definitely not aware that finite island universes (galaxies) do exist where not only that stars are not relatively at rest but they are rotating at faster speed than could be (officially) expected for such galaxies.

Thus in a real finite universe, there was no need of cosmological constant. It was needed only for a flawed hypothetical infinite universe which is at permanent rest.

From a theoretical perspective, we know how galaxies should form. We know that the Universe ought to start out governed by General Relativity, our law of gravity.

Here Ethan Siegel, just like majority of other ‘scientists’ is thinking that Universe must start in mode and manner as prescribed by the governing theory which is General Relativity.

However actually this is the issue of perspective. Modern Science especially Physics is under the influence of Idealism. The implications of idealism on Physics are profound and deep which I have explained somewhere else in following words:

In this modern idealism, we start from GR equations. We find ‘correct solutions’ on paper and take them for real. It means we are at least at an advanced stage than those ancient animist people for whom any idea would be as real as physical reality. Our “modern science” has only sorted out that status of reality cannot be assigned to each and every idea of mind. This status goes only to ‘correct solutions’ of GR equations.

The actual physical reality is only that we are getting redshifted light from everywhere such that more distant galaxies are more redshifted. But more real for scientists is the very first moment of creation of universe that is found out through so called ‘correct solutions and our scientists become able to tell us (like modern magicians) all the details of that early stage of universe as if it took place before their eyes. Not only that, rather than theorizing larger reality on the basis of observed facts (scientific approach), they have started explaining or interpreting observed facts on the basis of so-called already known larger facts of reality.

Modern ‘Scientists’ are actually more than magicians. They are the kINGS of whole Universe and their theories are the governors of Universe. As I stated earlier, basically this is the issue of perspective. Outlook of ‘scientists’ has been contaminated by idealism. Reality can however be captured or grasped only from realistic point of view such as Epistemological Realism where external world is real i.e. not construction of mind. Mind is reflection. Our theories do not govern Cosmos … Our best theories only best represent the physical reality into theoretical – narrative or mathematical – format. Knowledge is confined to the boundaries of mind. Mind works on observational data and ‘organizes’ sense data into the form of knowledge. And Scientific knowledge also does not cross the boundaries of mind.

Yes Idealism is more charming. But realistically speaking, our theories do not ‘govern’ physical world.

Relativists always keep telling us that General Relativity (GR) has passed every test with flying colors. More precisely, they always tell us that every ‘prediction’ of GR has come true. Here we choose to accept that OK every test within the dynamical boundaries of Solar System was passed.

We also choose to not question the failure of GR at galactic and clusters of galaxies scale where they had to balance out their equations with ghost object of dark matter. We prefer to not raise question on this failure of GR because, as will be explained in upcoming posts, the dark matter was not the failure of theory but was the result of incorrect application of theory. Therefore, to the extent of galactic dynamics, we choose not to raise objection on GR.

But in definite terms, GR has failed the test at Cosmological Scales with more than flying colors.

Before introducing Cosmological Constant, Einstein (1917) is saying that space (on cosmological scale) must have constant curvature i.e. whole cosmos is a huge sphere.

Now please see how Einstein has concluded this 1917 paper:

In starting lines of this page, Einstein is saying that introduction of cosmological constant has also given the result that space on cosmological scale is spherical. At the end, he is explaining that curvature of space is positive even if cosmological constant is not considered or taken into account.

Therefore, by all means, ‘prediction’ of GR for Cosmology was that Space (or Universe) is curved or spherical etc.

The so-called Standard Model of Cosmology i.e. Lambda-CDM (nickname Big Bang Theory) is actually based on wrong assumption that GR is true for Cosmic Scales. Fact is that GR has terribly failed the test of Cosmos.