Einstein's Cosmological Constant

With General Relativity, Einstein could conceive of a universe that was in a sense infinite/unbounded and yet had a finite volume, ergo a finite number of stars (answering Olbers paradox)

This involved the curvature of spacetime, caused by a sufficient density of matter in the volume. Going out into space one could travel onto eternity, as if space were infinite, but because spacetime formed a globe in which after a time one would be going back in time to approach your starting point from the past. There is no physical suggestion though that this would mean an eternally repeating cyclic time loop. Also, although this might in itself seem an infinite closed universe, it does not exclude the possibility of infinite space (and time) outside of this apparent universe (although Einstein speculated that time and space may not exist without the existence of matter as a reference frame).

Einstein also knew that there did not appear to be enough density of matter to make this universe.

The other problem he saw, was that if this universe was going to be a steady state eternal universe – the consensus view that he agreed with – then there needed to be something to stop gravity from making it collapse. So he introduced the idea of the ‘Cosmological constant’ i.e. some kind of constant pressure in space that on a large scale would hold things apart, in a steady state.

Naturally, as this was just a device or mathematical fix, some would be sceptical about it, and a mathematician called Alexander Friedman considered Einstein’s universe without the cosmological constant. He showed, using general relativity, that with respect to energy, this universe could expand, with gravity slowing down its expansion, or it could contract, with gravity then speeding up its contraction. The slowing-down-expansion means an increase of gravitational potential energy combined with a decrease of kinetic energy, whilst the contraction means a decrease of gravitational potential energy combined with an increase of kinetic energy. Either way the overall energy would be the same – but this scenario involved kinetic energy in its description, which means it ruled out the possibility of a steady state.

Even though Friedman’s solutions seemed true to General relativity, Einstein didn’t like it. They disagreed with his presumption of a steady state universe, but they also did not provide any physical reason why the universe should expand (against the gravity). They only said that it would be ok with respect to overall energy if things, or space, were expanding against the gravity. So Friedman had defined the expansion as caused by the ‘expansion of space’ (with no physical cause). Einstein thus rejected the idea on the basis it was neat maths, but not physics.

It was not long though before astronomers (Hubble and co.) discovered that the visible universe was expanding, and in proportion to distance, i.e. just as if space were expanding, and so it seemed that Einstein was wrong with his steady state universe (and its cosmological constant) and Friedman had been right, though he Friedman died before knowing this.

With the discovery of expansion, the big bang theory emerged and caught on (though many distinguished scientists still resisted the fall of the steady state scenario). The big bang theory still needed (and needs) some physical explanation for what caused the expansion (of space). And eventually the idea of ‘inflation’ was settled on – even though inflation has no physical cause – i.e. the theory is that inflation (a sudden expansion of space (that overcame gravity)) just happened.

And then for a long time the community of astronomers, cosmologists, physicists and mathematicians were all pretty much in agreement, some even thinking that soon, in time for the new millennium, the theory of everything would be sewn up, from the beginning of time to the present.

But then in 1998 came the observations (of type 1(a) supernovae by Perlmutter, Riess and Schmidt) that upset the whole applecart: the visible universe was actually accelerating apart. This was /is a huge shock to the theory, not just because of the obvious assumption that gravity would slow down the expansion, but because in terms of Friedman’s solutions (that supposedly observed General relativity and a conservation of overall energy) an expansion had to be slowed down, to whatever extent. One could not say that anything (even the device of inflation) could cause an acceleration of the expansion without a disobedience to conservation of energy.

So what now, wonders the community, could cause an accelerating expansion of the visible universe?

It was noted that if Einstein’s cosmological constant was reintroduced, this time for the dynamic expanding universe, then the constant pressure would mean an acceleration of the expansion. We should recall that Einstein inserted the constant for the purposes of making the universe a steady state, in which case he was not imagining a scenario that troubled the conservation of energy principle, but if the constant becomes responsible for an accelerating expansion, then it is revealing itself as a constant energy source, doing work, adding energy to the system, ergo breaking the conservation of energy. The same goes for the idea of Dark Energy i.e. the vacuum energy of space or the field of virtual particles. This exists in quantum physics but is not supposed to be doing work/adding energy/causing accelerations in macro reality. But if this energy is allowed to break these basic rules then the calculations say it should be at least 120 orders of magnitude too high to be the cause of the cosmic acceleration.

In principle, so long as one thinks that whatever is causing the cosmic acceleration is something that is going against gravity (adding both kinetic and potential gravitational energy to the system) then one is thinking of a device that is breaking the conservation of energy principle.

So that leaves only one agreeable cause for the acceleration, gravity itself.

And why not?

On the large scale, it is gravity that moves things about. And if you are thinking that the (accelerating) expansion is space expanding, then what could cause space to expand? We know, thanks to Einstein that it is gravity that affects the spatial context.

So how could gravity cause the accelerating expansion, against our usual expectation of what gravity does (pulls things together)?

Well, actually, it’s not that difficult to see why. A gravitational acceleration means falling towards something of mass, so if our cosmos is falling apart, it is probably falling towards the greater mass of a surrounding (infinite) universe of many other cosmoses. This is a scenario that anyone can grasp. So why then do the world’s cosmologists and astrophysicists fail to grasp it. Well, I might refer to that saying ‘There’s nowt more mysterious than folk!’

There are however a number of (historical) reasons why this scientific community does not (yet) see this multiverse scenario as the gravitational reason for the cosmic acceleration; why they say “It doesn’t work like that!”

According to the maths, their maths, the gravity of a surrounding possibly infinite universe could not have any effect on our cosmos.

But then I would follow this general rule…

Every physical scenario must be responsible for some physical effect (and nothing exists in isolation)

And thus think again

Noting that…

Presently we seem to have arrived at an era where the maths is seen as a governing guide of the physics. But that loses sight of the fact that in describing the physics, the maths may (always) be a simplification. And in some cases there is a subtle or crucial difference between what happens in reality /according to the physics and what the simplification of maths calculations (and computer simulations) say would happen. For example, when using maths we would say the gravitational pull of a planet results in a single vector coming from the centre of gravity of the planet. Whereas in physical reality that pull is made up of a multitude of vectors coming from every mass particle that the planet contains. The single vector coming from a single, narrow direction is the sum total of all those pulls, but if you kept the description of a multitude of pulls coming from a broad direction (the angular width of the planet) then there may be slightly different effects, e.g. the single direction will have a slight tendency to pull things together, width-wise, while the broad direction to pull things slightly apart.

So, returning to the issue of the accelerating expansion…

According to relativity there is no fixed/absolute/ static spatial context. Every reference frame has its own spatial context and its own view of reality. This in itself suggests the possibility of a multiverse, but before we go there let’s just deal with two objects, masses A and B that are gravitationally attracted and move towards each other. You could say that from each object’s view in their own reference frame they are static and see the other object as accelerating towards them. However for a shared reality that agrees with the laws of physics, the gravitational motion caused has to be equal and opposite in terms of momentum, so the spatial context is repositioned to agree. Now add another much larger mass to the scenario, C, and the spatial context is again redefined to make A and B accelerate towards C with the same momentum that C is accelerating towards A and B. But note also that whichever of A and B is nearer C it will accelerate faster to C. So now there’s a gravity context that can separate A and B rather than pull them together.

Now consider the greater scenario of any object, even a whole cosmos, surrounded by infinite others. For things in the relative proximity or foreground there are calculable/single direction gravitational relationships. But as one goes further into the distance, in a homogenous mass distribution/infinite universe, then the other objects effectively become a whole all-surrounding distant object.

This can be modelled, as in Newton’s shell theorem, as nearby objects within a great cavity. It works out that the gravity from everything outside the cavity (ad infinitum) has no net vector pull on anything within the cavity (that pull might be infinite but it is omnidirectional so it is nullified/ cannot pull anything in any particular direction). However, there is a pull from each object within the cavity on the collective objects outside the cavity, and that can pull those objects in a particular direction (towards the object).

Of course, this pull of every object on the surrounding infinity would be very slight, but proportional to its mass, so with the collective mass of an object like our cosmos, that becomes significant.

So, if the collective mass of our cosmos can be pulling the outer cosmoses in, should not the spatial context be redefined to agree with the action and equal and opposite reaction principle, or the conservation of overall momentum, such that the inward momentum of the outer cosmoses is matched by outward/expansive momentum of our cosmos?

Well, although there is no singular direction/ vector for things to go in to effect this expansion, the spatial context can (again) be redefined, this time to expand, to fulfil that ‘outward momentum’.

Even without the concept of expanding space, one can show that objects within the cavity, that are pulling on the surrounding infinity, will have some tendency to pull themselves apart and separate in an acceleration, both with the Newtonian model and with Einstein’s model of gravity (in which gravity forms wells in space-time (and takes time to travel (at the speed of light)). I show this in another paper. The ‘expansion of space’ is a simple way of describing the apparent effect.

As you scale things up to where you are considering a sphere of clusters of cosmoses surrounded by infinite others, then again the spatial context must be redefined to describe the cluster of cosmoses as separating while pulling the surrounding (clusters of)cosmoses in. In each scenario the spatial context defines a different motion/reality. There is no fixed shape of space/time, it all depends on the reference frame. And as you go up or down in scale/ collective mass, the expansion tendency changes accordingly, which means there would be subdivisions or clumping of matter on all scales, in association with the expansion.

The thing that all reference frames (that are in the same reality) share (even when they are moving relative to each other) is the same speed limit to their reality; the speed of light. This is also the speed at which gravity travels.

Gravity having a speed (rather than being a direct action at a distance force as described by Newton) also has a bearing on this cosmic acceleration. As explained, it is the gravitational pull of our cosmos on the surrounding infinity (not vice versa) that leads to our cosmos pulling itself apart in an accelerating expansion. Since our cosmos emerged at a certain time, it would take a time before its gravity wave to reached the neighbouring (already there) cosmoses and thus for the accelerating expansion to take effect. That seems to agree with observations.

This theory then explains the cosmic acceleration (without devising new or additional physics), the clumping of matter and the delay before the cosmic acceleration took hold. In another paper I show it also explains the discrepancy between Hubble constant as derived from the CMB versus that according astronomical observations. That’s due to an additional background gravitational redshift from the mass of the infinity (that also makes the infinity dark – answering Olbers paradox for an eternal and infinite greater universe).