The Scope of Expansion

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Within the concordance model, the nature of expanding space is normally constrained to a set of ideas that cosmologists believe best fits the observations to date. However, given that the exact mechanism of how space might actually be expanding is still a matter of debate, there is obvious scope for more radical ideas to be considered. Therefore, this discussion will introduce some speculative ideas primarily to widen the scope that surrounds the on-going debate; although some of these ideas might immediately be shot-down by current observations. However, at the beginning of the 20th century, most physicists would have probably been bias toward the idea that the universe was essentially static in nature, at least, on the very large scale. Of course, it was recognised that smaller scaled structures could be subject to change in as much that stars, and even galaxies, might be created and fade. However, it was generally assumed that the universe had no beginning and would have no end. After Einstein published his theory of general relativity, in 1916, he became increasingly concerned with the implication that the universe, as a whole, could not be maintained as a static system. In fact, in order to address this problem, he modified his theory to include a ‘cosmological constant’ that might help maintain the idea of the universe as a static system. However, after Hubble's observations appeared to provide conclusive proof that the universe was indeed expanding, Einstein retracted the modification and called it ‘the biggest blunder of his life’ .  Subsequently, the expansion of the universe became generally accepted as fact, although the mechanism was not really understood, but as a consequence the idea developed that if the expansion of the universe were reversed in time, it must lead back towards a point of creation.

So what was thought to exist before creation?

Well, one obvious conclusion is ‘absolute nothing’. In essence, time and space would have no existence, such that even the concept of empty space in the form of a vacuum, could have no meaning or existence. As such, you would be left with a concept of not just nothing, in terms of empty space, but 'absolute' nothing, which even philosophy and theology might find difficult to explain, let alone justify within the perspective of their worldview. However, based on the assumption of a single point of creation, you would then be forced to proceed with the assumption that the universe must have also expanded out of ‘absolute nothing’. However, quantum theory might now question the details of a model of the universe, which is simply run backwards in time towards a conceptual notion of a cosmic singularity in which the universe has to ultimately disappear below the Planck scale into absolute nothing. However, despite these issues, the general idea of an expanding universe remained intact and was eventually considered to be generally proved, i.e. beyond any reasonable doubt, with the discovery of the Cosmic Microwave Background (CMB) radiation by Penzias and Wilson in 1965.

But does an expanding universe require space itself to expand?

This is where the previous discussion of ‘infinite and finite models has some bearing. As indicated, the initial Big Bang model was predicated on a finite universe in the sense that ‘absolute nothing’ existed outside the boundary of this universe. Based on this assumption, any expansion of the universe demanded that space itself must either expand or be created within the confines of this universe. As such, it might be argued that the idea of space expanding was initially adopted, not because it was understood, but simply because it seemed to better explain the observed dependency of the redshift with distance. For example, CMB radiation has a measured redshift of z=1089, which is often described in terms of the wavelength of the photon being ‘stretched’ on route by the expansion of space.

However, are there any possible alternative ideas?

Within the scope of cosmology, there are some highly speculative models that are not generally accepted, but are worthy of some introduction simply because they reflect the potential scope of ideas being considered, and then rejected, if they do not conform to observations. One idea that has been forwarded is that space-time itself may be both infinite and eternal, which we might initially described in terms of a ‘deSitter Universe’ that aligns to a solution to Einstein's field equations of general relativity named after Willem deSitter. In this context, the infinite universe might be modelled as being spatially flat and consisting of just a ‘vacuum’ energy-density described in terms of the cosmological constant into which some sort of cosmic singularity emerged. Initially, we might want to assume that the cosmic singularity expands into existing spacetime in-line with the idea of inflation and the ΛCDM model, although not necessarily for the same reasons. However, in order to align to present-day observations, the cosmic singularity would have had to expand to the same critical energy-density in which matter can be modelled as dust, which is then assumed to exert no measurable pressure. As such, we might describe this model within infinite deSitter spacetime as a ‘dust-ball universe’ somewhere within which our own local perception of the universe is centred.

But where did pre-existing spacetime come from?

As implied in earlier discussions, all cosmological models eventually run up against unanswered questions. In this case, pre-existing space either has to have existed forever, and therefore also extends to infinity, or it was previously created by yet another process, which cannot be described by present-day science. In this context, it might appear that a recursion towards Aristotle’s prime mover philosophy is essentially being paralleled and while this statement might also appear to be just avoiding the question, you might equally apply this criticism to any of the models under discussion. For example:

How does the standard model of the universe appear out of absolute nothing?

Today, many cosmologists appear to describe the standard model in terms of a localised universe, which ‘inflated’ due to some quantum process, which is again not really understood. However, in doing so, there seems to be an implicit suggestion that this model requires the pre-existence of some sort of quantum universe. How a ‘cosmic singularity’ might ‘materialise’ within the description of deSitter spacetime is not really understood, as the whole idea is speculative at best. Of course, it might also be suggested that the cosmic singularity was a product of some form of latent quantum energy associated the vacuum of deSitter spacetime. However, what is interesting in this idea is that an infinite and eternal spacetime, as outlined, may ‘spawn’ multiple universes, which simply remain hidden beyond our local cosmological horizon. Of course, given the overall level of speculation, we need not be too pedantic about such details, at this stage, as the primary goal is simply to open up the scope of discussion to wider range of ideas. However, this said, the dust-ball model still needs to try and explain the observed expansion in terms of redshift, which at face value appears problematic for 2 reasons:

  • Expanding space reconciles the issue of superluminal recession velocities.
  • Expanding space reconciles the uniformity of isotropic expansion

While the accepted cosmological model is often referred to as the Big Bang, science has subsequently stressed that the expansion of the universe cannot be described, or modelled, as an explosion. This is because the distribution of the kinetic energy, associated with the observed energy-mass of the universe, does not conform to the profile of some central explosion. Therefore, a homogeneously expanding universe is usually modelled on the assumption that each unit volume of space expands, where the rate of expansion can also speed up with time. However, as already discussed, the effects of this expansion only seems to operate on the largest scale of the universe, as anything less than the size of a galaxy appears to be unaffected by this process.

How does the standard model explain the rate of expansion?

Within the overall concordance model, the original Big Bang model is now preceded by an inflationary stage, which expanded the universe by an exponential rate within the first second of existence. The subsequent ΛCDM model is then said to be basically explained by the Friedmann equations, which an earlier discussion derived using Newtonian principles, which still yielded the same result as when derived from Einstein’s field equations of general relativity. In this context, it was noted that the recessional velocity, as predicted by Hubble’s law, seems to correspond to the escape velocity with respect to some centre of mass, which would have to exist within the universe, as a whole. However, this coincidence needs to be reconciled within the cosmological principle that underpins the standard model, because the general assumption appears to be that the universe, or at least the observable universe, has no centre of mass. However, the speculative dust-ball model, as cross-referenced above and in the insets right, would exist as a finite homogeneous energy-density within an infinitely larger definition of deSitter spacetime with a very low homogeneous energy-density as defined by the cosmological constant. As such, this dust-ball universe might have a centre of gravity, as previously described in terms of Newton’s shells. However, at this point, we will only cross-reference an discussion entitled ‘Speculative Centre of Mass and the speculation forwarded under the discussion of Energy-Density.

But could this model really explain the observed redshift?

One point that would have to be considered is that due to the implicit variation of the gravitational field of the dust-ball universe with radial distance, there may also be a variation in time dilation. However, the scope of the time dilation and any other gravitational effects would depend on the position and relative size of our local observable universe within the dust-ball universe. For example, if the dust-ball universe was much bigger than our local universe, the consistency of cosmological time within a relatively small local universe might effectively be constant, such that it still would not be a factor in the cosmological redshift observed. However, if the dust-ball universe was expanding into pre-existing spacetime, the issue of explaining the apparent superluminal recession velocity implied by Hubble’s law appears to be problematic. However, as stated, the goal of this speculative model was never being forwarded as a serious alternative model, at least by this author, as the purpose was only to widen the scope of the discussion to other ‘possibilities’, which then have to be reconciled against established observation.

So how does the standard model explain the expansion at various stages?

As will be highlighted later in the specific discussion of the ΛCDM energy-density model, there appears to be no specific cause that explains how the universe continued to expand for the first 7 billion years after the initial expansion driven by inflation, other than inertia. While inflation forwards the idea that some form of negative pressure existed in the very earlier universe, prior to the unravelling of the gravitational force, the source of this negative pressure, i.e. the scalar field, is said to have decayed to essentially non-existent levels within the first second of this primordial expansion. The next idea of negative pressure, which is subsequently introduced in the form of dark energy, but does not have a sufficient energy-density to drive the accelerated expansion of the universe until some 7 billion years after the Big Bang.  However, at this point, there is often a degree of ambiguity in the various descriptions of the ΛCDM model, as some cite the role of gravity in the slowing down of expansion during the first 7 billion years, while rejecting the notion of any centre of mass. As such, it is difficult to understand how gravity works on the level of a larger-scaled homogeneous universe. Other descriptions can appear to be equally vague or dismissive by simply implying, but not necessarily proving, that all answers require an in-depth understanding of the field equations of general relativity. Yet another alternative is that some form of inertia maintained the ongoing expansion, which was set in motion by inflation. What is exactly meant by ‘inertia’ in this context is unclear, because within a self-contained finite universe, expansion of the universe requires the expansion or creation of space into which the universe can expand. In other words, this model does not appear to allow the mass of universe to simply expand into space that does not exist and therefore we return, yet again, to the fundamental question:

What physics allows space itself to expand, especially in the first 7 billion years?

As suggested, many potential models have been forwarded over the years to explain, or avoid, the issue of expanding space. However, the constraints imposed by the cosmological principle, which appears to be supported by observation, requires any model to explain the homogeneous and isotropic nature of the large-scale universe, at least, within the limits of our observable universe. While it may be ultimately proven wrong, the basic concept of each unit volume of space expanding due to some intrinsic quantum energy structure appears to be consistent to the cosmological principle and provides an explanation of superluminal recession velocities, which does not violate special relativity.

What energy considerations are associated with such a model?

A basic examination of the Friedmann equations, in particular the Fluid equation; seems to suggest that matter or radiation do not account for any expansive pressure. Equally, if we consider the universe, as a whole, there is no obvious energy gradient within the observable universe, because as a homogeneous and isotropic model, the expansion of space appears to occur simultaneously and uniformly throughout the universe. If we then assume a finite model, where the universe is considered to be a self-contained energy system, we might also reasonably assume that energy cannot be created or lost. However, it will be later shown that if we accept that the dark energy density does not change as a function of expansion, there must be some unidentified process by which new energy emerges into this universe. Based on the increase density of dark energy, the total energy within a finite universe must have grown by factor of ~2.3 over the time period defined by the current age of the universe. Of course, this might simply suggest that the universe is not a closed system or, at least, that our present perception of the full scope of the universe is incomplete - see Cosmic Calculator for more details.