I have always loved astronomy and cosmology and decided to do some research on the current state of cosmology as to what the current scientific consensus is regarding whether the universe is eternal or finite. Did the universe begin to exist? That’s probably one of the big questions of life. A question hotly debated today in the world of science…or so I thought.

To infinity and beyond

From a young age I always thought the universe couldn’t be eternal because of the problems one runs into whenever one deals with a succession of infinite events.

I always thought the existence of an eternal universe would have meant that an actual infinity of successive events would have passed prior to this moment. How is that possible? How could an infinite succession of events have passed? What about in the next 1000 years, surely a greater number of events would have passed compared to now and yet because there has already been an infinite succession of events it would still be infinite. Infinity plus 1000 is still equal to infinity. A clear logical absurdity.

Which is why in mathematics infinity is a concept and not a number – you cannot do with it the normal things you do with numbers or else it lands you in logical absurdities. Which is why David Hilbert one of the most brilliant mathematicians said “If an essential use of infinity occurs as a core part of any explanatory model, it’s not science”. George Ellis, South African world renowned cosmologist in his paper On the philosophy of Cosmology states that “One should remember here the true nature of infinity: it is an entity that can never be attained, it is by definition always beyond reach, so no physical process can create an infinity of anything”[i].

And so it seems my initial thoughts of the impossibility of an actual infinite and therefore a universe in which an actual infinite number of temporal events had occurred is impossible. It seems unavoidable that logically one must hold the position that the universe is finite in space and time.

The Scientific Evidence

Let us turn our attention to the Standard model, the Hot Big Bang – which everyone knows about but so few are willing to live with the implications. In a nutshell the standard big bang model describes the expansion of space-time from an initial singularity predicted by Einstein’s theory of General Relativity. It needs to be clear that if the big bang model is true then space-time is absolutely finite, as time tends to zero then the volume of space tends to zero. The singularity is not simply a change in matter or form but rather the absolute beginning of space-time.

Physicist Paul Davies, “If we extrapolate this prediction to its extreme, we reach a point when all distances in the universe have shrunk to zero. An initial cosmological singularity therefore forms a past temporal extremity to the universe. We cannot continue physical reasoning, or even the concept of spacetime, through such an extremity. For this reason most cosmologists think of the initial singularity as the beginning of the universe. On this view the big bang represents the creation event; the creation not only of all the matter and energy in the universe, but also of space-time itself.”[ii]

Almost everyone believes that the universe, and time itself, had a beginning at the big bang”- Hawking[iii]

George Ellis explaining the implications of the Friedman-Lemaitre Universe Singularity Theorem says,

“This is not merely a start to matter — it is a start to space, to time, to physics itself. It is the most dramatic event in the history of the universe: it is the start of existence of everything”[iv]

So that’s one thing that needs to be clear is that the standard model leads to an absolute beginning of space-time, not just a change in pre-existing matter from one form to another – but an absolute coming into being of space-time itself. The point where general relativity breaks down is the singularity, where space-time comes into existence.

Alternatives to the standard model

There are various alternative models to the Standard big bang model however none have the as much as explanatory power, or scientific evidence as the standard model.

Steady state model, Oscillating models, Vacuum fluctuation models, Chaotic Inflationary models, Quantum gravity models, String cosmologies.

The steady state model claims the universe is not expanding and is in a steady state condition. It has been demonstrated to be false because of nucleosynthesis of light elements and microwave background radiation. Light elements could only be created in the extreme conditions of the big bang; radiation showed photons were emitted during the hot and dense phase of the universe.[v]

Oscillating models tried to avoid the absolute beginning of the universe by assuming the universe is not the same everywhere (matter is not evenly distributed). The Penrose-Hawking Singularity Theorems showed under generalized conditions, even for inhomogenous universes a singularity is unavoidable.

Vacuum fluctuating models hypothesize that before inflation the universe was eternally existing in a vacuum state. It postulates that the universe is a virtual particle whose total energy is zero and is governed by quantum mechanical phase transitions[vi]. This vacuum has energy fluctuations that constantly occur to produce matter and universes, of which ours is just one of many. These models have no scientific evidence whatsoever and have deep incoherence issues and hence were abandoned in 1980’s. Moreover the inflating universes would eventually have expanded and coalesced into one another if they had existed for infinity and therefore we would be observing an infinitely old universe.

Chaotic Inflationary models propose that the inflationary expansion of the universe did not only occur during the early history of the universe but is eternal, with each inflating universe emerging from a prior inflating one. However the Borde-Vilenkin-Guth (BVG) theorem proved that any universe which has been on average expanding cannot be past eternal in the past but must have a space-time boundary. The BVG theorem is broad and general because it does not assume that gravity obeys general relativity – it would apply for models that have a different type of gravity, such as quantum gravity. Moreover it holds true even for a universe with higher dimensions. Vilenkin and Mathini further confirm this as they say:

“A more general incompleteness theorem was proved recently that does not rely on energy conditions or Einstein’s equations. Instead, it states simply that past geodesics are incomplete provided that the expansion rate averaged along the geodesic is positive: Hav > 0. This is a much weaker condition, and should certainly apply to the past of any inflating region of spacetime. Therefore, although inflation may be eternal in the future, it cannot be extended indefinitely to the past.”[xiii]

Quantum gravity models attempt to explain what occurred prior to the inflation period, when general relativity brakes down. Ellis remarks, we do not have a good theory of quantum gravity so all quantum gravity theories are extrapolating known physics to unknown physics. There are three classes of quantum gravity models; string models; loop quantum models, semi-classical models.

The most popular quantum gravity model today is the string model which itself includes 3 subset models (Ekypyrotic; Pre Big Bang Inflation; Multiverse).  String theory posits that fundamental matter is 1 dimensional strings of energy vibrating. Ekypyrotic cyclic models are cyclical models that use extra dimensional nature of string theory to produce cycling. String theory requires six extra dimensions which are curled tightly around our normal three dimensional universe making the extra dimensions unobservable. The model proposes that within the extra dimensions lies two three branes which could be our universe. These branes collide and release energy which is converted to the matter that we observe, when the universe reaches its heat death it collides with another brane thereby initiating another universe. The model is still subject to the BVG theorem and therefore cannot be past eternal with an infinite number of cycles.

Pre Big Bang inflation models are asymptotically static models – which means before the Big Bang the universe was in a static state (neither expanding nor contracting) and then transitioned via inflation to an expanding phase. The issue with this model is that the static state itself is not eternal and was created by quantum tunneling process. Secondly it is metastable- any random fluctuation will cause it to escape the static state and therefore could not have existed in that static state for eternity which means the expansion phase would already occurred an infinite time ago. Thirdly the 2nd law of thermodynamics states in a closed system the entropy of the system increases and reaches a maximum thermodynamic equilibrium where no heat transfer or chemical and nuclear reactions take place. An eternal static state would still obey the laws of thermodynamics and would have reached equilibrium by now, but it hasn’t which means it is finite.

The popular multiverse theory posits our universe is but one of a potentially infinite universe. Ellis has strong reservations about the string cosmologies and multiverse theories he says: “All the other domains considered in multiverse explanations are beyond the particle horizon and are therefore observable[viii]. Further on he adds “the multiverse is not based on known and tested physics[ix]  and even thinks the multiverse theory actually undermines science, “But the very nature of the scientific enterprise is at stake in the multiverse debate: the multiverse proponents are proposing weakening the nature of scientific proof in order to claim that multiverses provide a scientific explanation[x]. Moreover the string landscape cannot be eternal in the past because it is subject to the BVG theorem and also encounters problems with actual infinities.

Anyone who resorts to the multiverse as an explanation of the universe does so not on the basis of what is observed or what can possibly ever be observed!

A second category of QG models are the Loop quantum models (LQM) which have two sub-classes: cyclic and asymptotically static. LQM posits that space-time itself is quantized and it attempts to answer what happens at a singularity when general relativity breaks down. It proposes that singularity does not imply a beginning of space-time but something else which is either an asymptotically static past or a true cyclic past. A true cyclic model would increase and conserve its entropy with each cycle and therefore if the cycles had been eternal entropy would be infinite and the universe would have already faced its heat death. Seeing how the universe is not in equilibrium, it has not reached its maximum entropy and therefore cannot have been cycling for eternity.

The third category of Quantum gravity models is the semi-classical quantum gravity models which feature Vilenkin’s own Tunneling and Hawking’s No-boundary models.

Hawking’s No-boundary uses imaginary time to model the universe and therefore the model never has a space-time boundary, but this is simply a mathematical tool. Theoretical chemist Henry F Schaefar says:

“Hawking and Hartle’s no boundary proposal begins by adopting a grossly oversimplified model of the universe. Then the authors make time imaginary, and prove in their terribly restricted model that the universe has neither beginning nor end. The flaw in the exercise is that the authors never go back to real time. Thus the notion that the universe has neither beginning nor end is something that exists in mathematical terms only. In real time, to which we as human beings are necessarily attached, rather than in Hawking’s use of imaginary time, there will always be a singularity, that is, a beginning of time.[xi]

Vilenkin’s tunneling model postulates the universe is a tiny, closed metastable spherical universe filled with a false vacuum. If the universe’s radius is small it will collapse and there is a small chance it will tunnel into an inflationary phase, which would be our big bang. It faces the same problems as an asymptotic static model namely that a metastable universe cannot be stable for eternity. If it were eternal we would be observing an infinitely old universe and it would have reached thermodynamic equilibrium by now.

In the end Ellis says “all the alternative cosmological models proposed are highly speculative, untested physics, and most suffer from mathematical problems such as ill definition, or divergences, or arbitrary assumption of a matter behaviour that is nothing like what we have encountered in a laboratory”[xii].

After a century since it was proposed, the standard model, combined with Hawking-Penrose theorem which predicts a singularity where the universe began to exist remains the most scientifically supported and robust model. To believe that the universe began to exist is a legitimate scientific position to hold. On the basis of the current evidence and observations: standard model of the universe; general relativity;  BVG theorem ; and the accelerating expansion of the universe due to dark energy; the 2nd law of thermodynamics– it is a near certainty the universe began to exist.

The implications of a finite universe do not seem to fit well with naturalism or pantheistic worldviews, however that’s a topic I explore further in another post. For now my brief survey only seeks to show that to claim the universe began to exist, that it is finite, that it is not eternal, is a reasonable and well supported scientific claim.

I think Alexander Vilenkin’s words are worth repeating:

It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape: they have to face the problem of a cosmic beginning.”

 

References

[i] George F.R. Ellis, Studies in History and Philosophy of Modern Physics 46, p16

[ii] William Lane Craig and James Sinclair, Blackwell Companion to Natural Theology,

[iii] Stephen Hawking and Roger Penrose, The Nature of Space and Time, The Isaac Newton Institute Series of Lectures, p20

[iv] George F. R. Ellis, Issues in the Philosophy of Cosmology, p1190

[v] William Lane Craig, Reasonable Faith, p129

[vi] Ibid,p131

[vii] Alexander Vilenkin, Many worlds in one, p176

[viii] George F.R. Ellis, Studies in History and Philosophy of Modern Physics 46, p14

[ix] Ibid

[x] Ibid, p15

[xi] Henry F Schaefer III, Stephen Hawking, the Big Bang, and God, [http://www.leaderu.com/offices/schaefer/docs/bigbang.html]

[xii] George F.R. Ellis, Studies in History and Philosophy of Modern Physics 46, p17

[xiii] A. Vilenkin, A.Mathini, Did the universe have a beginning?,p1

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