The Quantum Origins of Our Universe

How did it all start? How was our Universe created? What were the initial conditions? Were there any conditions at all? Is our observable Universe just one patch of many in a much larger universe beyond our reach? Is our Universe unique? Did it pop out of nowhere? Will it expand forever or come crashing down at some point? Did it bubble forth from a bustling region of minute fluctuations? Has the Universe already been around for an eternity?

Cosmologists have been pondering about such questions for decades. To shed light on their work and get a more solid grasp on the moment when the Universe was being started up, this article digs into their research and spends time with three theoretical frameworks in particular: Chaotic Eternal Inflation, the Cyclic Model, and the No Boundary Proposal.

The Big Bang Conundrum

Classical theories, such as thermodynamics and Albert Einstein’s theory of general relativity, describe the course of physical events in space and time at macroscopic levels — specifically, general relativity tells us that gravity arises as a phenomenon when high energy densities or massive objects bend spacetime. In contrast, when we descend into the microscopic realm, down to the atomic and subatomic echelons of nature, we rather appeal to the laws of quantum mechanics to explain the observed behaviour.

So, simply and generally speaking, at large scales gravity is the dominant factor that impacts the dynamics of motion, and quantum effects become irrelevant, while at the smallest of scales, quantum behaviour prevails, and the effect of gravity becomes negligible.

Edwin Hubble taught us furthermore in 1927 that the farther away a galactic object (e.g., stars, galaxies, clusters, etc.) finds itself relative to our position, the higher its velocity with which it is moving away from us. In other words, the Universe is expanding and, conversely, everything must have been more closely packed together at earlier times — this is one of the key features of the Big Bang theory, which elucidates how the Universe came to be as we know it today.

Fig. 1 — Hubble’s law states that the velocity of a galaxy grows linearly with distance. It is the smoking gun for an expanding Universe and one of the main pillars of the Big Bang model. (Source: Gourav Khullar).

Following this logic all the way back to the birth of the Universe 13.8 billion years ago, the equations of general relativity dictate that the very beginning must have sprouted from a place plagued by infinite values: infinitely dense, infinitely hot, and infinitely small, i.e., the so-called cosmic singularity.

Tracing our steps backwards in this way, we essentially transition from a macroscopically sized world into one of microscopic dimensions where both quantum mechanical and gravitational effects hold sway — gravity now also plays a role due to the presence of high energy densities.

However, we stumble upon a problem here: General relativity, a classical theory that applies to macroscopic events and says nothing about quantum behaviour, has been used to arrive at the conclusion that the Universe was born out of a microscopic region in space where quantum effects are equally relevant. To rephrase the problem, we do not have an adequate theory at hand to account for systems that are simultaneously subject to quantum and gravitational behaviour.

As a consequence, making the claim that our Universe emerged from a singularity could actually be misplaced, which has been argued, for instance, by theoretical physicists Matt Strassler and Sean Carroll.

In fact, if we go back in time under the inflationary universe scenario — inflation theory proposes that the Universe expanded right after its birth by an unimaginably large amount in just a tiny fraction of a second, subsequently establishing the conditions for the Big Bang theory to kick in (see Fig. 2) — then it seems that we might never even reach a singularity, as suggested, for example, by theoretical astrophysicist Ethan Siegel.

Notwithstanding its lack of explanatory power as to how it all started in the first place, the Big Bang model along with the inflationary hypothesis is still the most accurate explanation currently available of the way in which our observable Universe was formed from the moment right after its inception up till the present day.

To better understand how gravity behaves at quantum scales, we would need a solid theory of quantum gravity — a theory that unites general relativity and quantum mechanics into one coherent mathematical framework — which could help clarify the origins of our Universe.

Let us now delve into three of the theories that provide us with a description of the dawn of the Universe.

We Are Not Alone

As a starting point, the Chaotic Cosmic Inflation theory, also called the Chaotic Eternal Inflation theory, conceives a hypothesized energy field — the inflaton field — whereby at random locations quantum fluctuations can knock the inflaton field out of its minimal energy equilibrium (true vacuum) and push it temporarily towards a higher energy state (false vacuum).

The time it then requires for the inflaton field to return to its original state matches exactly the time window during which inflation will occur. Such expansion of space is possible because the inflaton field is filled with gravitationally repulsive energy — unlike gravity which is attractive in nature.

Taking a step back for a moment, it is useful to remind ourselves that the language of particle physics is that of quantum fields. This means that a particle is basically a quantum field distributed throughout space, rather than the typical visualization of an isolated spherical object. More precisely, the particle itself can be viewed as a local excitation of energy within that particular quantum field. So, every electron, neutrino, Higgs boson, and any other fundamental particle in our Universe constitutes a localized perturbation of its own quantum field.

What is more, a quantum field that is not manifesting any particles is said to be in a vacuum state, i.e., a state of minimal energy. Even so, the vacuum energy is not zero, as a vacuum still experiences stochastic variations in energy values — designated as quantum fluctuations — as a result of Werner Heisenberg’s uncertainty principle, which postulates that for short-lived quantum states the energy measurement cannot be definitely determined.

Chaotic Inflation theory thus posits that these random quantum fluctuations in the vacuum of the inflaton quantum field are responsible for kickstarting the inflation period at the birth of our Universe, after which — once the locally perturbed inflaton field restores its initial equilibrium — inflaton particles metamorphose into the unfathomably hot and immensely dense hodgepodge of elementary particles (e.g., electrons and quarks), anti-particles (identical to ordinary particles but with opposite charge), and radiation (photons) — only at this point would the Big Bang model come into play and the ‘Big Bang’ then refers to this post-inflation energetic mishmash.

Fig. 3 — The Eternal Inflation model, whereby quantum fluctuations in a scalar field (inflaton) are supposedly responsible for triggering inflation. The (potential) energy density is indicated on the vertical axis, and the value of the field on the horizontal axis. Inflation occurs when the value of the field lies in the range [1, 1/m]. (Source: Paper Andrei Linde).

Due to the uncertainty principle, there is a short timeframe available in which a virtual pair of a particle and an anti-particle can pop into existence in the inflaton field and disappear again. However, during the brief burst of inflation, such pairs might have been effectively separated from one another. Together with the knowledge that at that specific instant all the energy of the Universe is inherently embedded in this quantum field, these virtual pair separation events help explain how quantum fluctuations were translated into energy density fluctuations.

In the post-inflation epoch, regions where the energy density is slightly above average contain more matter and give rise later on to the formation of large-scale structures throughout the Universe — remember that according to general relativity regions of higher energy density become gravitationally attractive so that clumps of energy and matter can form.

The evidence of these energy density variations is imprinted onto the map of the cosmic microwave background (CMB) radiation (see Fig. 4). The photons of this radiation stem from roughly 380,000 years after the Big Bang, when electrically neutral atoms were fashioned — the stage of recombination — and photons were subsequently free to roam the Universe for the first time — the moment of photon decoupling. It is these photons that are captured onto the CMB image.

Fig. 4 — The map of the cosmic microwave background (CMB) temperature distribution based on the data collected by the Planck satellite. [µK = microKelvin]. (Source: Paper Tien Bui).

Blue spots in the CMB image correspond to regions of greater energy density. Given that a stronger gravitational pull around these regions enlarge the wavelength of photons that travel away from those places — an effect called gravitational redshift — these escaping photons possess a reduced amount of energy and are therefore colder. Similarly, photons originating from regions with a lower energy density are gravitationally redshifted to a lesser degree and thus higher in energy and hotter — this situation is reflected by the red spots in the CMB picture.

Chaotic Inflation theory comes furthermore with an intriguing feature. Unlike the standard Big Bang model, which conjectures an absolute beginning from a cosmic singularity for the entire universe (not just for the part that we can observe, i.e., the observable Universe), Chaotic Inflation theory surmises a quantum field that generates an unlimited number of Big Bangs (which are not singularities), of which our own Big Bang is just one such manifestation.

That is to say, in light of the ubiquity of quantum fluctuations, the above-described chaotic inflation dynamics — inflation occurs when the vacuum decays to its original, lower energy state, after quantum fluctuations have taken it out of its initial equilibrium — happen continually and randomly throughout the inflaton field and will continue to do so eternally. Hence the name Chaotic Eternal Inflation.

As a result, the observable Universe is only one universe in an ever-expanding sea of universes, i.e., the multiverse. On top of that, every universe on its own can further spawn an infinite number of universes. In fact, if the inflaton field is conceptually connected to superstring theory — a unifying theory whereby nature’s fundamental building blocks are tiny vibrating strings rather than particles — then the population of the multiverse is not infinite but amounts to 10⁵⁰⁰.

Although every part (that is, every universe) of this multiverse has a beginning and an end in time (ours included), the multiverse as a whole does not. In other words, under this theoretical scenario, our Universe could not have arisen from a cosmic singularity.

What is more, as the space between different universes is expanding at rates beyond the speed of light, these universes will never be able to communicate with each other, unless some of them collide very early on in their existence. Ongoing studies hope to pinpoint traces of evidence of such collisions within the CMB map.

Another way to corroborate the validity of the chaotic inflationary model is the detection of primordial gravitational waves, i.e., ripples of spacetime itself during inflation. Since inflation is a high-energy event, it is conceivable that energy density fluctuations, so the argument goes, create oscillations in the fabric of spacetime. Experimental efforts are currently underway to observe such waves, relying mainly on ground- and space-based gravitational wave detectors as well as the CMB image.

The lack of evidence of primordial gravitational waves would strengthen other theoretical frameworks, including models that embrace a cyclic pattern in the Universe’s evolutionary dynamics.

No End in Sight

In the Cyclic Model proposed by Paul Steinhardt and Neil Turok, there is no singular point of beginning, as both time and our three-dimensional space remain infinite while the Universe undergoes a cyclic evolution of various phases, skipping an inflationary process altogether.

In a first stage, the Universe is very hot and dense, but the temperature and density values are finite, contrary to the Big Bang model — so, the issue of a singularity is circumvented. This phase is akin to the Big Bang, and often referred to as the Bang.

The three consecutive stages that then follow are a phase dominated by radiation, a phase where matter becomes predominant, and a third phase during which dark energy reigns — dark energy is a form of gravitationally repulsive energy that causes the expansion of the Universe to accelerate.

In a final stage, a period of contraction begins, whereby a gravitational force takes over whose energy is eventually converted to new energy and radiation, marking the onset of a new cycle. The epoch towards the end of contraction right before the incidence of a new Bang is sometimes called the Big Crunch.

Fig. 6 — A schematic overview of the inflationary theory versus the Cyclic Model. Note that in some accounts — as in this illustration — the ‘Big Bang’ refers to the origin of the Universe, instead of the post-inflation state, which introduces the radiation-dominated era. (Source: Prof. G. Venkataraman).

It is important to underline that all the matter and radiation contained within our three-dimensional space does not contract to a singularity during the final stage of the Cyclic Model. As a matter of fact, by the time the final stage of contraction is set in motion, the dark energy stage will have already diluted away all matter and energy over the course of trillions of years, basically completely thinning out the Universe and turning it into a smooth, flat, and empty place (a vacuum).

What is contracting though is a fourth spatial dimension borrowed from M-theory — an overarching, unifying theory that incorporates superstring theory. In fact, Steinhardt and Turok argue that our four-dimensional spacetime (three spatial dimensions and one time dimension) in which we live exists on one of two boundary membranes of the fourth spatial dimension. In between these two boundaries, there is the volume (bulk) of this additional spatial dimension.

So, the idea of contraction (the so-called ekpyrotic phase) is then understood as the process whereby the two boundary membranes slowly approach each other, essentially shrinking the bulk of the fourth spatial dimension — this stage of the Cyclic Model occurs over a time period of billions or even trillions of years.

The different stages of the Cyclic Model as described above develop according to a certain interplay with this additional spatial dimension. That is to say, a force interacting between the two membranes is experienced in our Universe as dark energy — put differently, dark energy is coupled to this inter-membrane force. Once our Universe is entirely flattened out, that force will pull the two membranes ever closer together (the ekpyrotic stage) and the dark energy will be consequently transformed into kinetic energy.

Their ultimate collision will heat up our Universe (and the other membrane), create new radiation and matter from the available kinetic energy, and push the two membranes back to their original positions — the energy for this final movement is tapped from the leftovers of the kinetic energy as well as from the gravitational energy due to the presence of new matter and radiation. At this point, a new cycle of expansion can begin.

The model explains the observed energy density fluctuations in the CMB map in the following way. As the two membranes move closer to each other, they exhibit quantum fluctuations — after all, the Universe is now effectively a vacuum, which is teeming with such oscillations — so that, when the collision takes place, not every region within one membrane collides with a corresponding region within the other membrane at the same time. Necessarily, there will be different rates of heating up, cooling, and matter formation across the Universe during the subsequent radiation- and matter-dominated eras.

Notwithstanding the coherent explanatory power of this theory, it must be pointed out that there is very little observational evidence for superstring theory (and thus for additional spatial dimensions) as of today, undermining to some degree the robustness of the Cyclic Model — yet it has been shown that the model based on additional dimensions is equivalent to an effective theory relying solely on quantum fields in a four-dimensional spacetime.

Nonetheless, if the absence of primordial gravitational waves is experimentally confirmed, it would, as previously mentioned, give a boost to this theoretical framework, since the gravitational effects it anticipates are exponentially smaller than those manifested in inflation theory — remember that the energies during the transition from the end of the contraction phase towards the beginning of a new cycle are lower compared to those of the inflationary phase.

The Cyclic Model presented by Steinhardt and Turok is not the only attempt in town that obliterates the cosmic singularity. Rather than envisaging endless cycles, the No-Boundary Proposal, which we will discuss next, suggests that everything around us arose from nothing.

No Boundaries

To outmanoeuvre the issue of an initial singularity, Stephen Hawking and James Hartle devised the No-Boundary Proposal, which postulates that the Universe, entirely described by a quantum wave function, came into being as space only — without time — out of a speck of nothingness.

In quantum mechanics, a quantum wave function is a mathematical expression that completely reflects the possible states or configurations of a quantum system — for reference, in classical mechanics, the configuration of, for example, an object is characterized by both its position and velocity (momentum).

Given that quantum mechanics is considered fundamental and universal, the No-Boundary Proposal assumes the existence of a universal quantum wave function — this wave function is distilled by a method called the path integral formulation — that is tasked with explicating the origin and evolution of our Universe. In other words, this theory regards the Universe as a whole as a quantum system.

Furthermore, in order to solve the equations of motion, which tell you how the state of a system evolves over time and are obtained through Newton’s laws and the Schrödinger equation (or path integrals) in classical and quantum mechanics, respectively, there is a need to specify some parameters in advance, i.e., the initial boundary conditions.

As time did not exist before the birth of our Universe in this particular model, there is no requirement to identify any initial boundary conditions, and hence the name the No-Boundary Proposal.

Fig. 9 — (a): The shuttlecock Universe according to the original No-Boundary Proposal, (b): The Universe with a cosmic singularity (as per the standard Big Bang model). (Sources: KITP (left) and adapted from Paper Feldbrugge et al. (right)).

According to this theory, the Universe sprang into existence from a point of zero diameter, a situation often likened to the bottommost point of a shuttlecock’s cork base (see Fig. 9a) — a shuttlecock is the projectile used in the sport of badminton. The Universe then smoothly expands, as we move up the cork towards the shuttlecock’s feathers, which follow an open conical shape.

Only when the Universe starts growing does time gradually come into the picture, inasmuch as time is defined in terms of correspondences between the size of adjacent cross-sections of space — additional factors are also contemplated, such as entropy, which calculates the extent of energy dispersal, as a function of temperature.

Even though the No-Boundary Proposal predicts several features of our Universe, including inhomogeneities that eventually result in the density fluctuations as per the CMB data, the model is not without its controversies and there are ongoing discussions with regard to, among other topics of contention, inherent instabilities, boundary conditions, and different ways to apply the path integral formulation, which gives us the quantum wave function.

For instance, Job Feldbrugge et al. demonstrate that quantum effects would exacerbate rather than suppress perturbations around the background geometry, rendering a smooth, stable unfolding of the Universe unlikely (see Fig. 10) — data indicate that we live in a smooth and flat Universe, so we want a theory that reproduces these observations.

Fig. 10 — Left: A smooth development of the Universe with no boundaries according to the original No-Boundary Proposal. Right: According to the research by Job Feldbrugge et al., the No-Boundary Proposal leads to surging instabilities whereby quantum fluctuations dominate and spin out of control. (Source: phys.org).

By giving the initial region from which the Universe emerges an approximately zero size (in lieu of precisely zero), Alice Di Tucci and Jean-Luc Lehners found a way to navigate around those burgeoning instabilities — they introduce a specific type of constraint called Robin boundary conditions — and thereby restore to some degree the idea of the No-Boundary Proposal.

However, one consequence of these authors’ redefinition of the model is that the Universe seems to not have appeared from nothing but instead cropped up amidst already existing quantum fluctuations of space and time.

Be that as it may, the No-Boundary Proposal is not generally accepted, as is self-evidently the case for every candidate theory currently in the running to explain the origins of our Universe.

One Step at a Time

With the objective of gaining more insight into the birth of our Universe, this article explored three cosmological models: Chaotic Eternal Inflation with its infinite number of Big Bangs, the Cyclic Model with its perpetual motion of expansion and contraction, and the No-Boundary Proposal with its quantum wave function of the universe.

Ever more accurate data delivered by ever increasingly powerful technology of the next generation will be guiding these efforts of theory building. Not only that, competition amongst the various conceptual frameworks as well as theoretical progress in itself ensure that our comprehension of how it all began continues to evolve.

As one person once said: “That’s one small step for a man, one giant leap for mankind”, perhaps someone will one day make one small theoretical adjustment that brings a giant shift in our understanding of the Universe.

---

Back to Articles