S3C7: Physical Cosmology

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a) Asking questions

Of all the chapters in this series, and perhaps across all series, none are going to be so removed from the description of tangible physical or chemical phenomena and centred around high-level abstractions, theories and hypotheses. There is a couple of very good reasons for this, namely that we are limited in our ability to both observe and test what would have happened during the very first instants of the universe, and these theories we advance form the base of the edifice of our knowledge about physics, including in many ways those dealing with the nature of the fundamental interactions and matter.

Everybody has heard about the Big Bang theory, it was put forward in a first incarnation in the 1930s and has gained traction ever since to the point where it is widely, though not universally, accepted as the best we have at the moment to explain our universe as it looks today, including its shape, structure and content. Before we dive into this topic however, it is crucial to understand the Big Bang theory addresses the problem of the expansion of the universe from its original state but it isn’t a theory about the creation of the universe, this would fall into the realm of what is sometimes termed “cosmogony”.

So what was there before the universe came to be? Of course we can only conjecture, and most likely we will never be able to go beyond the speculative. That said, the first comment I need to make is that the question may need rewording because, if space-time is a property of the universe and time doesn’t exist outside of it, then there was no “before”. Logical, no?

The question thus ought to be: how was the universe created? There is a variety of scenarios put forward, most of them not very fleshed out. The core issue seems to be that some amount of matter or energy, whatever the catchy name used, had to exist in the first place, but then the question arises of how this matter and energy came to be, and so on. This is the issue of infinite regress. Now, we know for certain there is a solution because we do exist in our universe, so this clearly is our own limits of conceptualization being on display, the same type of limitation we suffer from when trying to visualize the shape of our universe, a subject I will come back to in section c). Note that even if the Big Bang theory is wholly inaccurate and there was no beginning, as in the universe has always existed and may always do, the issue of how it came to be would not go away.

Perhaps the second most intriguing question is whether there are several universes and, if yes, whether they are connected or related, multiverse style, or if instead they exist separately without any way not just to explore them but even to know about them. Knowing the answer to the first question probably would give a very strong insight into the second. If I had to take an educated guess I would go with many independent universes and the reason for that has to do with what we call the laws of physics.

In the Big Bang theory there are three major assumptions – actually I was not able to narrow down to the same set of assumptions depending on sources so the following is my personal educated take in some sense, and in case you are wondering expansion is a prediction of the theory, not one of its assumptions. Using assumptions isn’t unusual, all theories have to define a “set of truths” for the framework in which they are being developed, just like Euclidian geometry for instance. For the Big Bang, these relate to the large-scale uniformity and homogeneity of matter in the universe, what is called the “cosmological principle”, the ability to model the behaviour of matter as a perfect fluid, and the universality of the laws of physics.

The latter of the three means the universe obeys the same physical constraints and have the same fundamental properties. This seems super intuitive; how could the laws of physics not be universal? Well, it is not like they were set externally, so we could instead think of them not as fixed assumptions but as outcomes of particular conditions, including the original amount of matter or energy in the universe. This means they could vary somewhat depending on local conditions and, going back to the question mark relating to the existence of other universes, they could be different in those other universes if the content and initial conditions diverged from ours. If we put our evolution cap on, we could even advance that many universes failed and those that survived have the right mix of conditions and exhibit some kind of equilibrium instantiated in the laws of physics. In fact, this is my personal position.

b) In the beginning

And there was time, energy and, perhaps, matter. We don’t know how, and the Big Bang theory starts with a point-like concentration of everything there, in an incredibly hot, dense, and small space. Perhaps this description doesn’t do justice to the reality because, if we were to run the expansion of the universe backward, we would end up with a space singularity and infinite temperature. During the first millionth of a second the protons and neutrons did not yet exist and the Standard Model (the dominant theory in particle physics) really only starts to apply between 1 and 10 picoseconds after the bang (a picosecond is one trillionth of a second), by which time the original universe had cooled down, relatively speaking, and sub-atomic particles had energy levels that can be replicated by particle accelerators.

Between T0 and the first 10⁻⁴³ seconds (there is no real word for this unit so it is called Planck time), the energy levels were too intense for the fundamental forces as we know them to apply. As the universe underwent an inflationary period, the density of matter and energy and the temperature all dropped as a result. This allowed for the “separation” of forces, I use quotation marks because I can’t reconcile myself to this idea since it gives the impression forces were one and the same initially and became independent entities afterwards. Maybe we can say the energy levels decreased to magnitudes allowing for the various fundamental forces to take effect, not necessarily at the same threshold levels and hence they seem to have become distinct but always were. Or maybe it is the correct way to look at it if the interactions are the result of the existence of certain types of particles since these gradually came to be as combination of more basic particles or forces.

Anyways, before the end of the first second the quarks combined into hadrons, including the protons and neutrons we are familiar with and then, within the first few minutes, the Big Bang nucleosynthesis took place. As mentioned in S3 Section 4.d, this would have yielded the hydrogen, helium and lithium isotopes that will ultimately accrete into first-generation stars. Afterward, for the first few thousand (Earth) years, most of the energy was contained in the form of photons and for the next several thousand years the electrons combined with protons and neutrons to form atoms.

Followed a period of up to 150 million years during which the first stars formed and then the galaxies, over the course of the subsequent hundreds of million years. Since then stars have come and gone and the universe kept expanding and so here we are today, an estimated 13.79 billion years after T0. How have we come up with this somewhat precise number? Essentially by measuring the speed at which galaxies are moving away from us and plugging this value into the current working model, which uses the general theory of relativity and other assumptions regarding parameters such as the fluidity of matter, to extrapolate the state of the universe backward in time.

The model is certainly not perfect, nor the Big Bang theory, but we know the odds of being on the right path are good when some of the phenomena it predicted are eventually observed, often years or decades later, just like the bending of light by the Sun’s gravity backing up the theory of general relativity. In particular, it was put forward that during the “recombination epoch” when the atoms formed, photons propagated to create microwave radiations which should still exist today, however faint. These residual radiations with temperatures of less than 3 kelvins have been measured and form what we call the cosmic microwave background.

c) Structure and evolution so far

Based on the initial mass-energy density and pressure, thermodynamics have run their course and we are today in an expanding universe. The most telling observation supporting this statement is the measured redshift of nebulae and galaxies demonstrating not only that they are moving away from us but they do so at an increasing rate. In a nutshell, as a radiation or wave-emitting object moves away from us, this results in a stretching of the wave so that the wavelength increases. For light, this means the spectrum moves towards the red and conversely, an object getting closer would experience a blueshift in its spectral signature. This is known as the Doppler effect and it also happens to mechanical waves like sound – the often-used example being the increase in pitch of the siren of an ambulance getting close to the observer then its lowering as it moves away from him. I am including a link to the Wikipedia entry on redshift at the end of this chapter for those keen to better understand.

As mentioned in the first section, the cosmological principle is not a prediction, it is an assumption. And quite a significant one because it doesn’t merely stipulate the large-scale structure or dynamics of matter and energy but it also has implications regarding the non-staticity and the geometry of the universe, including the fact that it will be perceived as being identical by an observer, wherever she happens to be.

What else do we know or would we want to know about the geometry of the universe? The first relates to curvature, i.e. whether we live in a flat “Euclidian” space or one with either a positive curvature (spherical) or negative (hyperbolic). This curvature is in line with the one created by mass-energy in the theory of general relativity and measurements point to a flat universe with spatial properties we are familiar with in a 3-dimensional space.

However, curvature is a local parameter and says nothing about global geometry, what we call the shape of the universe. We can’t deduce the latter from the former and, because of the pace of expansion of the universe, it is very likely we can only observe part of the existing universe, so we can’t directly work it out either. In this respect, the second key question is whether the universe is simply connected or multiply connected. To understand the difference, imagine you form a circle with your thumb and index fingers and place them on top of a tennis ball (it also works with a rugby ball even if it isn’t spherical), you will then be able to shrink this circle to any small point on the surface of the ball without leaving said surface, wherever you started from. Now take a ring or roll of tape and close your two fingers over the edge of the ring and try to contract them into a point. You will not be able to do it without leaving the surface; this is because there is a hole, the geometry of the ring is non-simply connected, the alternative term being multiply connected. It so happens that some of those multiply connected shapes are flat in the sense that they have zero curvature. Not convinced? Take a sheet of paper representing a flat space and roll it in a cylinder, it is still flat in technical term but it has edges. Now connect those edges so that it forms a circle, an object with the geometry of a doughnut, one with a hole in the centre. You now have a torus, specifically a 2-torus, it is flat as well as unbounded.

Using either analogy, sphere or torus, with the universe covering the surface (albeit in three dimensions, not two), it is easy to understand why we can say there is no centre to the universe: any point is as centred as any other. In addition, one could think that by travelling far enough we would eventually return to the same point in space. Theoretically this can’t be disproved at this juncture, and anyways the speed at which the universe is expanding makes this an impossible endeavour.

And finally, one may ask, expand in what? This brings up the third query regarding the nature of the geometry of the universe: is it finite? And if it is, is it bounded? Note that as per the sphere or torus example, being finite doesn’t automatically imply having edges. My personal metaphysical view on this is that assuming edges implies the existence of something outside of the universe, which calls for additional explanation and so, wielding Occam’s razor, I would think our universe is unbounded and is not expanding into anything, it is “merely” expanding. As for finiteness, I struggle to see how infinity would reconcile with a specific set of initial conditions at the time of the Big Bang and even if laws of physics could hold without applying any kind of constraint in terms of quantum and/or density. Once more this is pure personal speculation so use it as food for thought, nothing more.

Based on all the above, I would wager our universe is a three-dimensional unbounded and finite space, or in the jargon that it is a closed 3-manifold. A little more challenging to visualize than the 2-torus since it would involve creating loops by connecting all the opposite faces of a cube, which calls for a 4-dimensional space… even though each point on the object “lives” in three dimensions. By the way, this is a geometric option that is quite popular among physicists and mathematicians.

It seems we have both the ingredients and the formula, though we can’t quite explain how it all started. Or do we? As in, do we have all the ingredients and formula? Based on the existing model there is quite a gap in the quantum of mass required to properly explain the creation and motion of galaxies or the degree of gravitational lensing, among other phenomena. This gap is not trivial, it is more than 5 times the amount of known matter (comprising neutrinos and baryonic matter) and so the model calls for the existence of non-ordinary matter, a type that is subject to the gravitational interaction but not to light and more broadly electromagnetic interaction, hence it has been named dark matter, for the time being. Thus far, there are questions marks around what type of particles dark matter could consist of and what kind of experiments would enable physicists to detect those and understand their make-up and properties.

d) In the end

Assuming we had a comprehensive picture of the composition of the matter in the universe and of the fundamental interactions at play, then in theory we would have expected to see a decreasing rate in expansion under the effect of gravity until a time when expansion ceases altogether and the universe starts contracting, likely all the way back to the original singularity, going full circle.

However, not only expansion is still ongoing but according to various measurements, including the redshift of nebulae, our universe is experiencing just the opposite of what we expected: the expansion is accelerating and seems to have been doing so beginning at some point between 3 and 5 billion years ago. This implies some type of unseen energy is exerting negative pressure on, or pushing, ordinary matter and dark matter.

Running the maths, it seems there would be twice as much of this “dark energy” (remember, dark refers to the unseen, invisible aspect, there is no moral judgment involved) in terms of mass-energy as ordinary matter and dark matter combined. To use exact numbers, computations yield a breakdown of total mass-energy in the universe of 68.2% dark energy, 26.8% dark matter and 5% ordinary matter (baryonic matter and neutrinos).

A slightly counterintuitive aspect of dark energy is that it doesn’t weaken as space expands, this is because it is deemed to be a property of vacuum itself and so as space expands and the effect of gravitational force decreases, the relative impact of dark energy becomes more prominent, causing the universe to expand at an accelerating rate. Whether the density of this dark energy remains constant or varies in time and space is subject to debate in the relevant scientific community but constancy seems to be the more commonly held view.

Hence, it seems our universe is set to get larger, forever. Does this bode well or ill for our hypothetical generations a few billion years from now? Not so well, the two logical scenarios are both unappealing. The more dramatic of the two is nicknamed the “Big Rip” and would see the accelerating expansion overcome all fundamental interactions, uncoupling electrons as well as nucleons so that after our planets and entire galaxy are torn apart, every bit of the baryonic matter we are made of also will. The second is not as graphic and appears to be the most likely: it is a slow death of the entire universe, as in of everything that is alive in it, under the effect of increasing entropy. The concept of entropy is genuinely very interesting unto itself so I am including a link to the Wikipedia entry at the end of this chapter. For our immediate purpose here, the central idea is a direct consequence of classical thermodynamics: entropy in an isolated system cannot decrease. Think of entropy as a combination of structure and information, without external influence; over time the pyramids crumble and we are left with sand dunes. Even if the process is reversible by de-isolating the system, this requires increasing entropy in another system in the form of energy transfer. Ultimately, the universe as a whole being an isolated system, all matter will converge towards its lowest potential energy state at which point no energy or heat can be extracted from it, very similar to what happens in the core of dead stars. The end point would even see the decay of protons and neutrons into sub-atomic particles – this scenario is dubbed the “Heat Death”.

e) Areas of cosmological enquiry

We still have a fair amount of time though, plenty enough to work out a comprehensive model of the universe, its content and maybe even its very origin. Among the key questions to be answered are the nature and properties of both dark matter and dark energy of course, they make a complex picture even more challenging but, in a way, they are also forcing new hypotheses about the nature of matter, energy and the fabric of the universe. This hypotheses-generation dynamic is indispensable to the resolution of the problem, in time.

There is quite a long list of open questions and even issues, dynamics and phenomena that, on the face of it, meaning based on our current scientific knowledge, seem contradictory. For the purpose of this section, I have hand-selected four of them, starting with the marginal unbalance between the quantum of matter and anti-matter in the early universe that left a surplus of baryonic matter after most of the opposite elementary particles annihilated each other. This stage and dynamic are certainly hypothetical; however the main question is not to understand whether this is the accurate scenario and how it unfolded but, rather, how can such imbalance between matter and anti-matter be; the central challenge is the symmetry breaking aspect. If we play a zero-sum game, every point you score is a point I lose and if we sum up our scores the result is zero, nothing is left so to speak. In the case of the universe we are left with some matter, so we need to explain how it is not a zero-sum system.

Next, as I already alluded to at the end of section a), it would be informative to put our finger on the exact nature of the laws of physics. Whether they are hard, invariable constraints on matter and energy, or whether they can fluctuate logically, as matter-energy density vary, which would open the way to some degree of manipulation, perhaps. Clearly, if we ever come up with the right theory regarding the origin of the universe, the answer is very likely to be self-evident.

We have discussed the geometry of the universe, focusing on 3-dimensional space, but the nature of time is also a fundamental area of enquiry. Can time be dissociated from space? Is it a one-way arrow or is it theoretically reversible but practically not because entropy can only ever increase? If it is reversible, what does it say about causality? If it is not reversible, where does it come from? I know, some of these questions sound far-fetched and yet, those are genuine scientific queries to which there is an answer. I am afraid I have little to say on the matter at this point in time (!) though I would just venture I do not think time is reversible, not just because of entropy – and the fact that some of our own equations do not point to an arrow of time sounds like a dubious argument – rather because I think causality is a thing.

Moving to and concluding with the geometry of the universe, the laws of physics suggest one cannot travel faster than the speed of light and so many parts of the universe are inaccessible to us both in theoretical terms because of the cosmic expansion and because our lifetime is finite. And so the search is on for faster-than-light travel or shortcuts through space or maybe it is space-time. There is the popular science fiction wormhole relying on the assumption of a universe folding like a cylinder, a donut (2-torus) or a 3-torus, and thus the potential existence of passageways leading from one surface to the other without going all the way around. Except that our universe is this surface so that leaving it effectively implies leaving the universe and re-entering. As far as I am concerned, science fiction it is and will remain. But what about faster-than-light travel? To answer such a question, we first need to understand about light speed.

f) Trivia – The speed of light

The speed of light in a vacuum is understood and measured to be a constant with value of 299,792,458 metres per second and is noted with a lower case “c”. In fact, it is not c that is expressed in metres, it is the metre that is formally defined as a fraction of c. The speed of light is a property of photons or electromagnetic waves, and more broadly of any massless particles and even radiations such as gravitational waves that denote alterations in a force field.

When travelling through matter, i.e. not in a vacuum, light travels marginally slower with the difference being computed on the basis of the materials’ refractive index. For air it is 1.0003, for water it is 1.333 and yes, this is the same refractive index you hear about in optics, the one used to measure the bending of the path of light through a particular medium.

Importantly, the speed of light is invariant irrespective of the motion of the observer, or of the light source of course, it is the same for any inertial frame of reference. This gives rise to the phenomenon called “time dilation”. The example often used involves a person in space or in a train, anything that can move in relation with an observer standing still on Earth. Let’s use the astronaut scenario: she reflects light on a mirror which takes time T to leave the light source, bounce from the mirror and reach the receiver situated right next to the light source. In so doing, light has travelled distance D and taken as short a path as possible. From the perspective of the observer on Earth however, T is the same but light has covered a distance D’ that is different from D because the whole experiment was moving in relation with the observer – essentially the receiver incurred a translation. So the distance travelled is different, yet the speed at which light travel is a constant, this implies that time T in a moving frame of reference ran more slowly than the time in the frame of reference of the observer. This allows the maths to square up.

The formula for this is quadratic and features the ratio of the square of the speed of the observer divided by the square of the speed of light so the effect of time dilation only truly becomes noticeable as one approaches the speed of light, also called relativistic speeds. For a time dilation factor of two to be experienced, one would need to travel at 86.6% of c. This implies that by approaching the speed of light, interstellar travel could be experienced as taking only a few years, in theory.

Since distance is a function of speed and time, there is a corresponding effect to time dilation experienced by an observer with respect to distance, it is called “length contraction” and consists in the shrinking of the length of a moving object. I am including a link to the Wikipedia entry in the next section if you wish to read about it.

So, what does the above say about the possibility of faster-than-light? The answer is not conclusive per se but it does indicate that this notion would imply time travel and therefore violate the very concept of causality. It is thus perhaps possible to alter c , in the sense that the value of c might be different in other parts of our universe or in other universes but going faster than light does seem to be an impossibility, bordering on the contradiction in terms.