The Universe and Cosmology

The artistic impression below shows the early Universe, in which luminous matter can be seen coalescing into huge filaments and sheets, each tens of millions of light years across! These are the early galactic clusters containing proto-galaxies, in the process of forming stars. Hotter material is depicted in blue, cooler matter in red. The Universe at this stage was about one billion years old (caveat: read on!).



Above: close-up view showing the sheets and threads of galaxy clusters.

When one looks out across space at the distant stars and galaxies, one is looking back in time. This is because of the finite (though enormous) speed of light (about 300 000 kilometers per second or more exactly 2.998 x 108 m/s). The nearest star to the Sun is a red dwarf (of the flare star type) called Proxima Centauri, which is 4.22 light years from the Earth, meaning that it takes light 4.22 years to travel the enormous distance from Proxima Centauri to an observer on Earth and, therefore, the observer is seeing the star as it was 4.22 years ago. Galaxies have been seen as far as 13.23 billion light years away from the Earth, so an observer on Earth (with a very powerful telescope!) sees this galaxy as it was 13.23 billion years ago! This proves that the Universe is very old! We shall see, although it is by means obvious, that a galaxy some 13 billion light years away is much more than 13 billion years distant due to the expansion of space.


A distant spiral galaxy - image courtesy of Galaxy Zoo

The Universe is made up of galaxies. Galaxies are enormous clusters of stars, typically each galaxy contains 100 billion (1011) stars. The Sun is part of the Milky Way Galaxy, which is a spiral disc about 100 000 light years in diameter and containing 100 billion stars, including the Sun. There are billions of known galaxies and there are possibly an infinite number of galaxies in the Universe! (We can never observe them all, because we can never observe further in light years than the Universe is old in years). The age of the Universe is estimated (from observations) to be just under 14 billion years old.We shall discuss what we mean by the 'age of the Universe' shortly.

Galaxies occur in clusters containing tens to hundreds of galaxies. Your Milk Way Galaxy is one of a cluster, called the Local Group, of about 30 galaxies. Clusters are typically about 10 million light years in diameter (but vary tremendously) and the average distance between adjacent galaxy clusters is about 100 million light years. Thus, on a gigantic scale, the Universe can be thought of as a 'gas' of particles, where each particle is a cluster of galaxies! Clusters tend to associate loosely, forming filaments and walls of galaxy clusters, with vast voids in-between, forming a kind of 'honeycomb' structure.


A distant galaxy cluster - image courtesy of Galaxy Zoo

However, the luminous matter(such as stars and nebulae) that make up the clusters only accounts for about 10% of the mass of the Universe, the rest is cold and non-luminous and so is called dark matter.Note that estimates vary for the percentage of dark matter but all estimates place it in the majority. We know it exists because observations of the motions of stars in galaxies, as they revolve around the center of their own galaxy, shows the presence of this matter as its gravity effects the motions of the stars. Dark matter should really be called dark energy, since not all of it is mass, though most of it appears to be mass - it is energy that generates a gravitational field, including energy locked up as mass, or more specifically the mass-equivalent of energy (since E = mc2 where m is relativistic mass). In the Universe today, most of the energy appears to be in the form of mass, hence the term 'dark matter', while the term 'dark energy' has come to mean something entirely different!

Space is expanding according to General Relativity

When we look at these galaxy clusters, we notice something strange - they are moving away from us. No matter where you are in the Universe, the galaxy clusters around you are moving away from you. It is crucial to understand that it is not the galaxies moving away through space due to their own velocities, but space itself which is expanding. A good analogy is the dough with raisins in it - when the dough expands, the distance between the raisins increases even though the raisins are not moving through the dough. Furthermore, if the radius of the dough doubles, then a raisin 5 cm away from any given raisin will end up 10 cm away, whilst one that was 10 cm away will end up 20 cm away: that is the raisin furthest away appears to be moving away at a greater speed as the dough expands.

The General Theory of Relativity has all forms of energy contributing to the formation of a gravitational field (including pressure, momentum and gravity itself) which is simply the warping of space and time by the density and quantity of the energy. This gives rise to Einstein's Field Equations relating energy density to the curvature of space and time. These equations require a metric describing the distance between two points. For a universe which is homogeneous - meaning that the laws of physics are the same everywhere and at all times, in other words momentum and energy are conserved - and isotropic, and expanding, the metric is the Robertson-Walker metric. By isotropic, we mean that the laws of physics do not depend on direction, that is angular momentum is conserved. The Robertson-Walker metric is a mathematical expression that allows us to obtain the distance between two events in space and time in an expanding universe, given in co-moving coordinates, that is our coordinates (or map grid) expands as space expands. Feeding this metric into the field equations of general relativity then yields the Friedmann equations which relate the rate of change of expansion of spaectime with the energy density and the curvature of space this energy generates. These equations include a pressure term, which is the 'pressure' generated by the energy density which causes the expansion or contraction of space. Energy effectively curves spacetime and generates a pressure that causes spacetime to contract (positive pressure) or expand (negative pressure). Ordinary energy, such as the presence of particles with measurable mass (particles that are said to be on mass-shell) such as the quarks and electrons that make up atoms, causes space to contract, or if space is expanding rapidly to begin with, then they slow the rate of expansion.

Extrapolating back in time, one reaches the point where the galaxies merge together, and going back further still one ends up with all the energy and mass in the Universe, compressed to a very high density. Observations also suggest that the Universe is open (or very nearly so) meaning that is has no maximum size and so will expand forever. Update: most data seems to be suggesting that the Universe is flat but may have just the right energy density to eventually halt the expansion - such a universe will expand, slow down and then reach a fixed size. However, recent evidence also suggests that the Universe is actually expanding at an accelerating rate, which is rather hard to explain at present. A closed universe, is one in which space is finite, but expanding, and in which space expands until a maximum size is reached and then the galaxy clusters start to move closer together as space contracts, until the galaxies all implode together into a Big Crunch. Such a Big Crunch could lead to a Big Bounce in which the energy and matter rebound, causing the Universe to expand again. Appealing to our natural instincts as this cyclical closed Universe may be, it does appear that our Universe is open (though this has not been definitely settled). An open universe has a definite beginning and end, or does it?

Note that a closed Universe is one in which space is globally curved, such that if you set out in one direction, in a straight line, across the Universe, near to the speed of light, then you would eventually arrive back where you started! It is the presence of energy that curves space and time - this is the essence of gravity. The Earth orbits the Sun because it is bound by the Sun's strong gravitational field (the Sun has a lot of energy!). In fact, the Earth would be moving along a straight line, were it not for the fact that the Sun's energy has curved space around itself!! This curvature of space (and time) is the effect we call gravity! All energy, not just that in the form of mass, generates a gravitational field (including gravity itself!). The curvature of spacetime caused by the Sun is local, it has very little effect far from the Sun. However, if the density of energy in the Universe is sufficiently high, then spacetime will be curved globally and may then curve around back on itself, rather like a bubble, whereas an open Universe may be flat, as ours appears to be. Note that space is not curved in any sense that we can ordinarily see. Rather, the three dimensions of space curve in the 4th (pseudo)spatial dimension, rather like a two dimensional surface may curve around in three spatial dimensions to form the surface of a sphere.

So, if our universe is expanding, and is open (and more or less flat), then how did it begin? The answer is not known for certain, however, the movement of the galaxies away from one another does suggest that they are moving away from some past time when they were closer together, indeed observations verify that the galaxies in the early Universe were much closer together than they are today. Continuing back we arrive at a time when all the energy of the Universe existed as a very hot and very dense mass of energy. This energy clearly got propelled outwards, expanding and cooling as it did so. Once it cooled sufficiently, atoms could form, and then eventually stars and galaxies. This outward 'explosion' of this primordial energy is called the Big Bang. The exact nature of the Big Bang is still uncertain, but we can see the 'glow' left over by it. This afterglow heats space to the predicted 3 degrees Kelvin (it is cold microwave radiation and is called the cosmic microwave background radiation). Furthermore, the Big Bang model accurately predicts the abundance of elements (such as hydrogen, helium and lithium) that we see in the Universe today. Thus, all in all, there is very good empirical evidence for the Big Bang - evidence for which there appears to be no alternative scientific explanation.

When did the Big Bang occur? How old is the Universe?

When we say that the Universe is about 13.8 billion years old, we really mean that the Big Bang occurred 13.8 billion years ago. Some argue that this moment was when time began, in which case nothing existed before the Big Bang and nothing caused the Big Bang (as there was no time for the cause to act within). However, there appears to be a finite division of time, which is the smallest meaningful unit of time, and is called the Planck time. The Planck time is only about 5.39 x 10-44 seconds (or 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 0539 seconds!). It makes no real sense to talk about a smaller (or earlier) time as time begins to fluctuate chaotically on this small scale, so time may not have had a definite beginning, but may simply 'melt away' if we go back far enough! Indeed, it makes no sense to us to even talk of how long the Universe was in this chaotic state before the Big Bang. What really happened is still beyond our science to ascertain at present, but progress is being made all the time. Some models have a recurrent Big Bang, repeatedly sending out a tremendous burst of matter forming energy into space. These models invoke higher spatial dimensions (there is reason to believe that there are 10 or 11 dimensions of space and one of time, although we can only see three of the spatial dimensions and one of time).

Another objection to aging the Universe has to do with the scale factor, R(t) which is a function of time. R describes the current size of the (observable) universe, that is the degree to which space has expanded. Since space is expanding, R is increasing. Models that invoke a Big Bang extrapolate back to the point when R was zero, that is when the observable universe consisting of infinite density, since its mass was squeezed into a point or singularity.This time is assigned t = 0 by convention, so the age of the Universe is taken from the point R became non-zero, that is time after the supposed Big bang. However, as Lachi├Ęze-Rey points out (in Cosmology - a first course, 1995, Cambridge University Press) since no known laws of physics can describe a singularity, this is really a mathematical convention of convenience. It is impossible to say how long the Universe existed prior to the Big Bang, and indeed whether such a state at or prior to the Big bang has any meaning. Indeed, in some models R never reaches zero and the age of such a Universe is infinite and it is without beginning. nevertheless, setting t = 0 at the Big Bang in those models that have one enables us to describe meaningful how long the Universe has been doing anything meaningful in terms of familiar physics.

Where did the Big Bang take place?

If the Big Bang took place at a certain location in space, then we are talking about matter and energy exploding into a prior existing and (presumably) empty space. This would give the Universe a geometric center, somewhere close to the point where the Big Bang occurred. There are models that have the Big Bang occurring inside a black hole (with the black hole existing in the far future at the end of time, which does not violate causality since no signal can cross a black hole and emerge, as far as we know!) or rather a white hole (in some theories, black holes suck matter in and spew it out into another time and space via a white hole). However, it is hard to reconcile the idea of the Universe having a center with the fact that the galaxies move away from any point in space, no matter where you are in the Universe, and also that the radiation emitted by the Big Bang can be seen in all directions. This leads most cosmologists to regard the Big Bang as not occurring in a pre-existing space, but rather it was the beginning of space and time, such that space itself is expanding, in which case the Universe has no geometric center, since the Big Bang occurred everywhere when the Universe was much smaller than it is today. Within galaxies, the local curvature of spacetime by the high concentrations of energy prevent space expanding on this local scale, but space between the galactic clusters, in the near-empty voids, is expanding! Thus, you are not getting bigger, but galactic clusters are getting further away from one another!

How big was the Universe in the very beginning?

Since space came into existence at the moment of the big Bang (or like time was chaotically fluctuating!) the early Universe must have been as small as the smallest possible length, which is the Planck length (a mere 1.616 x 10^-35 meters, or 0.000 000 000 000 000 000 000 000 000 000 000 01616 meters!). It makes no sense to talk of anything smaller than the Planck length - space breaks down at this scale, much as time breaks down in the Planck time. Thus, the Universe may have been one Planck length in diameter! The reason why all the immense energy of the Universe confined in this small volume, reaching an infinite density, did not collapse into a black hole, was because space was rapidly expanding! (This really does sound like a white hole!). Personally, I cannot reconcile the fact that the Universe could expand from such a small finite size into an infinite extent in a finite time at a finite speed (less than the speed of light?) - something seems wrong with this theory somewhere! Perhaps the Universe is finite, or perhaps it was still infinite in extent (though much smaller than it is today) at the time of the Big Bang! (If anyone knows the answer to this then please email Bot at Ok, I think I have thought of the answer - when we speak of the minute size of the early Universe we really mean the 'observable Universe' - that is the part we see today. This region was very tiny indeed, but the whole may still have had an infinite extent.

Faster than light expansion and redshift

When we gave the raisins embedded in expanding dough analogy we found that more distant raisins appear to move away more rapidly, even though the dough expands everywhere at the same rate (at a given time, though expansion rate can of course vary over time). When it is space itself expanding then something very interesting happens - very distant galaxies will move away from us faster than light!

Light emitted by such a galaxy can still, however, reach us! This is because light still moves with its usual speed relative to space, even though the space itself is expanding. However, the light waves become stretched as space expand, so their wavelength increases, causing their frequency to decrease and the light becomes redder (red light has a longer wavelength and smaller frequency than blue light). Furthermore, the light becomes dimmer as its energy s spread over a larger length of space. There comes a point when the light is too red shifted and too dim to be seen and those far away galaxies move beyond the maximum possible range of detection. This happens to countless galaxies every day as the Universe gradually becomes lost and out of the reach of humanity forever. Thus, the observable universe is not the whole universe.

How large is the Universe?

If spacetime did not expand, then light that took 13 billion years to reach us from an object 13 billion years ago would indicate an object 13 billion light years away. Given the age of the Universe as about 13.8 billion years, this would make the maximum possible radius of the Universe also 13.8 billion years. However, the expansion of space means that the Universe is actually much larger and current estimates give it a radius of about 46.5 billion light years, or a diameter of 93 billion light years, more than three times as large as it is old! This is the diameter of the observable universe, still connected by visible light. The whole universe could be infinite.

A Summary of Evidence for the Big Bang

1. Recession of the galaxies (galaxy clusters): we see galaxies speeding away from us in all directions and the further away these galaxies are the faster they are moving. Since there is nothing unique about our own galaxy, the same phenomenon, as if the galaxies were speeding away from his own galaxy. The implication is that space is expanding and all the galaxy clusters are moving further apart.

2. The cosmic microwave background radiation: this radiation is very evenly dispersed throughout the whole of space and is cold but nevertheless warmer than the predicted background radiation in the absence of a Big Bang. The Big Bang predicts the formation of this radiation at the temperature we detect it at (3K). Only the rapid expansion of spacetime shortly after the Big Bang can explain the uniformity (homogeneity) of this background radiation - it is essentially the same wherever one looks (apart from very slight but important fluctuations or inhomogeneities). Only the continued expansion of space apparently explains why this radiation is so cold.

3. The Big Bang model accurately predicts the abundance of (light) elements (nuclear abundances) that we see in the Universe today. Heavier elements were since manufactured by stars as stars reprocess the lighter elements formed by the Big Bang (e.g. hydrogen, helium and lithium) into heavier ones. The contribution of stars to the fine adjustments of present-day elemental abundances is, admittedly, difficult to predict.

Currently no other scientific theory can explain all of these phenomena. Theories only differ in the fine details and such questions as the frequency of big bangs - was there only one or do they occur repeatedly, or are there many different universes each formed by a big bang?

How it all Happened

According to current models...

1. The beginning

To begin with the Universe was incredibly dense and incredibly hot. Putting aside the problems of defining time in the very first few moments when the Universe had the Planck density (and was at a very high temperature of 10^31 K, called the Planck temperature) we shall set the point of time at which time became a reasonably ordered phenomenon as the beginning of time (t = 0). This is the point at which the Universe fell below the Planck temperature and space as we understand it also came into being. Current theories break down at the Planck temperature and Planck density, but once our defined origin of time is reached, then our theories begin to kick-in. If this sounds confusing, then that is because nobody understands these very few moments when time and space may have emerged from some undefinable 'pre-existing' chaotic state. (The problem is how can anything pre-exist before time began, but as mentioned above, time seems to gradually melt away rather than having a precise start).

2. The first microsecond (millionth of a second)

In the first 10^-36 of a second (0.000 000 000 000 000 000 000 000 000 000 000 001 s) the material of the Universe was so dense that particles frequently collided with one another, ensuring an even mixing of heat and other energy, so that the observable Universe (the bit we can see today, which is most likely not all of it!), at this stage less than 10-31 meters across, was slowly expanding and had an even temperature and density. This stage is called thermalization. This continued until the Universe cooled, as it expanded (distributing the heat energy throughout a larger volume lowers the temperature which is a measure of heat energy density) to 1027 K.

3. Symmetry Breaking and Inflation

At this point the Universe was cool enough for a process called spontaneous symmetry breaking to occur. Prior to this point, everything was so hot and energetic that all the particles behaved the same - there was perhaps a sea of interacting quarks, or something similar. Once symmetry was broken, however, the strong, weak and electromagnetic forces became distinguishable from one another (the strong and weak forces govern certain aspects of sub-atomic particle behavior, whilst the electromagnetic force accounts for electricity and magnetism). Initially the strong force became distinguishable from the electroweak force (the weak and electromagnetic forces still indistinguishable and so called the electroweak force) but later (at 10-12 seconds) the electromagnetic and weak forces became distinguishable after further symmetry breaking.

Some models incorporate a period of extremely rapid expansion, called inflation, in the early universe. According to models that incorporate inflation, and not all do, inflation is driven by the vacuum energy. A vacuum is not empty space! Quantum fluctuations allow virtual particles (said to be off mass-shell) to spontaneously appear from nothing, as long as they disappear again after a certain period of time (determined by a quantum uncertainty principle). Such virtual particles form the backbone of the Standard Model used so successfully in particle physics. One might expect the gravitational field generated by these virtual particles to resist expansion. However, the vacuum has to have the same physics everywhere (what we call Lorentz invariance) and this can be achieved if it generates a negative pressure, that is if its energy density results in a negative pressure or tension. When this condition is fed into the Friedmann equations, the rate of expansion of the Universe accelerates. Inflation occurs at an exponential rate, allowing the universe to accomplish much of its expansion in a fraction of a second!

The onset of symmetry breaking could have initiated a period of very rapid expansion or inflation. On the other hand, any vacuum energy can drive expansion and some theories postulate that the quark state had the higher vacuum energy, driving a rapid phase of inflation and that after symmetry breaking occurred, the new vacuum energy was lower, causing inflation to cease. Why would it cease? After all we postulate that vacuum energy decreased, but it is still there. Well, something could be opposing it and some models introduced the cosmological constant to Einstein's Field Equations to achieve this effect. This 'mathematical fudge' meant that in models of the early universe, inflation dominated when the vacuum energy was too strong for the cosmological constant to oppose, but that the cosmological constant was strong enough to oppose the weaker vacuum energy state that follows spontaneous symmetry breaking. This was used to construct models in which expansion progressively slowed following inflation, on the evidence that the rate of expansion was still slowing today. However, more recent measurements suggest that the rate of expansion is currently accelerating and our models require more 'fudging' to fit current data. What all this really means is still controversial. In inflationary models, during inflation the observable Universe expanded from 10-31 meters to 0.1 meter (10 centimeters!) at a time from 10-36 seconds to 10-30 seconds.

Why this rapid burst of inflation?

If we point our telescopes far into the sky we can see galaxies existing very far away near to the beginning of time, when the Universe was only half its present size. However, pointing in the opposite direction our telescopes see the same numbers of galaxies just as far away on the other side. Additionally the cosmic background microwave radiation is also similar in opposite directions. However, the light from these very distant galaxies has only just reached us as we see them as they were billions of years ago. The Universe has not existed for long enough to allow light from these distant galaxies we see in one direction, to reach those distant galaxies we see in the opposite direction. If this has always been the case, then how did these two separate regions of space become so similar in density of galaxies, if they had never been in contact with one another. (Remember no signals can travel faster than light without violating causality. By causality I mean that if event A caused event B, then event A must always occur in the past of event B, unless we start reversing time!). Inflation is necessary to explain the homogeneity of the Universe. Additionally, for the cosmic microwave background to be so uniform over such a large region of space, it seems reasonable to suppose that these regions of space were once connected such that they could exchange heat energy and light with one another. Indeed energy must have been able to travel more or less across the entire region to even out the temperature.

Inflation explains the sameness or homogeneity of space in every direction. Since inflation involves a very rapid expansion of space, it means that if inflation occurred for long enough, then a very tiny region of space will have been expanded into a very large region. Prior to inflation, the observable Universe was small enough for light to cross it from one end to the other, but after inflation the Universe became too big for light to have crossed it, as it is today. Note that for inflation to work, spacetime must expand much faster than the speed of light at this time.

4. The formation of matter as we know it

When the Universe was one microsecond (one millionth of a second) old, it had cooled to 10^13 K, which was cool enough to allow particles called quarks to combine to form protons and neutrons. A detailed analysis predicts the final ratio to be 87% protons to 13% neutrons. This ratio is important when predicting the abundance of the first elements that formed, since protons and neutrons are constituents of the atomic nucleus. However, only after about the first minute when the Universe cooled to about 10^10 K was it cool enough for the protons and neutrons to come together (they were fused together by nuclear fusion) to form atomic nuclei (with the protons and neutrons bonded together by the strong force) without collisions smashing them apart. (One must understand that hotter particles move faster and so collide harder. Today we use huge particle accelerators to accelerate particles to the tremendous speeds needed to smash nuclei into protons and neutrons - nuclei are very strong indeed, but protons and neutrons are even harder and no particle accelerator has yet managed to smash them into quarks). When the Universe was ten minutes old, it had finished synthesizing the lighter elements, such as hydrogen, helium, deuterium (heavy hydrogen) and lithium and nuclear fusion fizzled out. The observable Universe continued to expand but was still only a tiny fraction of its current size.

5. Radiation dominates matter

From the first hour until the Universe was about 10 000 years old, although it contained matter, most of its energy was still in the form of energy (electromagnetic radiation). This is the opposite of what we see today, where most of the Universe's energy is locked up as mass in stars and planets. However, as the Universe continued to expand, the radiation diluted out faster than the matter and when the Universe was older than 10 000 years, matter came to dominate radiation - in that most of the energy was locked up as matter. The Universe became a plasma (a hot gas of electrically charged particles - electrons and nuclei) and remained like this for the next 300 000 years or so. A plasma as dense as this is opaque - so light could not travel very far at all.

6. The formation of atoms

At an age of 300 000 years, the Universe had cooled enough to allow atoms to form without them being easily smashed apart. Atoms formed as electrons and nuclei came together. This removed the free electrons as the plasma became a gas of atoms. The free electrons were responsible for making the plasma opaque - free electrons obstruct light and scatter it easily. Thus, when atoms formed, the Universe became transparent, as it is today. This allowed radiation to travel unimpeded and gave rise to the cosmic background radiation that we see today. This is as far back as we can see in time, as our telescopes look across space, because before this the Universe was opaque. As soon as it became transparent, the cosmic background radiation became visible. This radiation continued to cool, reaching the cold 3K that it is at today. (We talk about the moment when the Universe became transparent as the decoupling of radiation and matter, meaning that most of the radiation could travel far before being impeded by matter). At the time of decoupling, the Universe was 1200 times smaller than it is today. This is already too large to allow enough time for light (and heat) to spread from one end to the other, and yet the cosmic microwave background radiation gives a remarkable uniform temperature (suggesting that heat was transported from one end of the Universe to the other at some point). This can only be explained by inflation - the Universe was at one time much smaller, allowing heat and light to cross from one end to the other and so even out the temperature, later on spacetime expanded faster than the speed of light for a time, before slowing down again to give the Universe we see today, which is now too large and too young for light to have crossed its diameter. (The light got left behind when spacetime expanded during inflation).

7. The formation of galaxies, stars and planets

After 10 million years, the clouds of atoms were cool enough to contract under their own gravity (they collapses under their own weight!). As they collapsed into denser objects, they converted gravitational energy into heat and they became hot dense objects - the first stars were born! Smaller fragments became proto-planets and slowly cooled into planets proper, whilst the stars were hot enough to maintain their temperature by nuclear fusion reactions in their cores - the stars shined as the planets cooled. Stars do not live forever, and stars died as new ones were born. Indeed the remains of dead stars that get blasted across space form clouds of gas that can condense into new stars, so generations of stars lived out their lives. Stars manufacture heavier elements, such as carbon and oxygen, from the lighter elements present from the Big Bang (hydrogen and helium). These heavier elements are essential to life as we know it, so only after generations of stars had enriched the material of the Universe could life evolve! It is still not entirely clear how the stars came to be grouped into galaxies, though it is assumed that the galaxies formed first or at least simultaneously with the first stars.

Star birth and death continue in galaxies, such as the Milky Way, to this day.


Dust lanes in a spiral galaxy seen edge-on; image courtesy of Galaxy Zoo


Article updated 22 June 2022