A tale of two big bangs

In cosmology, “big bang” has two different meanings – and if you want to understand what’s going on, you should be aware of that difference.

An article by Markus Pössel

Whenever you hear or read about cosmology, there is one distinction you should have in the back of your mind – otherwise, matters might get a bit confusing: The term “big bang” has two slightly different meanings, and the answer to questions like “Did the big bang really happen” depends crucially on which of the two big bangs you are talking about.

Back to the beginning

The universe is expanding: The distance between far-away regions of space (for instance, between our galaxy and distant galaxy clusters) is steadily increasing with time. Accordingly, if we travel back in time, we will reach periods of cosmic history in which the galaxies were much closer together than they are today. Roughly 14 billion years ago, our voyage into the past leads us to a universe in which there were no individual galaxies, or even stars. The whole cosmos was filled with a homogeneous mixture of different types of matter particles and electromagnetic radiation. Quite generally, if you let a gas expand, it will cool down; if you compress it, it will heat up. Analogously, the temperature of the universe was significantly higher in the past. Going back, we will eventually reach times when the universe was thousands or millions of degrees hot and, beyond that, even hotter.

If we simply follow the predictions of Einstein’s theory of general relativity for the evolution of a simple expanding, homogeneous universe filled with matter and radiation, then our journey into the past will eventually come to an end – a point in time where we cannot go back any further. At this moment, all the galaxies that we see around us today were compressed into a region of zero volume – to a single point in space. Since density is defined as mass divided by volume, the density was infinite. In Einstein’s theory, matter influences the way that the geometry of space and time is distorted, and at this moment of infinite matter density, the curvature of spacetime was infinite, as well. Within the simple cosmological models based on general relativity, there is no possibility to go to any earlier times than this. Such a boundary of time (or, more generally, of spacetime) is called a singularity.

Big bang singularity and “big bang phase”

Now that we have followed the evolution of the universe as far as the simple models would let us, let us take stock: In those models, the beginning of the universe is a singularity which is commonly called the “big bang singularity” or simply the “big bang”. Directly afterwards, there followed a period of expansion during which the temperature and density of matter in the universe were so extreme that current science cannot tell us what happened – we simply do not have reliable physical theories describing the properties of matter under such extreme condition.

A mere millionth of a second later, we are back to normal – at least as far as high-energy physicists are concerned: Matter at such densities and temperatures can be produced in today’s most powerful particle accelerators, and this part of cosmic evolution can be described using a combination of the standard model of particle physics and general relativity. A few seconds later, we enter the period of Big Bang Nucleosynthesis, in which the first light elements such as helium are produced. Another 380,000 years later, the universe had cooled sufficiently to allow the formation of the first stable atoms. Over the next 14 or so billion years, the universe cools down ever further, stars and galaxies form, and eventually, on a planet close to a wholly unremarkable star, there evolves a species of intensely curious ape, whose representatives eventually take on the gargantuan task of trying to reconstruct what went on before.

And there we have them, the two senses in which the expression “big bang” is used, as sketched in the following illustration (not to scale), where time passes as you go from left to right, and where the expanding size of the universe is represented by an increase in vertical extent:

Schematic representation of the evolution of the universe from the big bang to the present

Sometimes, “big bang” stands for “big bang singularity” – the singular point in time that, according to the simple cosmological models, was the beginning of our universe. On other occasions, “big bang” encompasses the first minutes, or even the first 380,000 years of our universe’s early history – a whole “big bang phase”, if you will (though this is not a term that is commonly used). Often, the big bang phase is taken to include a hypothetical period of rapid, accelerated expansion called inflation, which began as early as 10^-43 seconds after the big bang singularity.

Compared with the age of the universe, the difference between the two meanings is tiny – like arguing whether or not the tip of a 30 inch ruler includes the first hundredth of a millimetre of the ruler’s length. Yet tiny as it may be, there are occasions on which the difference becomes important. Here are two examples.

Which is which?

Did the big bang really happen? If you are talking about the big bang phase, the hot early universe as described by well-known physical theories (or, if you include inflation, by extrapolation from those theories), then there is good evidence that, yes, nearly 14 billion years ago, the cosmos developed in just the way described by the cosmological models (the main exhibits are the original abundances of light elements as deduced from astronomical observation, the distribution of far-away galaxies and the existence and properties of the so-called cosmic background radiation).

Whether or not there really was a big bang singularity is a totally different question. Most cosmologists would be very surprised if it turned out that our universe really did have an infinitely dense, infinitely hot, infinitely curved beginning. Commonly, the fact that a model predicts infinite values for some physical quantity indicates that the model is too simple and fails to include some crucial aspect of the real world. In fact, we already know what the usual cosmological models fail to include: At ultra-high densities, with the whole of the observable universe squeezed into a volume much smaller than that of an atom, we would expect quantum effects to become crucially important. But the cosmological standard models do not include full quantum versions of space, time and geometry – they are not based on a quantum theory of gravity. However, at the present time we do not yet have a reliable theory of quantum gravity. While there are promising candidates for such a theory, none are developed far enough to yield reliable predictions for the very early universe.

Thus, while some cosmologists do not have a problem with assuming that our universe began in a singular state, most are convinced that the big bang singularity is an artefact – to be replaced by a more accurate description once quantum gravity research has made suitable progress. To be replaced with what? Nobody knows for sure. In some models, we can go infinitely far into the past (one example is presented in the spotlight text Avoiding the big bang). In others, the big bang is replaced by a beginning of the universe which avoids all infinities, but in which time itself is rather different from what we are used to (some more information about this can be found in the spotlight text Searching for the quantum beginning of the universe).

On the other hand, whenever cosmologists talk about something happening a second, a minute, or 400,000 years after the big bang, their reference point is indeed the big bang singularity. The reason is that, in the cosmological models based on general relativity, the formulae for the expansion of the universe become particularly simple if you define t=0, cosmic time zero, to coincide with the big bang singularity. This is a great advantage for physics calculations dealing with the early universe, so defining cosmic time in this way makes good sense.

Still, there is a potential for confusion. Anyone not familiar with the conventions of cosmology might assume that the use of a phrase like “one hundredth of a second after the big bang” implies that, in the opinion of the writer or speaker, there really was a big bang singularity. Not so: Such a phrase is merely shorthand for “at a cosmic time of one hundredth of a second, where cosmic time is defined in a way that makes the physics of the early universe especially simple”.

Further Information

For the basic concepts of relativity of interest for this spotlight topic, check out Elementary Einstein, in particular the chapters Relativity and the quantum and Cosmology.

More information about singularities is contained in the spotlight text Spacetime singularities. Some answers to the question what, if not a big bang singularity, happened at cosmic time zero are given in Avoiding the big bang and in Searching for the quantum beginning of the universe. Other related Spotlights on relativity on Einstein-Online can be found in the sections Relativity and the quantum and Cosmology.

Colophon

Markus Pössel

is the managing scientist at Haus der Astronomie, the Center for Astronomy Education and Outreach in Heidelberg, and senior outreach scientist at the Max Planck Institute for Astronomy. He initiated Einstein Online.

Citation

Cite this article as:
Markus Pössel, “A tale of two big bangs” in: Einstein Online Band 04 (2010), 02-1015

Definitioner

time

It is a fact of life that not all events in our universe happen concurrently - instead, there is a certain order. Defining a time coordinate or defining time, the way physicists do it, is to define a prescription to associate with each event a number so as to reflect that order - if event B happens after event A, then the number associated with B should be larger than that associated with A. The first step of this definition is to construct a clock: Choose a simple process that repeats regularly. (What is "regular"? Luckily, in our universe, all elementary processes such as a swinging pendulum, the oscillations of atoms or of electronic circuits lead to the same concept of regularity.) As a second step, install a counter: A mechanism that, with every repetition of the chosen process, raises the count by one. With this definition, one can at least assign a time (the numerical value of the counter) to events happening at location of the clock. For events at different locations, an additional definition is necessary: One needs to define simultaneity. After all, the statement that some far-away event A happens at 12 o'clock is the same as saying that event A and "our clock counter shows 12:00:00" are simultaneous. The how and why of defining simultaneity - a centre-piece of Einstein's special theory of relativity - are described in the spotlight topic Defining "now". With all these preparations, physicists can, in principle, assign a time coordinate value ("a time") to any possible events, and describes how fast or how slow processes happen, compared to that time coordinate.

temperature

In systems consisting of many particles, be they solid bodies, fluids or gases, the constitutents are in constant, chaotic motion: the atoms in a solid crystal oscillate a bit, the molecules of a gas are in rapid, disordered motion, and so on. The average energy with which each constitutent contributes to every part of the disorderly motion is the same, and it is called the temperature of the system. High average energy corresponds to high temperature - atoms vibrating wildly, gas molecules zipping around very fast -, low average energy to low temperature. In a slightly different context, certain mixtures of electromagnetic radiation can be assigned a temperature ("radiation temperature"), a single parameter that completely defines the basic properties of the radiation (more precisely, its spectrum). It corresponds to the thermal radiation emitted by a hot body with precisely that temperature. In physics, temperature is measured in Kelvin, in everyday life, depending on the country, in Fahrenheit or Celsius.

star

A cosmic gas ball that is massive enough for pressure and temperatur in its core to reach values where self-sustained nuclear fusion reactions set in. The energy set free in these reactions makes stars into very bright sources of light and other forms of electromagnetic radiation. Once the nuclear fuel is exhausted, the star becomes a white dwarf, a neutron star or a black hole.

stars (star)

space

In a strict sense: Space as we know it from everyday life: the totality of all locations in which objects can sit, with three dimensions. In a more general sense used by mathematicians, all kinds of sets of points are spaces - a line for instance, which has but a single dimension, or a two-dimensional surface, but also higher-dimensional spaces. Also, in such more general spaces, geometry can be different from the standard Euclidean geometry taught in high schools - such spaces can be curved.

spacetime

Already in special relativity, observers in motion relative to each other will not, in general, agree as to whether two events happen simultaneously, or as to how great is the distance between two objects. They do, however, agree as to what events there are, although not to when and where they happen. This observer-independent totality of all events is called spacetime. How spacetime is split into space and time can differ from observer to observer. Every-day space has three dimensions. Adding time adds another dimension - spacetime has four dimensions, all in all. We are used to the idea of a point in space - an object that has only one location and is completely defined once its space coordinates are given. In spacetime, a spacetime point is an object defined completely once its space coordinates and its time coordinate are given - which makes a spacetime point nothing but an elementary event. The idea of spacetime is, in addition to its role in special relativity, a building block of general relativity. Analogous to how a plane is flat, but the surface of a sphere is curved, in general relativity, curved or distorted versions of the simple, flat spacetime of special relativity play a role. Spacetime curvature, in general relativity, is intimately connected with gravity. For an introduction to the basics of both theories of relativity, check out the chapters Special relativity and General relativity in Elementary Einstein. Sometimes, it can be helpful to view spacetime in analogy to ordinary space - such analogies are explored in the spotlight topics Time dilation on the road (for time dilation) and Twins on the road (for the twin effect).

singularity

Irregular boundary of spacetime in general relativity - region where spacetime simply comes to an end. Often, such boundaries are associated with spacetime curvature growing beyond all bounds and becoming infinitely large - so-called curvature singularities (notably Ricci singularities or Weyl singularities - but there are exceptions (for instance a conic singularities). According to general relativity, a singularity exists inside every black hole, and the starting point of any universe described by a big bang model is a singularity as well. The occurrence of singularities is a failure of general relativity - and a strong indication that the theory is incomplete. Instead, one could describe the earliest universe and the interior of black holes using a theory of quantum gravity. More information about singularities can be found in the spotlight texts Spacetime singularities and Of singularities and breadmaking.

second

In the International System of units: the basic unit of time. Defined as a certain multiple of the oscillation period of electromagnetic radiation set free in a certain transition within the electron shell of atoms of the type Cesium-133.

radiation

In a general sense: Collective name for all phenomena in which energy is transported through space in the form of waves or particles. In a more restricted sense, the word is often used synonymously with electromagnetic radiation.

quantum gravity

Theory based both on the effects, concepts and laws of quantum theory and on those of general relativity. To date, no complete such theory exists; the best-known candidate theories are string theory and loop quantum gravity. Some information on the question of quantum gravity can be found in the chapter Relativity and the quantum of Elementary Einstein, starting with the page Border regions of gravity. Selected aspects of quantum gravity are described in the category Relativity and the quantum of our Spotlights on relativity.

point

Elementary "building block" of geometrical entities such as surfaces or more general spaces. For instance, a surface is the set of all its points, of all possible locations on the surface, and all geometrical objects in that surface are defined by the points that belong to them - for instance, a line on the surface is the set of (infinitely many) points.

planet

Planets are not-too-small companions of a star that are not stars themselves (nor ever were stars). In our solar system, the planets are, listed from the one closest to the sun to the one farthest: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. As of August 2006, Pluto, which used to be a proper planet, is officially a "dwarf planet". In the night sky, the distinguishing characteristic of planets is that they move around relative to the unchanging background of stars - which gave them their name, loosely translated from Greek as "wanderers".

matter

In general relativity: All contents of spacetime that contribute to its curvature: particles, dust, gases, fluids, electromagnetic and other fields. In particle physics: All elementary particles with half-integer spin, such as electrons and quarks, as well as their composites such as protons and neutrons, in contrast with force particles.

mass

In classical physics, mass plays a triple role. First of all, it is a measure for how easy it is to influence the motion of a body. Imagine that you're drifting in emtpy space. Drifting by are an elephant and a mouse, and you give each of them a push of equal strength. The fact that the mouse abruptly changes its path, while the elephant's course is as good as unaltered, is a sure sign that the mass (or, in the language of physics, the inertia or inertial mass) of the elephant is much greater than that of the mouse. Secondly, mass is a measure of how many atoms there are in a body, and of what type they are. All atoms of one and the same type have the same mass, and adding up all those tiny component masses, the total mass of the body results. Thirdly, in Newton's theory of gravity, mass determines how strongly a body attracts other bodies via the gravitational force, and how strongly these bodies attract it (in this sense, mass is the charge associated with the gravitational force). In special relativity, one can also define a mass that is a measure for a bodies resistance to changing its motion. However, the value of this relativistic mass depends on the relative motion of the body and the observer. The relativistic mass is the "m" in Einstein's famous E=mc² (cf. equivalence of mass and energy). The relativistic mass has a minimum for an observer that is at rest relative to the body in question. This value is the so-called rest mass of the body, and when particle physicists talk of mass, this is usually what they mean. Just as in classical physics, the rest mass is a kind of measure for how much matter the body is made up of - with one caveat: For composite bodies, the energies associated with the forces holding the body together contribute to the total mass, as well (another consequence of the equivalence of mass and energy). In general relativity, mass still plays a role as a source of gravity; however, it has been joined by physical quantities such as energy, momentum and pressure.

light

Light in the strict sense of the word is electromagnetic radiation the human eye can detect, with wave-lengths between 400 and 700 nano metres. In relativity theory and in astronomy, the word is often used in a more general sense, encompassing all kinds of electromagnetic radiation. For instance, astronomers might talk about "infrared light" or "gamma light"; in this context, light in the stricter sense is referred to as "visible light". Within classical physics, the properties of light are governed by Maxwell's equations; in quantum physics, it turns out that light is a stream of energy packets called light quanta or photons. In the context of relativistic physics, light is of great interest, and for a number of reasons. First of all, the speed of light plays a central role in both special and general relativity. Also, there are a number of interesting effects in general relativity which are associated with the propagation of light, namely deflection, the Shapiro effect and the gravitational redshift.

light elements

According to the big bang models, the early universe underwent a brief period of primordial nucleosynthesis between a few seconds and a few minutes cosmic time, during which nuclei of light elements such as heavy hydrogen, helium and lithium formed. A brief account of this Big Bang Nucleosynthesis can be found in the spotlight text Big Bang Nucleosynthesis, while Equilibrium and change provides more information about the physical processes involved and Elements of the past describes how the predictions of Big Bang Nucleosynthesis can be tested against astronomical observation.

inflation

Hypothetical phase in the earliest universe during which the cosmos underwent exponentially growing expansion.

helium

After hydrogen, the second lightest chemical element. Its atomic nucleus consists of two protons and, ordinarily, two neutrons ("helium-4"); such helium nuclei are also called alpha particles. Another variety of helium, helium-3, has only one neutron in its nucleus. In the context of general relativity, both helium-3 and helium-4 are is of interest as two species of light atomic nuclei that formed in the early universe during Big Bang Nucleosynthesis.

gravity

See gravitation

gravity (gravitation)

In classical physics: An action-at-a-distance force by which all bodies that possess mass attract each other (see Newtonian theory of gravity), synonym: gravitational force. In Einstein's general theory of relativity: The fact that matter that possesses mass, energy, pressure or similar properties distorts spacetime, and that this distortion in turn influences whatever matter might be present. An introduction to the basic ideas of general relativity is provided by the section General relativity of Elementary Einstein. More information about the nature of gravity in general relativity can be found in the spotlight text Gravity: From weightlessness to curvature.

geometry

That part of mathematics concerning itself with surfaces or more general spaces as well as objects defined on such spaces, such as points or lines as well as the objects constructable from points and lines, such as triangles.

general relativity (general theory of relativity)

Albert Einstein's theory of gravity; a generalization of his special theory of relativity. For information about the concepts and applications of this theory, we recommend the chapter general relativity of our introductory section Elementary Einstein. Further information about many different aspects of general relativity and its applications can be found in our section Spotlights on relativity.

gas

In a strict sense: A state of matter in which the atoms and/or molecules wildly careen and collide, without being bound to each other. This movement leads to an inner pressure, while the average kinetic energy of the moving particles is a measure for the temperature of the gas. Compare the other states of matter: solid state, liquid, plasma. In a broader sense, gas is also used to denote other mixtures of freely careening particles, for instance in the case of the electron gas whose pressure stabilizes a white dwarf against further collapse.

galaxy

Stars are rarely found alone - usually, they congregate in conglomerates of millions, billions or even more stars called galaxies. A case in point is our sun, part of a galaxy we call the milky way. The life of a young galaxy can be very turbulent. Examples of such young, active galactic nuclei are radio galaxies and quasars.

energy

Physical quantity with the special property that, in physical processes, energy is neither destroyed nor created, simply transformed from one form of energy to another. Some of the different forms of energy that are defined separately are kinetic energy, thermal energy and the energy carried by electromagnetic radiation. Processes that transform one form of energy into another take place in all machines we use in everyday life, from the engine of a subway train (electrical energy into kinetic energy of the train) to an electric blanket (electrical energy into thermal energy). One important consequence of special relativity is that energy and mass are completely equivalent - two different ways to define what is, on closer inspection, one and the same physical quantity. See the keyword equivalence between mass and energy.

density

In a stricter sense synonymous with "mass density": The average density of matter in a region of space is the total mass of all matter contained in that region, divided by the region's volume. More generally, density can refer to other physical quantities as well. The energy density, for instance, is the total sum of energy localized in a region divided by that region's volume.

curvature

For a two-dimensional surface: criterion that allows us to decide whether that surface is a plane, or part of a plane (i.e. a surface on which the usual rules of high school geometry apply), or not. Two possibilities to define the curvature of a plane are the following: Sum of the angles of a triangle. In a plane, the sum of the three angles in a triangle formed by three straight lines is always 180 degrees. In a more general surface, the sum of the angles of a more general triangle formed by three straightest-possible lines (i.e. geodesics) can be larger or smaller than 180 degrees. The difference (the surplus or deficit), divided by the area of the triangle, is a measure for the curvature of that region of the surface. Second possibility: the circumference of a circle. In the plane, that circumference is equal to 2 times pi times the circle's radius. On a more general surface, it can be larger or smaller. The difference, divided by the third power of the radius, leads to the same measure for the curvature as the first definition. Simple examples for curved surfaces are the surface of a sphere (positive curvature, that is to say: sum of the angles in a triangle larger than 180 degrees, circumference of a circle smaller than 2 times pi times radius) and that of a saddle (negative curvature, that is to say: sum of the angles in a triangle smaller than 180 degrees, circumference of a circle larger than 2 times pi times radius). Curvature cannot only be defined for surfaces, but also for higher-dimensional, more general spaces or spacetimes. However, the generalized definition is substantially more complicated, and curvature is defined not by a single number, but by a set of numbers (that, together, form the "curvature tensor"). It's basic meaning, however, is the same: it measures the space's deviation from a flat space of the same dimension. For physics, an important aspect of curvature is its connection with gravity, as described in Einstein's general theory of relativity. Basic information about this can be found in the spotlight text Gravity: From weightlessness to curvature.

current

Matter in coordinated, flowing motion - think of water flowing in a pipe. An important example is the electric current associated with moving electric charges. Electric currents are the sources of magnetic fields.

cosmology

That branch of physics and astronomy dealing with the structure and development of the universe as a whole. At the core of modern cosmology are the big bang models based on Einstein's general theory of relativity. Their basic features are reviewed in the chapter Cosmology of Elementary Einstein. In order to describe the very early universe, it will be necessary to take the effects of quantum gravity into account - this gives rise to models of quantum cosmology.

cosmic time

Measure for the progress of the evolution of an expanding universe such as that of the big bang models. It corresponds to time as measured by clocks that are at rest relative to the expanding space, and that have been set to zero at the very beginning, the time of the hypothetical big bang singularity. Synonym: Age of the universe. The basic features of the cosmological models that use cosmic time are reviewed in the chapter Cosmology of Elementary Einstein.

big bang

The big bang models are the foundation of modern cosmology. Firmly grounded in Einstein's theory of general relativity, they describe a universe that began in a very hot initial state and has expanded (and cooled down) ever since. They make precise predictions about nucleosynthesis in the early universe, the existence and properties of the cosmic background radiation, and the distribution of distant galaxies in the cosmos, which have been confirmed by astronomical observation. The word "big bang" has two different meanings. In a strict sense, the big bang is a spacetime singularity, a state of infinite density - the initial state the big bang models predict for our universe. In a more general sense, the term is applied to the earliest cosmic eras, in which the universe was exceedingly hot and dense. Further information about these two meanings and why it is important to distinguish between them can be found in the spotlight text A tale of two big bangs. The basic features of the big bang models are reviewed in the chapter Cosmology of Elementary Einstein. Selected aspects of cosmology are described in the category Cosmology of our Spotlights on relativity.

Big Bang Nucleosynthesis

Synonym: primordial nucleosynthesis. The formation of complicated nuclei from constituents such as protons and neutrons in the early universe. According to the big bang models, the early universe was filled with a particle soup of protons and neutrons. At cosmic times between a few seconds and a few minutes, nuclear reactions produced the first light elements, mainly nuclei of deuterium, different varieties of helium and lithium. Heavier nuclei up to those of iron formed and continue to form in the course of fusion processes inside stars; nuclei that are even more massive form in the course of supernova explosions. These explosions also serve to disseminate the complex nuclei formed inside stars (stellar nucleosynthesis) in space. A brief account of Big Bang Nucleosynthesis can be found in the spotlight text Big Bang Nucleosynthesis, while Equilibrium and change provides more information about the physical processes involved and Elements of the past describes how the predictions of Big Bang Nucleosynthesis can be tested against astronomical observation.

atom

All matter we encounter in everyday life consists of smallest units called atoms - the air we breath consists of a wildly careening crowd of little groups of atoms, my computer's keyboard of a tangle of atom chains, the metal surface it rests on is a crystal lattice of atoms. All the variety of matter consists of less than hundred species of atoms (in other words: less than a hundred different chemical elements). Every atom consists of an nucleus surrounded by a cloud of electrons. Nearly all of the atom's mass is concentrated in its nucleus, while the structure of the electron cloud determines how the atom can bind to other atoms (in other words: its chemical properties). Every chemical element can be defined via a characteristic number of protons in its nucleus. Atoms that have lost some of their usual number of electrons are called ions. Atoms are extremely small (typical diametres are in the region of tenths of a billionth of a metre = 10^-10 metres), and to describe their properties and behaviour, one has to resort to quantum theory.

age of the universe

Another word for cosmic time, the time coordinate of the big bang models: time as measured by clocks that are at rest relative to the expanding space, and that have been set to zero at the very beginning, the time of the hypothetical big bang singularity.