LAST SCATTERING SURFACE

Adapted from P. Coles, 1999, The Routledge Critical Dictionary of the New Cosmology, Routledge Inc., New York. Reprinted with the author's permission. To order this book click here: http://www.routledge-ny.com/books.cfm?isbn=0415923549

According to the standard Big Bang theory, the early Universe was sufficiently hot for all the matter in it to be fully ionised. Under these conditions, electromagnetic radiation was scattered very efficiently by matter, and this scattering kept the Universe in a state of thermal equilibrium. Eventually the Universe cooled to a temperature at which electrons could begin to recombine into atoms, and this had the effect of lowering the rate of scattering. This happened at what is called the recombination era of the thermal history of the Universe. At some point, when recombination was virtually complete, photons ceased to scatter at all and began to propagate freely through the Universe, suffering only the effects of the cosmological redshift. These photons reach present-day observers as the cosmic microwave background radiation (CMB). This radiation appears to come from a spherical surface around the observer such that the radius of the shell is the distance each photon has travelled since it was last scattered at the epoch of recombination. This surface is what is called the last scattering surface.

To visualise how this effect arises, imagine that you are in a large field filled with people screaming. You are screaming too. At some time t = 0 everyone stops screaming simultaneously. What will you hear? After 1 second you will still be able to hear the distant screaming of people more than 330 metres away (the speed of sound in air, v_s, is about 330 m/s). After 3 seconds you will be able to hear distant screams from people more than 1 kilometre away (even though those distant people stopped screaming when you did). At any time t, assuming a suitably heightened sense of hearing, you will hear some faint screams, but the closest and loudest will be coming from people a distance v_st away. This distance defines a `surface of last screaming' and this surface is receding from you at the speed of sound. Similarly, in a non-expanding universe, the surface of last scattering would recede from us at the speed of light. Since our Universe is expanding, the surface of last scattering is actually receding at about twice the speed of light. This leads to the paradoxical result that, on their way to us, photons are actually moving away from us until they reach regions of space that are receding at less than the speed of light. From then on they get closer to us. None of this violates any laws of physics because all material objects are locally at rest.

When something is hot and cools down it can undergo a phase transition. For example, hot steam cools down to become water, and when cooled further it becomes ice. The Universe went through similar phase transitions as it expanded and cooled. One such phase transition, the process of recombination discussed above, produced the last scattering surface. When the Universe was cool enough to allow the electrons and protons to fall together, they `recombined' to form neutral hydrogen. CMB photons do not interact with neutral hydrogen, so they were free to travel through the Universe without being scattered. They decoupled from matter. The opaque Universe then became transparent.

Imagine you are living 15 billion years ago. You would be surrounded by a very hot opaque plasma of electrons and protons. The Universe is expanding and cooling. When the Universe cools down below a critical temperature, the fog clears instantaneously everywhere. But you would not be able to see that it has cleared everywhere because, as you look into the far distance, you would be seeing into the opaque past of distant parts of the Universe. As the Universe continues to expand and cool you would be able to see farther, but you would always see the bright opaque fog in the distance, in the past. That bright fog is the surface of last scattering. It is the boundary between a transparent and an opaque universe and you can still see it today, 15 billion years later.

Although the surface of last scattering has a temperature of 3000 K, the cosmic microwave background photons now have a temperature of about 3 K. This factor-of-1000 reduction in temperature is the result of the factor-of-1000 expansion between the time the photons were emitted and now. The photons have cooled and become redshifted as a result of the expansion of the Universe. For example, when the Universe is three times bigger than it is now, the CMB will have a temperature of about 1 K.

The last scattering surface is sometimes called the cosmic photosphere, by analogy with the visible `surface' of the Sun where radiation produced by nuclear reactions is last scattered by the solar material. The energy source for the Sun's photons is not in the photosphere: it comes from nuclear fusion at the centre of the Sun. Similarly, the CMB photons were not created at the surface of last scattering: they were produced at a much earlier epoch in the evolution of the Universe. A tiny fraction (about one in a billion) of these photons, however, were created by recombination transitions at the last scattering surface. There should therefore be very weak emission lines in the black-body spectrum of the CMB radiation, but none has yet been detected.

Some interesting properties of the last scattering surface are illustrated in the Figure overleaf. Here, space is represented as two-dimensional. The time t since the Big Bang is the vertical axis; T is the temperature of the CMB and z is the redshift (for simplicity, the expansion of the Universe is ignored). The plane at the top corresponds to the Universe now. As stationary observers we move through time (but not space), and we are now at the apex of the cone in the Now plane. When we look around us into the past, we can see only photons on our past light cone. CMB photons travel from the waxy circle in the last scattering surface along the surface of the light cone to us. The unevenness of the circle represents temperature fluctuations at the last scattering surface. The bottom two planes are at fixed times, while the Now plane moves upwards. As it does, the size of the observable Universe (the diameter of the wavy circle) increases. The object which emitted light at C is currently at C', and the light emitted at C is currently entering our telescopes at the apex of the cone. Points A and C are on opposite sides of the sky. If the angle between B and C is greater than a few degrees, then B and C have never been able to exchange photons with each other, so they cannot even know about each other at the time of last scattering. How can it be that their temperatures are the same? This is the essence of the cosmological horizon problem, and was one of the motivations for the inflationary Universe theory.

Last scattering surface. The last scattering surface represented as a flat sheet. The expansion of the Universe is ignored in this diagram.