1.10 Summary and questions
The Universe was created at the instant of the Big Bang. As it has aged, the Universe has cooled and distances within it have increased. At the earliest times, the four fundamental interactions were unified, but as the temperature of the Universe decreased, so these interactions became distinct.
The earliest time about which anything can be said is the Planck time, when the gravitational interaction had a similar strength to the other fundamental interactions. Before this, the concept of 'time' itself may have no meaning.
Early in its history, the Universe is presumed to have undergone an extremely rapid period of expansion, known as inflation. One effect of this was to smooth out any irregularities, leading to today's remarkably uniform observable Universe.
The early Universe contained almost equal numbers of matter and antimatter particles (quarks and leptons). However, there was an asymmetry of a few parts per billion in favour of matter. The matter and antimatter underwent mutual annihilation and the result of this is that there are now about 109 photons for every matter particle in the Universe.
Equal numbers of protons and neutrons were initially produced in the Universe from the up and down quarks remaining after annihilation. However, free neutrons decay, and this reduced their number, leading to a Universe containing about seven protons for every neutron today.
All free neutrons were soon bound up within nuclei of deuterium, helium and lithium. The approximate distribution of mass in the Universe is about 25% helium-4 to 75% hydrogen, with small traces of other nuclei.
Neutrinos ceased to interact with the rest of the Universe soon after protons and neutrons were formed.
At 300 000 years after the Big Bang, when the temperature was about 3000 K, photons produced from the matter-antimatter annihilations had their last interaction with the matter of the Universe. These photons, redshifted by a factor of a thousand by the expansion of the Universe, form the cosmic microwave background that is observed today.
As the Universe cooled still further, galaxies and stars were able to form under the influence of gravity. Stars process light nuclei into heavier ones within their cores. The more massive stars then undergo supernova explosions, throwing material out into space ready to be included in later generations of stars and planets.
Figure 4, repeated above shows how top and bottom quarks can decay into bottom and charm quarks, respectively. Following the patterns shown there, draw Feynman diagrams to represent: (a) the decay of a charm quark into a strange quark, and (b) the decay of a strange quark into an up quark.
Feynman diagrams for these decay processes are shown in Figure 8.
(a) Figure 8a shows the decay of a charm quark into a strange quark and a W+ boson, which in turn decays into a positron and an electron neutrino.
(b) Figure 8b shows the decay of a strange quark into an up quark and a W− boson, which in turn decays into an electron and an electron antineutrino.
Imagine a hypothetical Universe in which weak interactions do not exist and in which only first-generation quarks and leptons are present (i.e. there are no charm, strange, top or bottom quarks, and no muons, muon neutrinos, tauons or tauon neutrinos). Speculate about the ways in which such a Universe would be different from our own. Your answer should be no longer than about 100 words.
If weak interactions did not exist in the hypothetical Universe, and if only up quarks, down quarks, electrons, electron neutrinos and their antiparticles were initially present:
Conversions between protons and neutrons would be impossible.
As protons cannot convert into neutrons, there would be no proton-proton chain of nuclear fusion in stars (including the Sun).
As primordial neutrons cannot convert into protons, there would be equal numbers of protons and neutrons in the Universe.
As there are equal numbers of primordial protons and neutrons, these would all combine (eventually) to form nuclei of helium-4. Consequently there would be no hydrogen in the Universe.
As there is no hydrogen in the Universe, there would be no water, no organic chemicals, and therefore no life as we know it.
In addition to the 'barrier' at a mass number of eight, there are also no stable nuclei with a mass number of five. Using the building blocks available in the early Universe, what nuclei could you combine to try to create a nucleus with a mass number of five?
In principle, you could combine with , or you could combine a proton with . Both of these would give a nucleus consisting of three protons and two neutrons: . (In practice this is unstable as it has too many protons, and splits apart into plus a proton.) Alternatively, you might try adding a free neutron to a nucleus to make . (However, this too is unstable as it contains too many neutrons, and splits apart.)
(a) Describe three times or sites at which nucleosynthesis has occurred in the history of the Universe.
(b) At which of these times or sites did most of the (i) helium, (ii) oxygen, and (iii) uranium in the Universe originate?
(a) Nucleosynthesis — the formation of nuclei — occurred in the early Universe, between about 100 and 1000 seconds after the Big Bang. During this epoch, only low-mass nuclei, such as deuterium, helium and lithium were formed. A second site for nucleosynthesis is in the heart of stars, such as the Sun. Here, hydrogen undergoes nuclear fusion to form helium, and later on helium can fuse to form carbon, oxygen, silicon and other (relatively) low-mass nuclei. In fact, most nuclei below a mass number of about 62 (nuclei up to iron, cobalt and nickel) can form in the heart of stars in this way. Finally, nucleosynthesis can occur at the end of a star's life during a supernova explosion. In this process, many nuclei more massive than iron are formed and thrown violently out into the Universe, where they can be incorporated into future generations of stars and planets.
(b) (i) Most of the helium nuclei were formed during the primordial nucleosynthesis, soon after the Big Bang.
(ii) Most of the oxygen nuclei were formed in the heart of stars.
(iii) All the uranium nuclei were formed as a result of supernova explosions.
In which order did the following events occur in the history of the Universe? (Hint: Consider the energy required for each process.)
the formation of atoms
the formation of light nuclei
the formation of quarks and leptons
the formation of protons and neutrons
the annihilation of electrons and positrons
the annihilation of quarks and antiquarks
neutrinos cease to interact further with matter or radiation
background photons cease to interact with matter
Perhaps the simplest way to decide in which order a sequence of events occurred is to think about the energy required for each process. If the processes are then arranged in descending order of energy, they will automatically be in a time-ordered sequence.
Clearly, the formation of the fundamental constituents of matter, quarks and leptons, require the most energy of these processes. This event must have occurred first. Next, as the energy dropped, quarks and antiquarks would have mutually annihilated, leaving behind the relatively few residual matter particles from which to construct the material content of the Universe. Protons and neutrons form next, from the residual quarks. When neutrinos cease to interact with matter, the equilibrium conversion between protons and neutrons effectively stops. After this, the electrons and positrons mutually annihilate, leaving relatively few electrons to balance the charge of the protons. From this point on, light nuclei are able to form from the protons and neutrons available. Atoms form next from the nuclei and electrons that now constitute the matter content of the Universe. Finally, background photons interact for the last time with matter when the Universe is about 300 000 years old.
The sequence of the processes listed in the question is therefore:
formation of quarks and leptons
annihilation of quarks and antiquarks
formation of protons and neutrons
neutrinos cease to interact with matter or radiation
annihilation of electrons and positrons
formation of light nuclei
formation of atoms
background photons cease to interact with matter
Summarise the contents of the Universe at the times corresponding to the end of each of Sections 2 to 7.
A summary of the contents of the Universe at the times indicated is shown in Table 1.
Table 1 The contents of the Universe at various times.
|Section||Time/s||Contents of the Universe|
|2 The very early Universe||10 −36||Six flavours of quark, six flavours of lepton, X bosons, photons (and presumably gluons, gravitons, W and Z bosons too).|
|3 Inflation||10 −32||The same as above, except that X bosons had largely disappeared.|
|4 The quark-lepton era||10 −5||Up and down quarks, electrons, positrons, neutrinos and antineutrinos, photons.|
|5 The hadron era||100||protons, neutrons, electrons, neutrinos and antineutrinos, photons.|
|6 Primordial nucleosynthesis||1000||Mainly hydrogen and helium-4 nuclei; traces of deuterium, helium-3, and lithium-7; electrons, neutrinos and antineutrinos, photons.|
|7 Structure in the Universe||today||Galaxies, stars, gas and dust (all of which are made of atoms, the vast majority of which are hydrogen and helium); photons (cosmic microwave background) fill all space; neutrinos and antineutrinos still present but almost undetectable.|
What are the three key pieces of observational evidence that support the idea of a hot big bang? Which of them do you think allows cosmologists to reach back furthest into the past, and why?
The three key pieces of observational evidence for the hot big bang are:
the Hubble relationship linking the speed and distance of distant galaxies;
the cosmic microwave background radiation;
the relative abundances of helium, lithium and other light elements.
The first galaxies formed when the Universe was at least a few hundred thousand years old, and possibly much later. So, in theory, observations of distant galaxies only allow cosmologists to reach back this far in time.
The cosmic background radiation last interacted with matter when the Universe was about 300 000 years old. So observations of it only let cosmologists investigate conditions at that epoch.
It is the relative abundances of the light elements that allow cosmologists to reach back the furthest. These elements were formed when the Universe was between 100 and 1000 seconds old, and the reactions that created them were sensitive to things like the ratio of neutrons to protons, which were determined even earlier.