Lecture 22

Cosmology

How big is the Universe? Is it in a steady state or is it continuously evolving? And if it is evolving, how did it start and will it ever end? These and other questions are addressed by cosmology, a branch of science that has developed over the last few decades, thanks to the most recent discoveries in the fields of Astrophysics and Elementary Particle Physics.

Discovery of Galaxies

Modern cosmology owes a lot to the pioneering work that Edwin Hubble (in whose honour the orbiting telescope is named) performed at the California Mount Wilson telescope. The first of Hubble's major achievements was to realize that some not well identified fuzzy objects in the sky, until then referred to as nebulae because of their "nebulous" (i.e. cloudy) appearance, were in fact clusters of millions and millions of stars. By identifying a Cepheid variable in one of these clusters, Hubble was able to estimate its distance as a few millions of light years away, and in so doing he opened a new window on the dimensions of the Universe.

The discovery of these stellar clusters also confirmed that our own sun and planetary systems belong to one such clusters.

For a long time it had been known that most of the visible stars could be located within distances of up to about 100,000 light years from the sun, whose location was in fact somewhere at the periphery of this large star cluster. The fuzzy luminous band you can see, more or less overhead, on a clear night, known from the days of antiquity and named the Milky Way, is what our eye sees when looking towards the region of higher star density in our cluster. Hubble's observations were the first step towards the realization that the Universe contains millions and millions of such clusters, each one containing millions or billions of stars. By extension from our own Milky Way, all such clusters were called galaxies, from the greek word for milk.

Hubble's Law and the Big Bang

The next of Hubble's achievements had extremely far reaching implications and, even though it can be presented in extremely simple terms, it provided the seed for a complete new vision of the Universe,

As we have mentioned a few times, the frequency (or wavelength) of a wave appears to be different when source and observer are in motion with respect to each other. If the frequency of the wave corresponding to source and detector being at rest is known, then the measured change in frequency (the "Doppler Shift") can be used to determine the speed at which the source is moving. This effect has been exploited in several applications (meteorology, highway patrol radar, etc.).

The same phenomenon, when applied to stars or galaxies, can determine whether a given celestial body is moving away or towards us, and at what speed. Let us remember that any given chemical element emits a well defined set of spectral lines which are unique to that element. If we now look at the emission spectrum from a star, and measure the frequency of the observed lines, we should expect that the frequencies will increase, i.e. they will be blue-shifted, if the object is moving towards us, while they will decrease, or be red-shifted if it is moving away.

Hubble's comprehensive collection of data on all the visible galaxies whose distances could be determined, yielded the following results:

1.

the more distant a galaxy is from us, the larger is the measured value of its velocity. More specifically, the ratio of velocity to distance has a more or less constant value : d/v = H, where H is the Hubble Constant.

2.

all observable galaxies exhibit a marked red-shift, i.e. they are all receding away from us

You might think that the first statement is rather obvious, but this is not necessarily the case for any possible type of universe configuration. Before Hubble, one possible way of imagining the universe was to compare it to a a volume of hot gas, with particles (i.e celestial bodies) moving randomly in all directions. In such a picture, you would expect that some bodies would be moving towards you and others away from you, and even a nearby body could be happening to have a high velocity.

A small amount of reflection should convince you that Hubble's findings lead to only one possible interpretation: the universe is in a phase of expansion, with its material bodies flying apart from each other, just like the fragments of an exploded bomb. The next necessary inference is that, if we were to run the motion of galaxies backwards in time, they would all come together to a point: this inference is the base of the hypothesis that our observable universe originated from an explosion of unimaginable intensity, the Big Bang. Another consequence of such a picture is that, at the moment of the Big Bang, all of the matter and energy constituting the present universe were all concentrated in one point!!

The argument can be made even more quantitative : from the knowledge of the distance of a given galaxy and of its velocity relative to our own galaxy, we can deduce for how long the two galaxies have been flying apart, through the obvious expression

distance = velocity x time, i.e. time = distance / velocity

Inserting the measured values of distance and velocity, and assuming that the rate of expansion has remained constant throughout the life of the universe, we get for the time an average value of 10¹⁰ (or ten billion) years : this is then the age of the universe !!! Remembering the definition of Hubble Constant, it is straightforward to show that the age of the universe is given by the inverse of H: age of the universe = 1/H.

Cosmic Radiation Background

Is there any other evidence, apart from the distance-velocity correlation, to support the theory of the Big Bang? The answer is yes, even though the most compelling corroboration was found almost by chance. In the mid 60's, two scientists at the Bell Labs were investigating possible source of disruption for radio and TV communication via satellites (the goal of their research was obviously oriented towards commercial applications). In the course of their measurements, they observed a homogeneous background of radio signals, with frequencies falling in the microwave range. Such a radiation appeared to have an extra-terrestrial origin, and, as it was observed to arrive with the same intensity from every possible direction in space, it could not be attributed to a single or a set of a few celestaial objects.

The explanation was offered by scientists working in a field completely removed from the Bell Lab researchers. According to the theoretical descriptions, the Big Bang involved a conflagration of both matter and energy. While the matter eventually congregated to form galaxies, stars, etc., the (electromagnetic) energy would gradually "cool down", the same way that a hot body will gradually decrease its temperature if left to itself.

When discussing the stars' temperature, we had stated that there is a unique correspondance between the temperature of a body and the spectrum of wavelenghts it will emit.

In the model of the Universe cooling down, over billions of years, after the Big Bang, cosmologists had estimated that the hot energy from the Big Bang should have cooled down to a temperature around 3 degrees Kelvin. It was a big moment of discovery when it was realized that the background radiation observed by the Bell scientists matched perfectly the spectrum corresponding to the emission from a body a 3 K !!

The observation of a uniform backround radiation, while it supported the Big Bang theory, left unanswered a rather fundamental question about the structure of the Universe. While it was logical to expect a very homogeneous distribution of energies, as it came from the explosion of an original state where no preferential direction existed, how could this be reconciled with the fact that the matter distribution in the Universe is far from being homogeneous, but it consists of large clumps of matter interspersed among huge "inter-galactic voids" ? We do not yet have a fully satisfactory answer to this question, but more detailed investigations of the cosmic background have revealed the presence of inhomogeneities in the radiation itself. Thanks to extremely precise measurements performed by the Cosmic Background Explorer, a satellite launched specifically for the purpose of performing such measurements, some minute inhomogeneities were detected in the otherwise uniform field of radiation. It is then rather natural to associate these "hotspots" with the regions of higher density, where the conglomeration of matter into what was eventually to become galaxies could take place in the earliest stages of the universe evolution.

The First Three Minutes

We believe that the Laws of Physics we have discovered are universally applicable at any point in space and time. Using our knowledge of the behaviour of elementary particles under conditions of extremely high temperatures (i.e. energy) we can model the sequence of events that took place even in the earliest stages of the Big Bang. As extreme as it might sound, we can attempt to describe what happened in the first fractions of seconds of life of the newborn universe. Even though we cannot describe in detail every feature, we can correlate our knowledge of the behaviour of particles at a certain energy with the instant in time at which that energy was the average one carried by the particles in the infant universe.

As discussed when learning about elementary particles, it is believed that in conditions of extremely high energies the four forces of nature, gravity, electromagnetism, weak and strong, are not distinct but a single unique force. As the energy decreases, Gravitation is the first force to go off on its own way, to be followed by the Strong Force. It should be pointed out anyway that we still do not have a satisfactory theory describing the "Unified Force", nor we are in the condition to perform experiments at energies as high as those corresponding to the unified situation. Our inferences on what happened at the very beginning remain therefore at the level of speculations.

Another open question, that neither theory nor experiment have yet been able to answer in full, is why the universe appears to be consisting purely of matter, with no appreciable presence of antimatter. If it all started with a huge blob of pure energy, our knowledge tells us that matter and antimatter would have been created in equal amounts. When the temperature of the young universe was cool enough to allow the irreversible annihilation of matter with antimatter to take place, all matter and antimatter should have annihilated with each other, and we wouldn't be here to wonder about it.

In spite of what the book says, this problem does not yet have a fully satisfactory answer. Even though a set of necessary and sufficient conditions to generate a matter-antimatter asymmetry has been put forward, there is not yet clear experimental evidence that such conditions do occur in the realm of elementary particles. Research in this field is actively pursued by several physicists, including the UVa High Energy Physics Group.

Extrapolating from our knowledge of the relative strenghts of the forces and their variation as a function of energy, we can infer that gravity and the strong force acquired their distinct individuality at times of respectively 10^-43 and 10^-35 seconds from the start of the Big Bang.

By the time we reach 10^-10 seconds, we can move on firmer ground, since our deductions can be supported by both successful theories and experimental evidence. From this instant onwards, an observer of the Big Bang would have witnessed that the matter of the universe, still concentrated in a microscopic volume of unimaginably high density, consisted mainly of a quark and lepton "primordial soup". This stage would have been followed, at about 10^-5 seconds, by the coalescing of the quarks to form protons and neutrons, and eventually, after a "three minute eternity", the average energy of the particles would have been low enough to allow the formation of light nuclei, mainly Deuterium, Helium and Lithium. The measured relative abundance of such nuclei in the inter-galactic space is another rather strong corroboration of the Big Bang theory. After the nuclei formation, no other major events took place and the further growth of the universe became rather boring.

Big Crunch vs. Big Chill

How will it all end? We have compelling evidence that the Universe is expanding , but we can ask ourselves whether such expansion will continue indefinitely. A reliable answer could be given if we had a better knowledge of the total amount of matter contained in the Universe.

Even though the universe is currently expanding, this expansion is driven by inertia, since, we believe, there is no intervening force re-fueling the outward motion. On the other side, gravity exerts a continuous pull on all matter, tending to bring it back together. One can then envisage two possible scenarii :

1.

on the one side, if the density of matter in the universe was below a certain value, it would not be enough to bring the expansion to a halt. The Universe would continue to expand, gradually cooling down in the process. This is the Big Chill scenario

2.

on the other side, larger values of total matter in the universe could succeed in stopping the expansion and start a process of contraction (the same way that a ball thrown into the air will eventually come to a stop and start falling backwards). In this scenario, gravity would eventually bring together all the matter of the universe, ending up with a catastrophic Big Crunch !!

Within our present level of knowledge, we cannot make firm predictions, since we have become aware that we do not know for sure how much matter there actually is in the universe. Indications for the existence of large quantities of yet unseen matter, the so called dark matter are becoming more and more compelling, but we do not yet have the final answer.