When did the Big Bang Occur?

  There are many ways to determine when the origin of the universe occurred.  The one we have previously discussed is through using the Hubble time.  However, the Hubble time approaches the actual age of the universe only if the density of the universe is much less than the critical density.  The Hubble Time becomes the upper limit to the actual length of the time that the universe has been expanding.  Although the value of Hubble’s constant is somewhat uncertain as well, it is quite likely to be in the range between 50 and 100 km/s/Mpc.  These values for Hubble’s constant yield a Hubble time between 10 and 20 billion years respectively.  Recent Hubble Space Telescope observations yield a Hubble time of 12 billion years and a Hubble constant of 80 km/s/Mpc.

  Another means for estimating the age of the universe comes through finding and dating the oldest objects it contains.  This method provides a lower limit on the age because the universe must be older than the oldest object.  The oldest objects in the vicinity of the sun are white dwarf stars.  Because these white dwarfs dim with age, the less luminous the stars are, the older they must be.  These stars seem to have a maximum age of about 10 billion years.  However, these stars lie within the galactic plane and could not have been formed until out galaxy had assumed its current structure, meaning the galaxy could be much older.  Farther from the sun are the globular clusters that are probably as old as the galaxy itself.  Analysis of the stars contained within these clusters indicates they must be at least 15 billion years old.  Therefore, the universe needs to be older by the amount of time required for galaxies to begin to form after the expansion of the universe began.

  Another way to determine the age of the universe is to ascertain the amount of time required for radioactive elements in the solar system and nearby stars to have decayed to their present abundance.  This method is complicated by the need to know the rate at which radioactive materials have been formed within stars and supernova explosions since the galaxy formed.  However, studies involving different elements conclude that between 10 to 15 billion years were needed to establish current concentrations.

  Therefore, these disparate means for estimating the age of the universe agree that it began between 10 billion and 15 billion years ago.  Although this is just an estimate, there does seem to be a serious problem with a Hubble time of 10 billion years resulting from a Hubble constant of 100 km/s/Mpc.  Even a Hubble time of 20 billion years might be a problem is the average density of the universe is near its critical density.  In that case, the universe would only be 2/3 of the Hubble time, or 13 billion years old.  If the recent Hubble Space Telescope’s result of a Hubble constant that is 80 km/s/Mpc is correct, and the density of the universe is equal to the critical density (which many astronomers believe to be the case), then the actual age of the universe if 2/3 that of 12 billion years or only 8 billion years.  This would imply that something is seriously wrong with our ideas about the evolution of stars, or there is a fundamental problem with our understanding of how the universe evolved.

  Time Course of the Big Bang

  There are two aspects of the Big Bang that need to be considered.  First, during the initial instants after the Big Bang, there were extreme densities and temperatures present in the matter that spontaneously was created.  These properties of the initial universe imply reactions and changes occurring at tremendous rates.  Even a tiny length of time meant tremendous changes in the universe.  Second, it is necessary to understand that as time lengthened, the rate at which changes occurred reduced significantly.

  The First Second.  One microsecond after the creation of the universe the temperature was about 10 trillion degrees K – about a million times hotter than the center of the Sun.  The glow of radiation would have been intense and uniform in all directions, and there would have been a bright fog that limited vision to a small fraction of a centimeter.  The high-energy gamma rays that made up most of the radiation at that time were so energetic that they were capable of pair production.  Pair production is the production of matter from energy whereby the collision of two photons yields a particle and its antimatter counterpart.  Therefore, one set of products of pair production is an electron and a positron (which is as massive as an electron but has a positive charge).  Other possible pairs would be a neutrino and an antineutrino, and many others.  Pair production is one of the most spectacular consequences of Einstein’s famous equation; E=mc2.  For two photons to produce a pair of particles, these photons must have energy at least equal to mc2, where m is the combined mass of the particle and antiparticle, and c is the speed of light.  A microsecond after the universe began, the gamma ray photons present had sufficient energy to produce protons, neutrons, electrons and their antiparticles.

  However, at the same time that this pair production was occurring, there was simultaneous annihilation of these pairs.  This occurs when a pair and its antiparticle collide and disappear in a burst of radiation.  Annihilation is the opposite of pair production and converts matter back into energy.  Thus, during this time period, the entire universe was a dense mixture of radiation and matter.  Pairs of particles appeared from nowhere, and then instantly disappeared again in a flash of gamma radiation.

  As the universe gradually grew older, temperatures decreased and the energy of photons decreased as well.  After the first microsecond, the gamma rays that dominated the universe would have lacked sufficient energy to product proton antiproton pairs, or neutron, antineutron pairs although less massive electron, positron pairs could still be produced.  However, although protons and neutrons could no longer be made, they continued to annihilate with their antiparticles destroying most of the matter that had been build up from the radiation during the first microsecond.  By the time the universe was one second old, the temperature had dropped to about 10 billion K.  At this time, the photons present lacked sufficient energy to make even electrons and positrons so pair production ceased entirely.  The annihilation of electrons and positrons continued to occur, however, thereby reducing the abundance of these particles in the universe as well.

  One consequence of this massive production of matter and its destruction is the production of large amounts of neutrinos that became abundant in the early universe (as they are today).  Neutrinos interact only very weakly with matter and are very difficult to detect.  At the high density of the initial universe before it was 1 second old and with the large abundance of electrons and positrons, neutrinos interacted often enough with electrons and positrons that they were coupled to the matter in the universe.  Neutrinos traveled only short distances between interactions with matter due to the tremendous densities involved.  However, after about 1 second from the Big Bang, the frequency of these interactions between matter and neutrinos was decreasing extremely rapidly.  After one second, neutrinos stopped interacting with the rest of the universe and the neutrinos that existed at that time have traveled freely through the universe moving at or near the speed of light.  Only an insignificant number of these neutrinos have ever interacted with matter again.  There are about 1 billion primordial neutrinos in every cubic meter of the universe, and about 10^18 of them pass through us every second.  There is no danger, however, of this truly massive number of neutrinos passing through us since the probability of them interacting with our matter is so tremendously small.

  Formation of Helium.  One second after its formation, the universe was a seething sea of high-energy radiation (gamma rays and X-rays) with a small number of neutrons, protons, and electrons.  Neutrons are slightly more massive than protons, can be produced by the reaction of a proton and an electron.  Neutrons, however, spontaneously decay into an electron and proton with a half-life of 13 minutes.  The interaction between electrons, protons, and neutrons resulted in one neutron being produced for every five protons.  The protons and neutrons continually collided with each other and reacted to form deuterons – hydrogen nuclei containing a proton and a neutron.  At first, deuterons could not survive das they were constantly bombarded by photons that had sufficient energy to turn them back into protons and neutrons again.  Not until about 100 seconds after the Big Bang did the temperature drop to 1 billion degrees K did the energy of a typical photon decline to the point where it could no longer break apart a deuteron.  After that time, the abundance of deuterons climbed swiftly.

  Deuterons react quickly with protons to initiate a series of dozens of other nuclear reactions that led to more massive nuclei.  For about 200 seconds, the temperature of the primordial universe remained high enough to sustain these nuclear reactions to change the chemical makeup of the universe from that of entirely hydrogen, to that of a more complex mixture including protons, deuterons, two isotopes of helium, and small amounts of lithium and beryllium.  One of the most important clues about the beginning of the universe is the relative abundance of these elements in primordial material that has not been incorporated into the nuclear furnaces of stars.  If the density of protons and neutrons were very high at the time the nuclear reactions in the big Bang began, then the rate of nuclear reactions would similarly have been quite high.  One consequence would have been the almost complete consumption of deuterons.  Alternatively, if the density had been very low, then there would not have been enough time for deuterons to be entirely consumed or for 3He to be entirely used up to make 4He. 

  Astronomers have been able to discover the primordial abundances of these chemicals by examining the spectra of very old stars.  These studies demonstrate that 4He makes up 24% of primordial matter, 3He makes up about 1 part in 10,000, deuterium makes up about one part in 100,000, and 7Li about one part in 1,000,000,000.  These are the kind of abundances that would have been produced from a low-density environment rather than a high-density environment.  The most probable value of the density of the universe at the time nuclear reactions were taking place was only a few percent of the critical density.  Thus, the abundances of the isotopes produced during the first few minutes of the Big Bang indicate that matter in the form of electrons and nuclei falls far short of providing the self-gravity required to produce a positively curved, finite universe.  However, there might still be other “exotic” forms of matter that were formed in those few minutes which still might produce a critical density and which might still influence the shape and destiny of the universe.

  The Radiation Era.  Radiation dominated the early universe, from the first few minutes after expansion began and for several thousand years later.  Thus, if the radiation energy of a cubic meter of space could be represented by E = MC2, it would have had a density larger than that of matter.  This state in the development of the universe is known as the radiation age.  During this era, the universe was still too hot (1 million degrees K after the first few years) for atoms to be stable.  Therefore, whenever an electron and a proton combined to form an atom of hydrogen, the atom was almost immediately torn apart by an energetic photon (radiation).  The gas in this early universe was also very opaque because free electrons are very efficient at absorbing and scattering radiation.  The light in the universe never got very far from its source before it was destroyed or scattered again.  Therefore, a bright mist through which it was impossible to view anything more than a few centimeters away would have surrounded a theoretical observer within this universe.

  Things would have gradually improved with time, however, as the temperature of the universe gradually subsided.  Collisions among elemental particles became less violent, and the radiation that flooded the universe gradually changed from gamma rays and X-rays (radiation which was high energy, very high frequency with short wavelengths), to ultraviolet and even visible light (with much lower energy and much longer wavelengths).  The surrounding mist became dimmer and redder as time went on, and the distance through which it was possible to see gradually increased.  Furthermore, the relative importance of matter and energy changed, whereby the density of radiation was falling faster than the density of matter as the expansion continued.  A few hundred thousand years after expansion started, when the temperature of the universe had fallen to a few thousand degrees Kelvin, two events happened almost simultaneously.  First, mater began to dominate the universe, and secondly the universe quite suddenly became transparent!

  Clearing of the Universe.  The universe changed from opaque to transparent because the temperatures became low enough for atoms to survive.  Collisions and radiation that had previously torn atoms apart now no longer had sufficient energy to do so.  Therefore, electrons were captured by protons that made stable hydrogen gas.  Atoms absorb and scatter radiation much less efficiently than free electrons and therefore, radiation could not be absorbed or scattered as soon as it produced.  Light and other forms of electromagnetic radiation could therefore travel through space almost indefinitely and with almost complete freedom – light could travel through space without being destroyed by matter.  The moment when light was liberated from matter is called the decoupling epoch or the recombination epoch, because electrons and nuclei combined to form atoms. 

  The decoupling epoch also has special significance for our efforts to explore the universe by looking farther and farther out into space, because all light emitted prior to the decoupling epoch was destroyed.  Therefore, it is impossible to study the first few hundred thousands years of the history of the universe using electromagnetic radiation.  In contrast, nearly all the radiation emitted during and after the decoupling epoch is still present in the universe.  Indeed, by looking far enough into space it is possible to see the glowing gas that made up the universe at the time that radiation broke free from its matter jailers.  The discovery of that glow called the cosmic background radiation was one of the most important discoveries of the last century.

  Cosmic Background Radiation

  Like so many fundamentally important discoveries, the cosmic background radiation was found by accident.  By the time of its discovery, however, its general properties had been understood and worked out for about a decade.

  What should the cosmic background radiation look like?  The cosmic background radiation is the electromagnetic radiation emitted by the universe at the epoch of decoupling.  At that time, the universe had a temperature of about 3000 degrees Kelvin, so the radiation was visible mostly in the visible and infrared parts of the spectrum.  However, to see the cosmic background radiation, we need to observe the universe as it was only a few hundred thousand years after expansion began; therefore, we need to use a telescope as a time machine and look backward nearly to the beginning of the universe.

  The farther we look into space, however, the greater the redshift we observe because it is traveling faster and faster away from us.  To see far enough to observe the cosmic background radiation, we need to view parts of the universe that have a redshift of about 1000.  This means that the cosmic background radiation has 1000 times the wavelength it had when it was emitted.  To detect it, infrared and radio telescope are needed rather than optical telescopes.  Instead of showing the spectrum emitted by the universe when its temperature was 3000 degrees K, the radiation appears today with a spectrum characteristic of a body with a temperature of 3 degrees K.

  The cosmic background radiation is not to be observed in only one particular direction, but rather it should be visible in all directions.  More specifically, it should be visible in any direction in which we can look outward to a redshift of 1000.  A like that which would be emitted by a blackbody with a temperature of about 3 degrees K should be seen In any direction of the sky that has not been blocked by foreground objects.  The cosmic background radiation formed by the decoupling of matter that formed our galaxy left our galaxy billions of years ago at the speed of light and now forms the background radiation for other imaginary observers in remote parts of the universe.

  Discovery of the Cosmic Background Radiation.  George Gamow and other astronomers first determined that the universe derived from the Big Bang was initially extremely hot.  They also predicted that the radiation surviving from the early universe would have a temperature now of between 5 and 50 degrees K – but made no effort to look for it.  A team of astronomers at Princeton University refined the calculations in 1964 and concluded that the surviving radiation would have a temperature of only a few kelvins.  They began to build a telescope to look for it.

  However, before these Princeton University astronomers could complete their experiments, Arno Penzias and Robert Wilson of the Bell Telephone Laboratories in New Jersey found the cosmic background radiation.  They used a small antenna that had been originally built for satellite communications.  Although they had carefully built and tuned their telescope to account for many sources of noise, including that of the Earth’s atmosphere, the Sun and the Milky Way, they were unable to explain a source of noice that seemed to be coming at them from all directions and to be of uniform strength.  They consulted a colleague who was aware of the work being done at Princeton University.  When Penzias and Wilson talked with these astronomers, the two groups realized the source of the radiation was the cosmic background radiation.  Since its original discovery in 1964, the entire spectrum of this radiation has been measured and found to correspond to those of a blackbody with a temperature of 2.74 degrees K.

  Isotropy of the Cosmic Background Radiation.  Penzias and Wilson found the background to be of isotropic brightness; that is, its brightness is nearly the same in all directions.  Until 1992, the motion of the solar system with respect to the cosmic background radiation produced the only departure from perfect isotropy that had been found.  The Doppler shift resulting from that motion made the radiation appear to be hotter and brighter by about 0.1% in the direction toward which the solar system is moving compared with the opposite direction.  This finding was of tremendous significance because it indicates that the structure of the early universe at the time of decoupling must have been remarkably uniform.  Before that time, photons, which dominated the matter of the universe, were capable of pushing matter around thereby preventing significant slumping from taking place.  Still, there must have been some irregularities in the early universe to account for the subsequent production of structure such as galaxies.  A satellite launched in 1992 (COBE – Cosmic Background Explorer) explored the background radiation in order to more precisely determine its homogeneity and whether there were variations that might explain subsequent structure of the universe.  The satellite discovered fluctuations of 6 parts per million which are just barely great enough to be consistent with the observed clustering of matter after the epoch of recombination.  Within about 1 billion years after this epoch, the matter in the universe collected in large concentrations that eventually became galaxies and clusters of galaxies.  However, in the standard model of the Big Bang, it is difficult to explain the origin of the fluctuations that are present at the time of decoupling.

  Inflation

  The standard model for the Big Bang is not without its difficulties despite its tremendous success in explaining the origin of the universe.  To overcome these difficulties, cosmologists have developed a modification of the standard Big Bang model in which the early universe underwent a brief period of extremely fast and enormous expansion.  This expansion process is called inflation.

  Problems with the Standard Big Bang Model.  There are three difficulties with the standard model of the Big Bang.

·         The Horizon Problem.  The cosmic background radiation comes to us from opposite regions of the universe that are very distant from each other.  These regions were 1000 times closer at the time of decoupling when the background radiation originated; still, they were many millions of light years apart at that time when the universe was about 300,000 years old.  Nothing, not even light, could travel from one extreme region of the universe to the other during the history of the universe up to that time.  There was no way that either region could have ever received any information regarding another region of the universe that was millions of light-years away during the 300,000 years that the universe existed.  If one of the regions of the universe were hotter than the other extremely far away region, there would not have been time for energy to flow from the hottest region to the cooler region to equalize the temperature between the two regions.  The horizon problem then is how did the temperature and density from such distant regions of the universe at the decoupling time become equilibrated?  In the standard Big Bang model, there is no explanation for this difficulty.

·         The Flatness Problem.  It is the opinion of most cosmologists that the average density of the universe is very near the critical density meaning the universe is very close to being very flat.  Certainly, the average density of the universe relative to the critical density is somewhere between 0.1 and 2.  This is remarkable because there was a strong tendency during the early history of the universe for curvature to grow.  If the early universe had been precisely flat, then it would have remained flat for all time.  Taken a step farther, for the average density of the universe today to be so close to critical density, it must have been even closer during very early stages of the universe.  Thus, the value of the average density of the universe one second after expansion began must have been different from critical density by only one part in 10^15!  Earlier than one second after the expansion began the average density would have to be equal to critical density by even a greater accuracy.  The standard Big Bang model cannot explain the extreme flatness of the current universe.  It would rather seem reasonable that the initial average density of the universe could have been very different from critical density, leading to a universe of either extremely positive curvature or extremely negative curvature.  There is no way to determine why this did not happen with the standard Big Bang model.

·         The Structure Problem.  Even though the universe is extremely homogeneous in all directions on both temperature and density in very large details, the current universe is very heterogeneous on small details such as the stars of clusters and galaxies.  This irregular structure currently observed today is due to the small irregularities that were present in the universe at the time of its decoupling from energy.  The question that arises is how did this structure originate?  There is no way to account for this structure based upon the standard models of the Big Bang theory.  Instead, according to the original theory these irregularities must have been present from the very beginning of the Big Bang. 

The standard model of the Big Bang theory can only explain these three difficulties by noting that it just happened without any reason.  However, they can all be explained as a natural result of the period of inflation in the very early universe.

  The inflationary model for the early universe posits that starting about 10^-34 second after expansion began, the rate of expansion increased rapidly with time.  Thus, during the next 10^-34 second, the universe doubled in size and continued to double in size during succeeding 10^-34 seconds until the inflationary epoch ended at a time of about 10^-32 second.  There were 100 doublings in size of the universe contained within this expansionary time of 10^-32 seconds.  Thus, while inflation was going on, the universe grew in size by at least a factor of 10^25 and perhaps much more depending on exactly how long the inflationary period lasted.

  The inflationary model easily explains the horizon problem.  The region from which we currently receive the cosmic background radiation was once extremely small just before inflation began.  The region was small enough so that there had been enough time for energy to flow from one portion of the universe to the other and make the temperature uniform throughout.  During inflation, this very tiny universe was then expanded to become the entire part of the universe we see today.  Therefore, the uniformity of the background radiation was established before inflation began when the entire region was much smaller than the nucleus of an atom. 

  Similarly, the inflationary model solves the flatness problem too.  During inflation, the curvature of the universe was rapidly driven toward flatness in much the same way that a balloon is driven toward flatness when it is inflated.  As the balloon gets larger and larger, it appears more and more flat to a small imaginary observer on its surface.  As the universe expanded, it too became flatter and the mean density approached the critical density.  In fact, the mean density became so nearly equal to one at the end of the inflationary period that they should still be the same to 1 part in 10,000.  Indeed, if it could be established that the mean density of the universe was not equal to one, then the inflationary theory in its present form would need to be abandoned. 

  Finally, inflation provides an answer to the origin of the structure that later formed the galaxies and clusters that we now see today.   On large scales, things behave predictably according to familiar laws of physics.  However, on very small scales, such as those that apply to individual particles, behavior can be described only as probabilities – quantum mechanics begins to assert itself.  That is, it is impossible to determine when a particular atomic nucleus will disintegrate; however, it is possible that there is a certain probability that it will decay during a given period of time.  Before inflation, the part of the universe that we currently observe was so small that density fluctuations appeared and disappeared in a random matter that can only be described by quantum mechanics and probabilities.  At the instant inflation began, these tiny existing irregularities were magnified to great sizes and became the fluctuations in the background radiation and the seeds of the large structures we see today.

  Why did Inflation Occur?  While inflation seems to provide a good construct for solving some of the most difficult problems associated with the Big Bang theory, it is still difficult to understand why inflation occurred in the first place.  The explanation is that it represents a phase change in the universe when its temperature was 10^27 degrees K.  A phase change occurs when the physical state of a material changes from one form to another.  In our usual world, melting, boiling, and freezing represent phase changes occurring with water.  The condition that changed when the temperature of the universe cooled was the ability to distinguish three of the four fundamental forces from each other.  Today, there are four fundamental distinct forces at work in the universe.  One of these is gravity.  The other three are electromagnetism; the weak force that is involved in certain radioactive decays, and the strong force that binds protons and neutrons inside a nucleus.  These forces all have different strengths and work at different distances.  The relative strengths of electromagnetism, the weak force, and the strong force all depend on temperature and energy.  Physicists predict that at a temperature of 10^27 K, The three forces would have the same strengths and would be indistinguishable.  The phase change that occurs at 10^27 is that electromagnetism, the strong force, and the weak force assume their individual identities.  As the universe cooled, however, the phase change didn’t take place at the expected temperature.  Instead, the change was delayed as the universe became “supercooled.”  Supercooling can also occur in water which can be lowered to temperatures well below the freezing point as long as there are no impurities in the water. When disturbed, however, the water very quickly freezes.

  A bizarre consequence of the supercooling of the universe below the temperature of the phase change was that gravity became a repulsive force rather than attractive.  Gravitational repulsion produces the period of accelerating expansion called inflation.  When the phase change finally took place, inflation ended and the normal expansion of the universe began.  Although this explanation may seem imaginary, it is based upon the results of high energy physics experiments.

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