Chapter 33 Outline: Astrophysics and Cosmology

Introduction

A.     Stars and galaxies are the largest objects in the universe. The use of the techniques and ideas of physics to study the heavens is referred to as astrophysics. Some galaxies are newer, some are older, but all eventually die out.

B.      The base of the present theoretical understanding of the universe is Einstein’s general theory of relativity (which is part of astrophysics) and its theory of gravitation. Gravity is the dominant force in the universe. The universe is made up of all matter and energy and it is finite. It can expand like a balloon and is currently expanding at the speed of light.

C.     Physicists do not address anything that happened before the Big Bang because there was no physics before that. Right now they believe in the Big Bang and that the universe will expand indefinitely.

D.     Dark matter is hydrogen that cannot be seen and is unknown.

E.      Cosmology is a study of the universe as a whole and deals with understanding the universe’s origin and future.

33-1: Stars and Galaxies

          A. Statistics and Facts

       1 light-second (ls) = 3.0 x 10⁸ m = 3.0 x 10⁵ km

     1 light-minute (lm) = 18 x 10⁶ km

     1 light-year (ly) = 9.46 x 10¹⁵ m ≈ 10¹³ km

       Earth-Moon Distance: 384,000 km = 1.28 ls

     Earth-Sun Distance: 1.50 x 10¹¹ m = 150,000,000 km = 8.3 lm

     Pluto-Sun Distance: 6 x 10⁹ m = 6 x 10^-4 ly

     Earth-Proxima Centauri: 4.3 ly

       Galileo was the first person to discover in around 1610 that the Milky Way was made up of countless individual stars. Then around 1750, Thomas Wright said that the Milky War was a flat disc of stars that we call the Galaxy (Greek for “milky way”).

       Milky Way’s Diameter: almost 100,000 ly

     Milky War’s Thickness: roughly 2000 ly

       The sun is located about 28,000 ly from the center and orbits the galactic center once every 200 million years. It rotates at a speed of 250km/s relative to the center of the Galaxy. Our Galaxy has about 10¹¹ stars and the total mass of all the stars is about 3 x 10⁴¹.

          B. Terms and Definitions

       star cluster: a group of stars so numerous that they appear to be a cloud

       nebulae: glowing clouds of gas or dust

       extragalactic: outside our Galaxy

       galaxy: extragalactic nebulae that are similar to our own Galaxy (the Milky Way is referred to with a capital G in Galaxy)

       galaxy cluster: a cluster of a few to thousands of galaxies

       supercluster: clusters of clusters of galaxies

       novae/supernovae: exploding stars

       quasars (kway-ZHERS): “quasistellar radio sources”, galaxies thousands of times brighter than ordinary galaxies. There is also radiation that reaches the Earth that does not come from stars, and it is a background radiation that arrives from all directions of the universe.

       Other kinds of stars include red giants, white dwarfs, neutron stars, and black holes.

F.      Conceptual Example

       Astronomers think of their telescopes as time machines because they look back toward the origin of the universe.

       The distance in light-years measures exactly how long in years the light has been traveling in order to reach us. For example, if we saw Proxima Centauri explode into a supernova today, then the event would have really occurred 4.3 years ago. Therefore, the light we see from the most distant objects, like galaxies 10¹⁰ ly away, is the light that the galaxies emitted 10¹⁰ years ago. Thus, what we see now is how they were then, close to the beginning of the universe.

G.     Measuring Distances

       One technique to find the distance of a star is to measure the parallax of a star. Due to the Earth’s motion around the Sun, we can use simple geometry to find how far away it is.

                   The angle φ is 0.00006° and angle Θ is measured to be 89.99994°.                          Estimate the distance D to the star using parallax.

                        D = d/tanφ = d/φ = (1.5 x 10⁸)/(1.0 x 10^-6) = 1.5 x 10¹⁴ or 15 ly

       The distance to stars is often measured in seconds of an arc:

     1 second (1”) is 1/3600 of a degree

     1 minute (1’) is 1/60 of a degree

     note: degrees are similar to hours

       The distance is specified in parsecs (pc), parallax angle in seconds of arc. So in the example above, φ = 0.00006° (3600) = 0.22” of arc. 1/0.22 = 4.5 pc. 1 pc = 3.26 ly

       Parallax can only determine the distance of stars as far away as 100 light-years because beyond that distance, the parallax angles are too small to measure.

       Thus, more subtle techniques are employed by using the apparent brightness of galaxies, which would be a measure of how far away a star was.

33-2: Stellar Evolution: The Birth and Death of Stars

          A. Luminosity and Brightness

       Absolute Luminosity (L): the total power of a star radiated in watts

       Apparent Brightness (l): the power crossing a unit area perpendicular to the path of the light at the Earth

       l = L/4πd²

       Careful study of nearby stars indicate that the more massive the star, the greater its luminosity is. Color is also related to the absolute luminosity and therefore also to the mass. The Hertzsprung-Russell (H-R) diagram shows the temperate T compared to the luminosity L.

       Most stars fall in the main sequence, but the ones who fall in the lower left are called white dwarfs and the ones in the upper right are called the red giants.

          B. Birth of Stars, to the Main Sequence

       Astronomers and astrophysicists believe that the reason there are different types of stars, such as red giants and white dwarfs, is because each different type of star represents a different age in the life cycle of a star.

       Stellar evolution is a process from the birth to the death of a star. Stars are born when gaseous clouds contract due to a pull of gravity where a mass might be centered in the middle of the cloud. These “globules” are formed and as these particles of this protostar accelerate inward toward the mass, their kinetic energy increases.

       When the kinetic energy is high enough, the hydrogen nuclei are no longer repulsed from each other and instead, nuclear fusion takes place when four protons fuse to form a ⁴₂He nucleus (proton-proton cycle). This requires about a temperature of 10⁷K.

       The tremendous release of energy in these fusion reactions produces a pressure sufficient enough to stop the gravitational contraction so that the protostar can stabilize on the main sequence.

       Exactly where the star is depends on its mass because the more massive it is, the farther up and left is will be on the H-R diagram. But to reach the main sequence, it takes 30 million years, and it will remain on the main sequence for about 10 billion years.

       When the hydrogen “burned”, or rather, fuses, to form helium, it is very dense and will tend to accumulate in the central core where it was formed. As the core of helium grows, the hydrogen continues to fuse in a shell around the core.

          C. Evolution of Stars, to the Red Giant Stage

       When the hydrogen is finally all consumed, the production of energy decreases and the production of energy decreases. It becomes no longer sufficient to stop the gravitational forces from contracting the star. The hydrogen fuses even more fiercely because of the rise in temperature, which causes the outer envelope of the star to expand and to cool.

       Now the star as left the main sequence and it becomes redder, larger in size, and more luminous. It now enters the red giant stage.

       As the star’s envelope begins to expand, the core is shrinking and heating up. When the temperature reaches 10⁸, the helium nuclei undergoes fusion and the burning of the helium makes the star become hotter and hotter.

       Then the process of nucleosynthesis, the formation of heavy nuclei from lighter ones by fusion, ends.

          D. Death of Stars, to the Black Dwarf

       Now if the mass of the star is less than 1.4 solar masses, then it means that no further fusion energy can be obtained so the star collapses. It shrinks and cools down, becoming a white dwarf.

       The white dwarf will continue to lose internal energy, decreasing in temperature, and becoming dimmer and dimmer until its light goes out. Then it will become a black dwarf, a dark cold chunk of ash.

       Larger stars with a mass greater than 1.4 solar masses will contract under gravity and heat up further, reaching extremely high temperatures. The core contracts under the huge gravitational forces and the massive star becomes an enormous nucleus made up of almost all neutrons.

       It still continues to contract rapidly to form a very dense neutron star. This great contraction causes it to lose gravitational potential energy and the energy would have to be released. The energy that had to be released would take place as a catastrophic explosion that blew away the entire outer envelope of the star.

       Those explosions are believed to cause supernovas. In a supernova explosion, the star’s brightness suddenly increases billions of times in a period of just a few days and then fades away in a few months.

       Then the star becomes a pulsar, which is an astronomical object that emits sharp pulses of radiation at regular intervals. They are believed to be neutron stars that increase greatly in rotation speed during their contraction.

       The intense magnetic field of the rapidly rotating star traps charged particles that give off radiation. The core of the neutron star contracts to about two or three solar masses and then its evolution becomes similar to a white dwarf.

       However, if the mass of the neutron star is still greater than two or three solar masses, then its gravitation force becomes so strong and it becomes so dense that even light cannot escape its gravitational pull.

       No radiation could escape from such a star, so it would be black. Anything that came too close would be swallowed up, never to escape. This is called a black hole and is predicted by theories to exist. Evidence for their existence is strong but they are not fully confirmed yet. It is also possible that maybe or all galaxies have black holes at their centers.

33-3 General Relativity: Gravity and the Curvature of Space

          A. Force of Gravity

       Gravity is the dominant force in the universe over the other three forces because it is 1) long range and 2) always attractive.

       Gravity acts over astronomical distances and can be either attractive or repulsive. It acts as an attractive force between all masses.

          B. Einstein’s Theories

       Special Theory of Relativity: there is no way for an observer to determine if a given frame of reference is at rest or moving at a constant velocity.

       In the General Theory of Relativity, Einstein tackled the problem of accelerating reference frames and developed a theory of gravity.

          C. Principle of Equivalence

       Principle of Equivalence: No observer can determine by experiment whether he or she is accelerating or is rather in a gravitational field.

       For example, passengers on a vehicle speeding around a sharp curve could not prove if they were accelerating or being pulled by gravity.

       Another example, if an elevator was out in space where there was no gravity, the book would just float. But if the elevator was accelerating upward at an acceleration of 9.8 m/s², the book would fall to the floor with an acceleration of 9.8 m/s². But according to the principle of equivalence, we cannot experimentally determine whether the book fell because the elevator could be accelerating upward at 9.8 m/s² in the absence of gravity or the book was being pulled by gravity on Earth and the elevator was at rest. The two descriptions are equivalent.

       The principle of equivalence is related to the idea that there are two types of mass. One is inertial mass, and the more inertial mass a body has, the less it is affected by a given force.

       Another is gravitational mass. The strength of a gravitational force is proportional to the product of the gravitational masses of the two bodies. Another way to express the Principle of Equivalence: gravitational mass is equivalent to inertial mass.

          D. Curvature of Light

       The principle of equivalence also shows the light should be deflected due to gravitational force. For example, an elevator at rest is in free space with no gravity. There is a small hole on one side of the elevator and a beam of light enters from outside. The beam will travel straight across and make a spot on the opposite side. However, if the elevator is accelerating upward, the beam of light will curve downward because the elevator is accelerating. Now according to the equivalence principle, if the elevator was on Earth, the light would still curve downwards due to the gravitational force. However, such deflection is very tiny and needs a large gravitation pull to deflect it.

       It is a known fact that light always travels by the shortest path to its destination. So if light curves due to gravity or acceleration, then it means that the curved path is the shortest distance, which means that space itself is curved. The gravitational field itself causes this curvature of space.

       In Euclidean plane geometry, the sum of all the angles in a triangle is 180°. However, in non-Euclidean geometry that involves curved space, imagine a globe. If the top of the triangle is at the North Pole and the lines coming down form a 90° angle to the equator, 90 + 90 + 90 = 270°. That means there are 270° in a triangle in curved space.

       A geodesic (jee-uh-DES-ik) is whatever that is the shortest distance between two points. On a globe, the arc (or line in Euclidean geometry) of the triangle is the geodesic because it is the shortest distance from the North Pole to the equator.

       The curvature of space can also be seen when measuring the radius and circumference of a circle. On a plane surface, C=2πr. But on a two-dimensional curved surface, imagine a globe cut horizontally at the equator. The circle is like a skin that spreads over the top half of the globe. Thus, the radius is an arc from the North Pole to the equator and the circumference is less than 2πr. When the circumference is less than 2πr, it is called positive curvature.

       However, if the two-dimensional curved circle was on a saddle-like surface, the circumference of the circle would be greater than 2πr, and the sum of the angles of a triangle would be less than 180°. Those are called negative curvatures.

       Carol Friedrich Gauss tried to see if there was any curvature in our universe, but was unable to find any deviation from 180° when creating a triangle by mountain peaks. Nor have any experiments today detected any deviation.

       The question of curvature has many theories, and the real answer is not known. If the universe had a positive curvature, where it is like the outside skin of a globe, then the universe would be finite (FYE-night) and closed. If one traveled for millions of years, he/she would eventually end up in the same spot again.

       However, if the universe’s curvature was negative or zero (flat), then the universe would be infinite and open. It would never fold back on itself. This is the currently accepted theory.

       According to Einstein’s theory, space and time is curved, especially near massive bodies. The more mass something has, the more space and time is curved to it. To comprehend this, imagine a thin flat rubber sheet, and if a heavy weight is hung from the center, it will pull the rubber sheet down from the center. It creates a curve, which represents how near heavy masses (like the weight), the more curvy space is.

       For example, a black hole is massive and has a large force field. Bodies and light rays that near the black hole will curve towards it because the massive black hole causes a more curvy space. Thus, the light rays would travel along a geodesic, which is a curve, the shortest distance between two points.

       To become a black hole, a body of mass M must undergo gravitational collapse, contracting by gravitational self-attraction to within a radius called the Schwarzschild radius:

              R = (2GM)/(c²)                  G = gravitational constant

                                                     c = speed of light

       Black holes cannot be seen because light is sucked inside it and cannot escape, but black holes exert a gravitational force on nearby bodies. In a binary system, one star is visible and another is not. If the unseen one is a black hole, it tends to pull of gaseous material from the visible star and emit X-rays.

33-4: The Expanding Universe

          A. Fleeing Galaxies: Doppler Effect and Redshift

       Since stars evolve from birth to death as white dwarfs, neutron stars, and black holes, their evolution suggests that the universe as a whole evolves as well.

       Astronomers proposed that the distant galaxies are moving farther and farther away from us, and the farther they are away from us, the faster they are moving.

       The Doppler Effect also occurs for light, but the formula is slightly different from the one for sound due to special relativity:

          λ’ = λ sqrt[ (a + v/c) / (1 – v/c) ]

     λ = emitted wavelength (source’s reference frame)

λ’ = wavelength (moving frame with velocity)

v = relative velocity, v>0

       When a source is emitting light toward an object, and the source is moving away from the object, the color of light becomes more reddish, and this effect is called a redshift. When the source moves toward the object, the color shifts to a bluish color.

       The amount of shift depends on the velocity of the source. The fractional change in wavelength is proportional to the velocity:

              Δλ / λ  =  (λ’ – λ)/ λ  =  v / c

          B. Hubble’s Law and Hubble parameter

       Hubble noticed that the lines seen in the spectra of galaxies were generally redshifted, and the amount of the shift was proportional to the distance of the galaxy away from us. Thus, since redshifts mean the source of light is moving away, galaxies are moving away from us.

       The velocity of a galaxy moving away from us is proportional to its distance:  v = Hd      <-- called Hubble’s Law, the constant H is called the Hubble parameter. The value of H is not known very precisely, but is generally taken to be about H ≈ 80 km/s/Mpc (megaparsec)

       However, Hubble’s Law does not work well for nearby galaxies because some of them are seen to me moving closer to us (blue-shifted).

          C. Quasars

       At first it might seem that galaxies are moving away from us, with Earth as the center. But that is not necessarily true because this expansion appears the same from any other point in the universe. Thus the expansion of the universe is: all galaxies are racing away from each other at an average rate of 80km/s/Mpc of distance between them.

       But a class of objects called quasars (quasistellar radio sources) that do not conform to Hubble’s Law because they are as bright as our nearby stars but display very large redshifts. Since they are so far away and yet so brightly visible to us, they must be thousands of times brighter than normal galaxies.

       However, quasars pose many problems. Their abnormal brightness may be an unresolved brightness problem. However, if quasars are in actuality very close to us, then we have an unresolved redshift problem.

       An interesting fact is that the density of quasars increase with the distance they are away from us. And if these quasars are actually closer to us (as their brightness suggests), then it would mean that we are in a special place in the universe where quasars are the least populous.

       But astronomers are unwilling to accept that quasars are least populous here because it would violate the cosmological principle that space has uniformity.

       Some think that quasars are mysterious galaxies in which the center is a black hole that gives off a humongous amount of energy. It seems possible, then, that quasars are powered by black holes.

          D. Cosmological Principle

       The Cosmological Principle states that the universe is both isotropic (looks the same in all directions) and homogeneous (would look the same if we lived elsewhere).

       Currently, there is some doubt about the validity of the principle. One possible resolution might be that over 90% of the universe is nonluminous dark matter that is uniformly distributed.

          E. Universe’s Possible Past and Age

       The expansion of the universe suggests that the galaxies used to be closer together than they are now. This is the basis for the Big Bang theory, which states that the origin of the universe started as a great big explosion.

       It is possible to estimate the age of the universe using the Hubble parameter, H ≈ 22 km/s per million light-years.

              t = d/v = d/Hd = 1/H ≈ (10⁶ly)(10¹³km/ly)/

                                               (22km/s)(3 x 10⁷s/y)

                                            ≈ 15 x 10⁹ years

       This age of the universe, 15 billion years, is called the characteristic expansion time or Hubble age. It is not very precise because we don’t know the exact value of H.

       NOTE: In 2002, the exact age was found out to be 13.7 billion years.

       Another way is to use the age of the Earth and solar system by using uranium, which is about 4½ billion years. By using the theory of stellar evolution, stars have estimated to be about 10-15 billion years old. These numbers are consistent with the Big Bang Theory.

       An alternative to the Big Bang Theory is called the steady-state model. The steady-state model states that the universe has always been like this and is indefinitely old. No large-scale changes are ever made, especially not a Big Bang. However, then the theory of the recession of the galaxies must be violated.

       Matter would have to be created continuously to keep the density of the universe constant. The rate of mass creation is one nucleon per cubic meter every 10⁹ years and is very small.

33-5: The Big Bang and the Cosmic Microwave Background

          A. Specifications of the Big Bang

       If there was a Big Bang, it would have to have occurred simultaneously at all points in the universe.

       If the universe is finite, the explosion occurred as a point of extremely dense matter (which is the whole universe) that exploded to become larger (which is still the whole universe) and there would not have been anything else.

       If the universe if infinite, then the explosion occurred at all points of the universe at once since if it is infinite, it must have started off as infinite as well, even though it was much smaller back then. Even though the universe is infinite, when it is said that it was smaller, it is meant that the average size between the galaxies was smaller back then. Therefore, since the Big Bang, the average size between the galaxies has increased.

       Evidence supporting the Big Bang: age of the universe calculated by the Hubble expansion, stellar evolution, & radioactivity all point to a consistent time of origin in our universe.

          B. CMB Radiation

       in 1964, Arno Penzias and Robert Wilson experienced difficulty with their radio telescope because something was interfering with it. They assumed it to be “static” or background noise and became convinced that it was coming from outside our Galaxy.

       The intensity of the radiation did not vary from day to night and instead, came from all directions in the universe with equal intensity. With precise measurements, the wavelength was round to be λ = 7.35 cm, and that length is found to be in the microwave region of the electromagnetic spectrum (called microwave because of its short length).

       Thus, it was named cosmic microwave background radiation. Since it had remarkable uniformity, it agreed with the cosmological principle. However, some theorists felt that there had to be some inconsistencies with the CMB radiation that maybe could possibly help explain the origin of the universe.

       The intensity of CMB radiation was λ = 7.35, which corresponded to blackbody radiation, which was a temperature of 2.7 ± 0.1 K. when the CMB radiation at other wavelengths were measured, their intensities fell upon the blackbody curve, and so it proved that the CMB radiation was at a temperature of 2.7 K.

          C. CMB Radiation as Evidence for the Big Bang

       CMB radiation provides strong evidence for the Big Bang Theory because they are related. In the Big Bang, there must have been a tremendous release of concentrated energy that was at a temperature so high that atoms could not have existed.

       Instead, the universe was radiation-dominated and consisted of radiation (photons) and elementary particles. The universe would have been opaque (oh-PACK, meaning resistant to light). There was also a point in time when matter and radiation were once in equilibrium at a high temperature. The reason they were once in equilibrium is because there used to be no atoms (high temp) and once there was, it equaled, then surpassed, the amount of radiation.

       As the universe expanded, the energy spread out over the universe, and thus, the temperature would have dropped. Some 300,000 years later when the temperature reached 3000K, the nuclei and electrons would have been able to combine to form atoms and the radiation would have been “released” from the matter to spread throughout the universe.

       As the universe expanded further, the wavelengths of the radiation expanded and the temperature of it would have become lower and lower to reach the 2.7 K that we observe today.

       Today, radiation is known to make up less than 1/1000 of the energy in the universe, and today the universe is matter-dominated.

33-6: The Standard Cosmological Model: The Early History of the Universe

          A. Stages of the Universe

       In the first few moments of the Big Bang, the evolution of the universe was determined. Thus, a convincing theory of the origin and evolution of the universe, called the standard model, has developed.

       Graphical Representation of the Standard Model:

       Before 10^-43s, the four forces in nature were unified into only one force. At 10^-43s, the temperature was about 10³²K and a phase transition occurred when gas condenses into liquid, and then freezes into ice. The four forces are broken down and the universe enters the grand unified (GUT) era.

       Then at 10^-35s, the temperature cools down to 10²⁷K, the universe is filled with a soup of leptons (electrons, muons, taus, neutrinos) and quarks (nucleons, hadrons). Then they begin to condense and this becomes the Hadron Era. This “soup” consists of particles that frequently collide and exchange energy. There are more quarks than antiquarks, and these leftover quarks (becomes matter) are what we are made up of today.

       By 10^-6s, the universe cools down to about 10¹³K, and most of the hadrons have disappeared. Then after 10^-4s, the universe enters the Lepton Era.

       Now one second has passed, the universe has cooled to 10 billion degrees, and after 10 seconds, the universe enters the Radiation Era. The universe becomes radiation-dominated and stays that way for hundreds of thousands of years until there is an energy balanced between matter and radiation.

       Two to three minutes after the Big Bang, nuclear fusion occurs and deuterium, helium, and lithium nuclei were made. Then the universe immediately cools, so that nucleosynthesis stops and will not continue until millions of years later (in stars).

       After the first hour or so of the universe, matter only consisted of bare nuclei of hydrogen (75%), helium (25%), and electrons. Radiation (photons) continued to dominate.

       300,000 years later, when the temperature has cooled down to 3000K, the electrons could finally orbit the bare nuclei and could form atoms.  The free electrons became much freer in spreading across the universe and the total energy from radiation decreases (redshifting as the universe expands).

       As the universe continues to expand, the radiation moves further and further away from us as it continues to fill up the universe. In addition, the radiation has cooled to 2.7K today, which forms the CMB radiation. The universe became matter-dominated, as it remains today.

          B. Millions of Years after the Big Bang and Unanswered Questions

       Stars and galaxies formed from the self-gravitation around mass concentrations a million years after the Big Bang.

       However, this scenario has not been proven per se, and it does not answer all of our questions, but it does provide a tentative picture of how the universe may have become.

       It does have problems, however, and one modification proposed is known as the inflationary scenario. Around 10^-35s after the Big Bang, the universe underwent a rapid exponential expansion that separated the strong force from the electroweak.

33-7: The Future of the Universe?

          A. The Question

       One question that cosmologists do not know the answer to is if the universe will continue to expand forever, and this question is connected to the curvature of space (time) and whether the universe is finite or infinite.

       If the curvature of space is negative, the expansion will never stop, but might decrease due to the gravitation attraction of its parts. This universe would be open and infinite.

       If the universe was flat (no curvature), then it would be open, infinite, and its expansion would slowly stop.

       If there was positive curvature, the universe would be closed and finite, the universe would contract, and all matter would eventually collapse back onto itself in a big crunch. If this is correct, the maximum expansion would occur in about 30 or 40 billion years.

          B. Using Density to Answer the Question

       A possible way to answer that question is to find the average mass density in the universe. If the average mass density if above the critical density (p_c ≈ 10^-26kg/m³), then gravity will p revent expansion from continuing on forever and the universe will have a big crunch.

       If the actual density is equal to the critical density, p = p_c, then the universe is flat and open.

       If the actual density is less than the critical density, then the universe has a negative curvature and will be open and expanding forever.

          B. Dark Matter (“Missing” Mass)

       There is evidence in the universe of a significant amount of nonluminous matter, which is referred to as “missing” mass or dark matter. This matter would bring the density to almost exactly p_c.

       By observing the galaxies, they often look like they rotate with more mass than they seem to have, which may be the dark matter. If there is nonluminous matter, then what is it?

       One suggestion is that the dark matter consists of weakly interacting massive particles (WIMPS), or small primordial black holes that were made in the early stages of the universe.

       Another suggestion is that dark matter consists of massive compact halo objects (MACHOS), which are chunks of matter in the form of large planets (like Jupiter) or stars too small to sustain fusion and too faint to be seen (sometimes referred to as brown dwarfs).

          C. Using the Deceleration Parameter to Answer the Question

       The deceleration parameter is a measure of the rate at which the expansion of the universe is slowing. However, to measure this rate, you would have to look back in time and at that time, the rate of expansion was much faster than today.

       Unfortunately, we do not know the distance to these galaxies very precisely, so this method does not yield an answer to the question.

          D. Ifs

       If the universe is open, after about 10¹⁸, galaxies would have much of their matter knocked away and scattered throughout the universe by collisions with other stars. The remaining matter would eventually condense into massive “galactic black holes”. Clusters of these would form “super galactic black holes”.

       Then the black holes would evaporate the matter within them and this would take 10¹⁰⁰ years. Our universe would then be mainly a thin gas of electrons, positrons, neutrinos, and photons.

       If the universe was closed, it might contract before the stars all burnt out and the background radiation would increase in energy and temperature, basically retracing its steps during the first few stages. In the big crunch, the black holes would simply gobble up more and more matter until the whole universe was one big black hole.

       After the big crunch, the universe might just repeat itself again with another Big Bang and it might be a cyclic or pulsating universe.

       Calculations have been done where the formation and evolution of the universe have been slightly altered in certain fundamental physical constants. The result was that life could not exist. That gives rise to the Anthropic Principle: if the universe was slightly different than it is, we would not be here. It is as if the universe was created just right to accommodate us.