Cosmology Lecture 7 Mr. Kiledjian

Transcription

1 Cosmology Lecture 7 Mr. Kiledjian Lecture 7: The Age, Shape, Makeup, and Fate of our Brane Universe 1) In this final lecture, we will trace the history and development of our understanding of the Universe in which we live. We will see what questions and puzzles have haunted Cosmologists in their search for a meaningful model of the universe. We will also see that many questions have remained unanswered as of yet. To begin with, let s discuss the tenets of the Cosmological Principle (given its name by Edward Milne). Homogeneous means that the Universe looks the same everywhere over LARGE SCALES; there might be local differences and irregularities, but no region should look considerably different than all other regions of the universe. Another way to state this is that, no place in the universe should be able to call itself the CENTER or the EDGE. Isotropic, on the other hand, means that the Universe looks and feels the same in all directions over LARGE SCALES. There is no direction that is NORTH or SOUTH for all observers. From Earth, the North Star is Polaris for now, but that is different from another planet. Even that will change for the Earth; at 14,000 AD, our north star will be Vega due to the precession of the Earth s axis. 2) Another issue that Cosmologists have had to explain is known as the He wanted to see what kind of universe would satisfy both Einstein s equations and the Cosmological Principle. He also assumed that the Cosmological constant was zero. (The Cosmological constant was a term in Einstein s field equation of General Relativity, which predicted that the Universe would either collapse or expand and Einstein set it equal to zero, because he believed in the Static Model of the universe. Later, he would say that this was the greatest blunder of my life.) Based on these assumptions, he came up with 3 kinds of universes, Flat, Spherical, and Hyperbolic. Not only were their shapes different, but each model predicted a different time frame for when the Big Bang had occurred depending on the value of the Hubble constant, and each model predicted a different fate for how the universe would end. The Hubble time gives the age for a universe with no matter and gravity in it, a universe that expands uniformly for all time. It sets an upper limit for the age of the universe. Therefore, the greater the Hubble constant, the smaller the Hubble Time is and the younger our universe is. For a Hubble constant of 71 km/sec/megaparsec, the Hubble time comes out to be about billion yrs old. (The presently accepted value of the Hubble constant is 71 km/sec/megaparsec. That means that a galaxy which is 1 megaparsec away

2 from us moves away from us at an average rate of 71 km/sec; a galaxy which is 10 megaparsecs away moves away at an average rate of 710 km/sec, etc). The Flat (also called the Marginally bounded) model predicted that the age of the universe is 2/3 of this Hubble time and that the universe would continue to expand forever, but it would always be on the verge of recollapsing. The Spherical (also called the Bounded) model predicted that the age of the universe was less than 2/3 of the Hubble time and that the universe would expand and reach a maximum size and then recollapse into the Big Crunch This was also called the open or unbounded model. All measurements of the shape of the Universe that were done in Friedmann s time and even to this date, have found the Universe has a flat shape. This came to be known as the Flatness Problem. The reason it was called a problem, was that the likelihood of being flat was very little, and everything had to be just right at the beginning of the universe to cause such an accident. (Namely, its density must be exactly equal to some critical density; in other words, the ratio of the density of the universe to this critical density must exactly equal 1 in order for the universe to have flat geometry!!) If the conditions had just been a little different, then the universe would either be closed and eventually collapse or it would be open and expand forever. Eventually, the Inflationary model of the universe explained this flatness problem by explaining how the universe grew so tremendously during its beginning and it smoothed out all the irregularities; this was a super luminous expansion period. This expansion also smoothed out irregularities and caused the extinction of magnetic monopoles!! 3) Recently since the 1990 s, the possibility that the Cosmological model might not be zero has led cosmologists to come up with yet other models that contain the. In 1998, teams of astronomers that were studying the brightness of supernovae and using them to calculate distances to far galaxies, found out that distant supernovae were farther away than their red shifts suggest. Another way to put this is that distant supernovae have less red shift than we predicted that they would have based on the value of the Hubble constant. This suggested that the Hubble constant was smaller earlier in the history of the universe, and that therefore, the Hubble constant was getting bigger and the Universe was accelerating. It seemed like Einstein s cosmological constant was not such a bad idea after all. However, what was the nature of this constant, where did it come from, and what gave it the value that it had; these were all questions yet unanswered. According to this model, the universe will continue to expand at an ever increasing pace until galaxies are so far away, and the average temperature of the universe will drop, life-hosting stars will cease to exist, and it will end up as a Big Freeze. The last stars to remain will be the black hole star remnants, and they will eventually re-evaporate due to Hawking radiation. Therefore, cosmologists quickly went to work searching for this cosmological constant. They knew for some years that the Universe didn t have enough ordinary matter to make it Flat; it had to have something known as Dark Matter. They had known this by studying the rotation rate

3 of galaxies like our Milky Way, which did not exhibit Keplerian rotation rates. The outer portions of these galaxies rotated faster than Kepler s equations predicted; there must be some weird unseen matter that kept them rotating that fast. Also, they had studied clusters of galaxies and observed their individual velocities. They had concluded that with such velocities, the clusters should eventually disperse, but they weren t. Something must have held them and presently is holding them intact. From such calculations, cosmologists had already calculated that the percentage of ordinary matter & energy must be about 1/3 of the total mass/energy of the universe. So now, they set out to answer the question of what the new shape of the universe was considering the fact that it was accelerating; what was this cosmological constant and portion of the universe did it make up. 4) Now, let s discuss the nature of the different components making up the universe. First, we have ordinary matter & radiation. This is composed of all the elements in the periodic table plus their constituents such as electrons, neutron, protons, and quarks. Also included are other elementary particles such as muons, neutrinos, etc. These could include such things as Baryonic Dark Matter (ordinary non-luminous matter); an example of such a proposed object is brown or black dwarfs which are hard for us to see called MACHOS (massive compact halo objects). Another category is the non-baryonic dark mater; otherwise known as Exotic Dark Matter; these include Exotic Particles such as axions and photinos, and it also includes neutrinos with mass, and WIMPS (weakly interacting massive particles). Neutrinos are also called Hot Dark Matter because they travel near the speed of light. Dark Matter is not quite well understood yet. The 3 rd component of the universe is now believed to be related to Einstein s cosmological constant. It is also called Quintessence, Vacuum energy, or Dark Energy. The sum of this Quintessence factor and the Cosmological constant comprises about 70% of the known universe. (The term quintessence comes from the Greeks who believed the universe to be comprised of 4 essential elements of Earth, Wind, Fire, and Water, and a 5 th mysterious element called quintessence. This mysterious element is akin to our Dark Energy!!) A simple way to understand quintessence is that it is some kind of energy associated with the quantum mechanical fluctuations inside vacuum space, and it is causing the universe to accelerate its pace of expansion. (Dark Energy is reminiscent of the Force concept in Star Wars!!) However, the weird thing is that all calculations so far have shown that this predicted quantum mechanical energy is 120 orders of magnitude greater than zero; in other words, the universe should have expanded tremendously more than it has. So, why is its value so much smaller than the theory predicts? This is one of the most perplexing questions of cosmology. Now, we still hold to a Spatially flat universe but not a Temporally Flat universe. Such a universe is allowed if one includes the presence of the Cosmological constant and Dark energy!! Therefore, we presently believe that the Universe is spatially

4 flat, but temporally accelerating. The other advantage of the accelerating universe model is that it proposes the oldest age for the universe among the different models. As was mentioned earlier, the open model of the universe predicted an age > 2/3 of the Hubble time. However, the accelerating model predicts an age even greater than the open model up to and closer to its maximum age = Hubble time = billion years. Since we have discovered stars and planets that are about 13 billion years old, this model allows for the oldest universe, and gives enough time to create those galaxies, stars, and planets!!! 5) Now, let s divert our attention into Brane Universes. According to this theory, our universe is only one universe among many; it s also called the multiverse theory. The Stephen Hawking book covers this topic very well in Chapter 7 of the Universe in a Nutshell book. Our universe is imagined as one Brane universe, which is growing like a Bubble. It contains some 11 dimensions, only 4 of which are enlarged. Another possibility is that the extra dimensions are so large that they are not visible or noticed by us. Hawking compares the 4 dimensions to the surface of the bubble and the other extra dimensions to the space within or outside the bubble. He states that only the force of gravity can leak out of our 4 dimensions and into the center area or outside the bubble. That causes its strength to weaken quicker than the other 3 forces of nature, which is attested by physics. However, too rapid a falloff rate would make the orbits of the planets unstable and would cause them to not hold together. It is speculated that we live on one of these branes and we can t see the other brane, but we know its presence by the behavior of physical laws that we observe such as the falloff rate of gravity. Dark Matter could be the result of the influence of matter from our shadow brane on our brane; since light is confined to a brane, we would not see this dark matter but we would feel its gravitational effects! Also, gravitational waves would be bound between the two branes and would be due to the perturbation of our shadow brane!! Another way to cause gravity to falloff the correct way is called the Gravitational waves would carry energy away from our brane, unlike the Shadow Brane model where the gravitational waves are trapped between our brane and our shadow brane. The result of this would be that a black hole would seem to lose energy without us being able to detect this energy, because it would be lost through this saddle. This mass-loss would be significantly more prominent for a Small Black hole which would have a radius in the extra saddle dimension equal to its radius in our 4 dimensions. This would seem to violate our conservation laws of energy; the final evaporation of the black hole would seem less energetic than it was. So far these arguments explain how to explain the physical laws and black hole evaporation using branes. But where and how do branes originate? This can be explained by quantum mechanical fluctuations much the same way as the quantum mechanical explanation of the

5 origin of our universe. Most brane universes would recollapse, but certain number of them would continue to expand once they pass a critical size. In this model, The history of our Nutshell in Imaginary time would determine its history in real time. A perfectly round Nutshell would lead to a universe that continues to accelerate in its rate of expansion in real time; it therefore never forms galaxies, stars, planets, and life! A Nutshell which has deformities and irregularities in imaginary time, could lead to our present universe which accelerated in its early stage (called the Inflationary Period), then slowed down its rate of growth and gave opportunity for life to form, and then continued to accelerate once. But do we really live on the surface of this Nutshell? According to the principle of Holography, information about a higher dimensional object can be coded by a lower dimensional shadow of an object. An example of this is that information about a black hole such as its entropy in encoded into the area of its event horizon; therefore, the event horizon is acting as some kind of lesser dimensional mirror about what is happening inside the black hole. Therefore, The final question Hawking tackles in that chapter is the question, what is outside our brane or nutshell universe? The answer is either nothing or other similar branes, depending if the shadow brane model is correct or the Randall-Sundrum model is correct or some combination of these models. It is altogether possible that our brane is all that there is and it is even wrong to ask the question, what is outside?, because that presupposes that there is something outside. However, it is mathematically more probable that there is a whole host of branes each growing, collapsing, and even colliding with each other. The collision of two branes would produce catastrophic results such as our Big Bang. This harks back to the Eckpyrotic model of the beginning of the universe, which proposes that 2 branes collided together and the ripples that they produced became the Big Bang. This Brane model that is described by Hawking is a hot and controversial model of the universe!!!!