AST 6416: Physical Cosmology Instructor: Gonzalez Fall 2009 This document contains the lecture notes for the graduate level cosmology course at the University of Florida, AST 6416. The course is 15 weeks long, with three class periods per week (one on Tuesday and two on Friday). These notes are based upon a collection of sources. The most notable of these are lecture notes from George Blumenthal and Henry Kandrup, and the textbooks by Coles & Lucchin (2002), Peacock (1999), and Peebles (1993). 1 Introduction, Early Cosmology Week 1 Reading Assignment: Chapter 1 1.1 Course Overview Cosmology, defined as man’s attempt to understand the origin of the universe, is as old as mankind. Cosmology, as a field of scientific inquiry, is one of the newest of topics. The first theoretical underpinnings of the field date to the dawn of the 20th century; a significant fraction of the landmark cosmological observations have occurred in the past two decades — and the field certainly holds a plethora of fundamental unanswered questions. It is only during this past century that we have gained the ability to start answering questions about the origin of the universe, and I hope to share with you some of the excitement of this field. The title of this course is Physical Cosmology, and the central aim of this semester will be for you to understand the underlying physics that defines the formation and evolution of the universe. We will together explore the development of Big Bang cosmology, investigate the successes (and failures) of the current paradigm, and discuss topics of current relevance. By the end of the course, you will have a basic understanding of the foundations upon which our current picture of the universe is based and (hopefully) a sense of the direction in which this field is headed. What you will not have is comprehensive knowledge of the entire discipline of cosmology. The field has grown dramatically in recent years, and a semester is sufficient time to cover only a fraction of the material. This semester will be primarily taught from a theoretical perspective, with limited discussion of the details of the observations that have helped define our current picture of the universe. General Relativity is the foundation that underpins all of modern cosmology, as it defines the structure of spacetime and thereby provides the physical framework for describing the Universe. I realize that not all of you have taken a course in GR; and a detailed discussion of GR is beyond the scope of this class. Consequently, I will tread lightly in this area, and GR will not be considered a prerequisite for this class. For many of the key results, we will use pseudo-Newtonian derivations to facilitate intuition (which is useful even if you do know GR). In practice, this detracts very little from the scope of the course. Once we have 1 established a few fundamental equations, the bulk of the semester will be quite independent of one’s knowledge of General Relativity. For those of you who wish to learn more about General Relativity, I refer you to PHZ 6607. Finally, please review your copy of the syllabus for the semester. You will see that the textbook is Coles & Lucchin. The advantages of this text are that it is generally readable and should serve as a good reference source for you both for this class and in the future. Moreover, this text is used both for my course and for Observational Cosmology. Be aware however that the organization of this course does not directly parallel the organization of the book – we will be jumping around, and sometimes covering material in a different fashion than the text. The first half of the semester will be dedicated to what I would call “classical” cosmology, which broadly refers to the fundamental description of the universe that was developed from 1916-1970 – the global structure of the universe, expansion of the universe, and development of the Big Bang model, Big Bang nucleosynthesis, etc. The second half of the semester will focus upon more recent topics in the field – things such as dark matter, dark energy, inflation, modern cosmological tests, and gravitational lensing. I emphasize that the division between the two halves of the semesters is only a preliminary plan, and schedule may shift depending on the pace of the course. Homework will be assigned every two weeks, starting on Friday, and will comprise 50% of your grade. I strongly encourage you to work together on these assignments. Astronomy and cosmology are collaborative fields and you are best served by helping each other to learn the material. Make sure though that you clearly understand everything you write down – otherwise you will be poorly served for the exam and the future. The final will be comprehensive for the semester and account for the other 50%. 1.2 The Big Questions Before we begin, it is worth taking a few moments to consider the scope of the field of cosmology by considering, in broad terms, the aim of the subject. More so than most other fields, cosmology is all encompassing and aims for a detailed understanding of the universe and our place therein. Fundamental questions that the field aims include: What is the history of the Universe? How did it begin? How did the structures • that we see today – matter, galaxies, and everything else – come to be? What is the future of the Universe? What happens next? How does the Universe • end, or does it end?a How does the Universe, and the matter/energy it contains, change with • time? What are the matter/energy constituents of the Universe and how were • they made? What is the geometry of the Universe? • 2 Why are the physical laws in the Universe as they are? • What, if anything, exists outside our own Universe? • Clearly an ambitious set of questions. We by no means have complete answers to all of the above, but it is remarkable the progress – and rate of progress – towards answers that has transpired in recent times. In this course we will touch upon all these topics, but primarily focus upon the first five. 1.3 Olbers’ Paradox And so with that introduction, let us begin. Let us for a moment step back 200 years to 1807. Newtonian physics and calculus were well-established, but electromagnetism was still over 50 years in the future, and it would be a similar year before Monsieur Messier would begin to map his nebulae (and hence the concepts of Galaxy and Universe were essentially equivalent). Copernicus had successfully displaced us from the center of the solar system, but our position in the larger Universe was essentially unknown. At the time, as would remain the case for another 100 years, cosmology was the realm of the philosopher – but even in this realm one can ask physically meaningful questions to attempt to understand the Universe. Consider Olbers’ Paradox, which was actually first posited in ancient Greece before being rediscovered by several people in the 18th and 19th century. When Olbers posed the paradox in 1826, the general belief was the Universe was infinite, uniform, and unchanging (“as fixed as the stars in the firmament”). The question that Olbers asked was: Why is the night sky dark? Let us make the following assumptions: 1. Stars (or in a more modern version galaxies) are uniformly distributed throughout the universe with mean density n and luminosity L. This a corollary of the Cosmological Principle, which we will discuss in a moment. 2. The universe is infinitely old and static, son ˙ = L˙ = 0. 3. The geometry of space is Euclidean. And in 1800, what else would one even consider? 4. There is no large scale systematic motion of stars (galaxies) in the Universe. Specifi- cally, the Universe is not expanding or contracting. 5. The known laws of physics, derived locally, are valid throughout the Universe. For a Euclidean geometry, the flux from an object is defined simply as L f = , (1) 4πr2 where L is the luminosity and r is the distance to the object. In this case, the total incident flux arriving at the Earth is 3 ∞ 2 L ftot = 4πr dr n 2 = (2) Z0 4πr ∞ The incident flux that we observe should therefore be infinite, as should the energy density, <u> f/c. Clearly the night sky is not that bright! ≡ Can we get around this by including some sort of absorption of the radiation? Adding an absorbing dust between us doesn’t help much. For a static, infinitely old universe (as- sumption 2), the dust must eventually come into thermodynamic equilibrium with the stars and itself radiate. This would predict a night sky as bright as the surface of a typical star. We get the same result if we include absorption by the stars themselves (through their geometric cross section). Specifically, consider the paradox in terms of surface brightness. For a Euclidean geometry, surface brightness (flux per unit solid angle) is independent of distance since L πd2 L I f/dΩ= 2 / 2 = 2 2 , (3) ≡ 4πr r ! 4π d where d is the physical size of the object. If the surface brightness is constant, and there is a star in every direction that we look (which is a the logical result of the above assumptions), then every point in space should have the same surface brightness as the surface of a star – and hence T 5000 K. That the sky looks dark to us tells us that T < 1000 K, and sky ≈ sky from modern observations of the background radiation we know that Tsky =2.726 K.