syllabus

Syllabus

Lectures: Tu Th 10:00 -- 11:15 pm, Math Sciences E116 Professor: Katherine Benson Math Sciences N210, phone 7-4083, e-mail benson@physics.emory.edu Assistant: Jon Toebbe Math Sciences N117C, phone 712-2441, e-mail jtoebbe@physics.emory.edu Help Session: Wednesday 3:30 -- 5 pm, TBA (JT) Office Hours: Thursday 2 - 4 pm (KB) Grading: Homework 40%, Exams 30%, Final Project 30%

Homework:

Homework will be assigned weekly to biweekly. It will come in two forms:

Problem sets.

Working through problems is the only way to really learn quantitative material. While problem sets comprise a large fraction of your grade, they are meant to be an informal learning tool. You are encouraged to discuss the problems together, then write up your conclusions independently. This means that sharing solutions in written form is not permitted, but verbal and blackboard discussion is. Your write-up should make your reasoning, as well as your final answer, clear; the argument should be written so that a student unfamiliar with the problem could understand the logical steps. Problems will be graded as follows: 3 points, basically correct; 2 points, got the gist but failed in implementation; 1 point, tried but missed the point; 0 points, made no relevant attempt. I will distribute written solutions when problem sets are collected.

As in all upper-level physics courses, problems are your opportunity to flesh out abstract formalism and heuristics in tangible examples; this application is often highly nontrivial, and provides the context where you construct your understanding of what the formalism really means. If it were trivial, it would not be worthwhile. You should expect all problem sets to require more than one sitting to complete; indeed, to usually require retreat and reflection and a re-approach to some problems. Problem sets will normally be due Thursdays at 4 pm. Our assistant Jon Toebbe will offer a help session Wednesdays from 3:30 -- 5:00, where he will answer questions you have developed and guide you through sticking points in your understanding and analysis. This help session is extraordinarily useful; it enables you to return to the problem set after initial setbacks and work through and learn the material most effectively. It is most useful when all students attend and all make a serious first attempt at the homework beforehand. I also will have office hours tuned to the homework cycle, on Thursdays 2:00 -- 4:00.

Writing Assignments

Some of the material in this course will be semiquantitative, and will not give you enough sophistication or stamina to fully work out specific physical predictions. You nevertheless should master the basic formal concepts and structures involved. The best way to both test and deepen such conceptual understanding is to explain the arguments, from beginning to end, yourself. Writing assignments will develop your ability to do this; typically, you will be asked to critique an entirely qualitative passage for accuracy, and to rewrite the argument at this course's level of mathematical sophistication. This will bring your work distribution in this course closer to the typical activities of a practicing scientist, who communicates and refines new physical understanding by writing journal articles.

Completing these homework activities is essential to building your understanding of the course material as the course progresses. Thus the homework 1) determines a significant portion of your grade; and 2) will not be accepted late without prior approval.

Exams:

There will be two midsemester take-home exams, in early March and early April. Exams will cover quantitative problem-solving, as well as familiarity with and mastery of the key concepts and qualitative arguments that establish our understanding of relativity and cosmology.

Final Projects:

This course will have no final exam: instead students must complete a final project. Such projects will involve a 20-minute oral presentation on some cosmology topic not covered in class. I will distribute a list of suggested topics in late March and approve final project proposals by April 26; presentations of approved projects will be in our final exam slot, April 29 from 4:30 to 7:00 p.m.

Texts:

M. Roos, Introduction to Cosmology, John Wiley and Sons, 3rd edition, New York (2003).

supplemental readings (provided)

The subject matter for this course -- cosmology and its theoretical foundation in general relativity -- tends to be taught either at an entirely descriptive level, or an entirely technical one. We adopt an intermediate ground, understanding the essential physics somewhat quantitatively, without losing an intuitive overview of our how our universe, a curved spacetime filled with matter, evolves. No single textbook provides good coverage of both relativity and cosmology at this level. The cosmology coverage in Roos is reasonable and current (published last month, incorporating a standard cosmological model which changed markedly in recent years). We will study general relativity and its mathematical basis in differential geometry more thoroughly than Roos; supplemental reading will be provided.

Course Content:

We will survey both the standard big bang cosmology, and its problems and tentative extensions. The standard model was motivated to explain Hubble's 1929 observation of an expanding universe, and reached fruition in the observations in the 1960's of its two key predictions: the 3K blackbody spectrum of cosmological photons (called the cosmic microwave background or CMB); and the abundances of light elements, whose nuclei were produced early in the big bang (called big bang nucleosynthesis or BBN).

The classic standard model consists of an adiabatically expanding Friedmann-Robertson-Walker universe, whose spatial expansion is driven by its particle content according to general relativity. At early times, that particle content is dominated by radiation (ultrarelativistic particles like photons); while at late times, nonrelativistic matter (such as dust) predominates. Particles in the universe also interact nongravitationally, through familiar weak and electromagnetic interactions.

Extensions of the standard model attempt two refinements : establishing consistency with new observations of the universe; and pushing our understanding of the universe's history further back in time, to temperatures where particle interactions are less familiar. Several recent cosmological measurements established the surprising result that our universe's expansion is accelerating, which suggests most simply the presence of a dominant nonzero cosmological constant. This cosmological constant, called $\Lambda$ , came to dominate radiation and dust only recently; thus the contemporary standard model includes, after radiation and matter-dominated epochs, a current extraordinarily recent period of $\Lambda$ -dominated accelerating expansion. We study earlier times out of curiosity -- but also in hopes of justifying the standard model's initial conditions, while checking the consistency of particle theory. We'll discuss some of these extensions, particularly one whose consonance with new detailed measurements of CMB anisotropy has made it a near-standard: inflation.

Our trajectory through this subject will be as follows. Note general relativity is a substantial element of this course: it is both the theoretical underpinning for cosmological models, and one of physics' great triumphs of the last century. Our goal is to establish a basic understanding of the content of Einstein's equations, which, when applied to homogeneous and isotropic spacetimes, determines the basic principles of cosmology.

The Standard Big Bang Cosmology

Breakdown of the Static Newtonian Picture 2 weeks
1. CONCEPTUAL: Olbers' Paradox, Newtonian Instability
2. OBSERVATIONAL: Hubble Expansion (Nuts and Bolts)
3. QuasiNewtonian model of Hubble expansion
General Relativity and Curved Spacetime 6 weeks
1. Precepts2 weeks
  1. Special Relativity, Causality and Covariance
  2. Equivalence Principle
2. Curved Space (Differential Geometry)2 - 3 weeks
  1. Surfaces and Non-Euclidean Geometry; Extrinsic Notions
  2. Intrinsic and Modern Characterizations of Curvature
3. Deriving Einstein's Equations 1 week
Cosmological Solutions to Einstein's equations1 - 2 weeks
1. Friedmann-Robertson-Walker universes
2. Evolution, Matter, Radiation and $\Lambda$ Dominated Cases
Thermodynamics in an Expanding Universe1 -- 2 weeks
1. Interactions and Equilibrium
2. Thermal History of Equilibrium Universe in ``First Three Minutes''
3. Observational Relics: Blackbody CMB, BBN

Beyond the Standard Cosmology

Problems with the Standard Model 1 week
Inflation, Quintessence, Braneworlds? 1 -- 2 weeks

Resources:

I will make all course-related files available on the worldwide web. The location is http://www.physics.emory.edu/Faculty/Benson/380-04/380.html. Included will be all handouts, and a notes mail file, with one message summarizing the main points of each lecture.

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