# A&C reference library

by Phobos
Tags: aandc, library, reference
 Share this thread:
 Astronomy Sci Advisor PF Gold P: 23,199 Quantum Gravity Phenomenology http://ws2004.ift.uni.wroc.pl/html.html WS-2004 symposium, Feb 4-14 notes for all the talks are online, click on "lectures" for a listing a number of the talks are also on arxiv. search under author name.
 Astronomy Sci Advisor PF Gold P: 23,199 Chronos supplied this link http://www.astrosociety.org/pubs/mer...2/nothing.html to a non-technical discussion by Filippenko and Pasachoff of how the universe can have zero total energy (positive mass-energy of matter balanced by negative gravitational potential)
Astronomy
Sci Advisor
PF Gold
P: 23,199
 Quote by sol2
sol put this curvegraphing applet link
which is good

but we somehow dont have a good post about the Friedmann eqns.
on this sticky thread and we should. I will try to get something

but please if anybody has a better discussion of the basic equations of cosmology, showing the Lambda which has become so important, please
post it
 Astronomy Sci Advisor PF Gold P: 23,199 in an earlier post on this thread we had a little bit about the Friedmann eqns. but this is better and also here is a link to a Sean Carroll piece in LivingReviews. the people at Albert Einstein Institute-Potsdam MPI asked Carroll to do the piece on "Cosmological Constant" for LivingReviews http://relativity.livingreviews.org/...1-1/node3.html Sean Carroll is a blogger as well as one of the worlds foremost cosmologists. he's at chicago. check out his blog sometime--it can be entertaining---the name is "preposterousuniverse" ------------------ In what follows I am using the same notation Sean Carroll uses in LivingReviews which is pretty standard. First here is a version of the Friedmann equations which conceals the cosmological constant as "dark energy" added into the rho term as another kind of energy density. So you dont see the Lambda explicitly in this version. This is how a lot of people do it nowadays, and the dark energy fraction is given as 73 percent of total energy density rho. $$(\frac{a'}{a})^2 = \frac{8\pi G}{3}\rho - \frac{k}{a^2}$$ $$\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)$$ Now I'm going to separate the cosmological constant part out as Lamda, an inverse distance squared term. Now rho is all the other stuff, not counting dark energy, and the equations are: $$(\frac{a'}{a})^2 = \frac{8\pi G}{3}\rho - \frac{k}{a^2} + \frac{\Lambda}{3}$$ $$\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)+\frac{\Lambda}{3}$$ EXPLAINING THE NOTATION this is with c = 1 units, which simplifies things some. the scale factor of the metric (whose increase is the expansion of the universe) is denoted by the letter a. k is a spatial curvature parameter used to distinguish three cases k = -1, 0, +1 for negative curvature, spatially flat, positive curvature rho is an energy density, and easy to confuse with p pressure the universe appears to be spatially flat, the critical density rhocrit is that needed for it to be perfectly flat with k = 0 HOW THE HUBBLE PARAMETER COMES IN the Hubble parameter H is defined to be the time derivative a' of the scale parameter a, divided by a. $$H^2 = (\frac{a'}{a})^2$$ for the time being assume we've included the Lambda term in rho as "dark energy, because this is a convenient way to set things up for calculating stuff, like the critical density. In the case of a spatially flat universe the first Friedmann equation boils down to $$H^2 = \frac{8\pi G}{3}\rho_{crit}$$ algebraically that turns into the formula for the critical density $$\rho_{crit} = \frac{3}{8\pi G}H^2$$ the Hubble parameter has been measured really accurately at 71 km/s per Mpc and this lets us calculate the critical density at 0.83 joule per cubic km.since the U tests out flat or very nearly so, this is taken to be the density of all the stuff, stars galaxies, light, dark matter, dust, dark energy etc. It all amounts to 0.83 joule per cubic km. And the dark energy being 73 percent (from supernova data) means that its share is 0.6 joule per cubic km.
P: 915
 Quote by marcus sol put this curvegraphing applet link which is good but we somehow dont have a good post about the Friedmann eqns. on this sticky thread and we should. I will try to get something but please if anybody has a better discussion of the basic equations of cosmology, showing the Lambda which has become so important, please post it
http://hyperphysics.phy-astr.gsu.edu...tro/fried.html

This is a good link Marcus as well, and will lead you to many of the equations.

Marcus, part of this journey for me, was recognizng how the universe could move from our past, to our now, and if we could not look beyond to the hyper geometries, how could we have ever accepted any views in cosmology like Reimann's?

What comes next? Omega?
 Astronomy Sci Advisor PF Gold P: 23,199 Pete contributed this to the "Dark Energy" thread. this shows the cosm. const. Lambda in the context of the full GR equation. I have usually been discussing this in the simplified context of the Friedmann equations, derived from the full Einstein equation. What Pete has taken the trouble to put in LaTex is a useful reference, so I'll just copy it here: ---exerpt from Pete--- The term Dark Energy is given to that matter which is causing the universe to expand at an accelerating rate. This is what some call "anti-gravity" since this is clearly gravity acting in a repulsive manner. Back in Einstein's day nobody knew of any kind of matter which could produce such an effect. since Einstein assumed that the universe was static he added a term to his field equations to allow for this repulsive effect. Einstein's equations changed from $$G^{\alpha\beta} = \frac{8\pi G}{c^4}T^{\alpha\beta}$$ to $$G^{\alpha\beta} + \Lambda g^{\alpha\beta} = \frac{8\pi G}{c^4}T^{\alpha\beta}$$ $\Lambda$ is called the cosmological constant. In modern terms the cosmological constant is also called "Dark Energy." This is the term which, for normal matter, allows for anti-gravity when $\Lambda$ > 0.... ---endquote--- for full post see http://www.physicsforums.com/showthr...180#post301180 some more links for good measure http://math.ucr.edu/home/baez/gr/outline1.html http://math.ucr.edu/home/baez/einstein/einstein.html
 Astronomy Sci Advisor PF Gold P: 23,199 Correction to previous post (too late to edit) where one of the links was wrong Ned Wright's balloon animation http://www.astro.ucla.edu/~wright/balloon0.html Cartoon strip about the particle horizon being 3X what you naively expect http://www.astro.ucla.edu/~wright/photons_outrun.html Microlensing by a star http://www.astro.ucla.edu/~wright/microlensing.html Cluster of galaxies lensing animation http://www.astro.ucla.edu/~wright/cluster-lensing.html Inflation animation http://www.astro.ucla.edu/~wright/CM...ng_bubble.html Animation of what "Equal Power on All Scales" means---part of understanding the fluctuations shown by the Microwave Background http://www.astro.ucla.edu/~wright/CMB-MN-03/epas.html
 PF Gold P: 7,363 Here's a nice non-technical overview of the state of quantum gravity research, including some basic information about how studying cosmic rays and gamma ray bursts might help probe the structure of spacetime. http://arxiv.org/abs/physics/0311037
 Astronomy Sci Advisor PF Gold P: 23,199 Here is an introductions to cosmology, in about 60 pages: http://arxiv.org/abs/astro-ph/0409426 An overview of Cosmology Authors: Julien Lesgourgues Lecture notes for the Summer Students Programme of CERN (2002-2004). 62 pages, 30 figures. Very basic conceptual introduction to Cosmology, aimed at undergraduate students with no previous knowledge of General Relativity ---abstract--- While purely philosophical in the early times, and still very speculative at the beginning of the twentieth century, Cosmology has gradually entered into the realm of experimental science over the past eighty years. It has raised some fascinating questions like: is the Universe static or expanding ? How old is it and what will be its future evolution ? Is it flat, open or closed ? Of what type of matter is it composed ? How did structures like galaxies form ? In this course, we will try to give an overview of these questions, and of the partial answers that can be given today. In the first chapter, we will introduce some fundamental concepts, in particular from General Relativity. In the second chapter, we will apply these concepts to the real Universe and deal with concrete results, observations, and testable predictions. ---end quote---
 P: 915 Helioseismology: the study of the interior of the sun by observing the oscillations on its surface. This is a 60 pages paper that offers an introduction to the subject, also includes an historical review. All that you want to know about f-modes, g-modes, ring-diagram analysis, helioseismic holography,...can be found here. Title of the paper: "Helioseismology" http://arxiv.org/abs/astro-ph/0207403
 Astronomy Sci Advisor PF Gold P: 23,199 Sean Carroll online Cosmology Primer good FAQ http://pancake.uchicago.edu/%7Ecarro...rimer/faq.html rest of Primer is probably very good also, but havent reviewed it yet. see what you think
 P: 3 New member, first post Streaming video of lectures/talks on current topics by Hawking, Weinberg, others. Especially good is "Brane New World" (2003) By Steven Hawking. http://www.phys.cwru.edu/events/cerca_video_archive.php Enjoy .
Astronomy
Sci Advisor
PF Gold
P: 23,199
 Quote by meyer_lev3 New member, first post Streaming video of lectures/talks on current topics by Hawking, Weinberg, others. Especially good is "Brane New World" (2003) By Steven Hawking. http://www.phys.cwru.edu/events/cerca_video_archive.php Enjoy .
thanks for the link, meyer_lev, and welcome.
Personally, I wasn't aware of this Case Western Reserve archive of public lectures on cosmology topics. Impressive list of speakers and panelists.
 PF Gold P: 7,363 My apologies if this has been posted previously. It is a fascinating overview of Physics papers from the last 110 years or so. You can browse by field, author, decade, etc. http://fangio.magnet.fsu.edu/~vlad/pr100/
 PF Gold P: 7,363 http://www.sundog.clara.co.uk/halo/halosim.htm The graphics are not hot-linked, but they are well-labeled, and the menus at the left will link you to further information.
 Astronomy Sci Advisor PF Gold P: 23,199 Peter Dunsby's online course. special and general relativity very basic for the most part http://vishnu.mth.uct.ac.za/omei/gr/index.html
 Astronomy Sci Advisor PF Gold P: 23,199 Here is a link with some physical data about Titan http://library.thinkquest.org/18188/...oons/titan.htm I will try to get some other links, just to confirm the numbers. they say mass 1.35E23 kilogram (2.259 percent of earth) radius 2575 km density 1.88 distance from Saturn 1,221,850 km orbital period 15.945 days surface temperature -178 celsius surface pressure 1.6 bar (60 percent more pressure than earth) escape velocity 2.65 km/second this data is before Huygens and some of it might have already been improved on. If anybody knows some better please post it. TIA. Possibly the most reliable source is a JPL site I just found: http://ssd.jpl.nasa.gov/sat_props.html http://ssd.jpl.nasa.gov/sat_elem.html Here is a sample---BTW they dont show mass in kilograms, they show GM (which is what astronomers measure, and then infer mass from it) Titan GM (km3/sec2) 8978.0 ± 0.8 Radius (km) 2575.5 ± 2. Density (g/cm3) 1.880 ± 0.004 this site was updated as recently as November 2004 just for comparison here's what JPL NASA has for 4 jovians Io 5959.916 ± 0.012 1821.6 ± 0.5 3.528 ± 0.006 Europa 3202.739 ± 0.009 1560.8 ± 0.5 3.013 ± 0.005 Ganymede 9887.834 ± 0.017 2631.2 ± 1.7 1.942 ± 0.005 Callisto 7179.289 ± 0.013 2410.3 ± 1.5 1.834 ± 0.004 Here's the main address http://ssd.jpl.nasa.gov/
 Astronomy Sci Advisor PF Gold P: 23,199 intriguing new technique for measuring the mass of a star http://arxiv.org/abs/astro-ph/0501548 European Space Agency page of facts about Titan http://www.esa.int/SPECIALS/Cassini-...F2HHZTD_0.html

 Related Discussions Forum Feedback & Announcements 183