Martin

what is dark energy why does it have negative pressure how does negative pressure accelerate the universe's expansion does anyone want to offer some explanations? I will try to give some partial answers for a start, which can be elaborated or disagreed with The key to the whole discussion of dark energy is the Friedmann equation (a simplified version of the basic Einstein equation of GR gotten from the Einstein equation by assuming a kind of uniformity to the universe that makes things easier to calculate) [math]\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)[/math] a is the scale factor, so expansion corresponds to a' positive and acceleration corresponds to a'' positive and so we cant have acceleration unless [math](\rho + 3p)[/math] is negative. rho is the average energy density in space and p is the average pressure both change with time for most of the history of the universe the large-scale pressure from matter and light has been negligible (we are talking global averages, not local concentrations around stars etc.) so we can forget about pressure except what comes from dark energy rho the density of energy of all kinds, total, is always positive so how can that term up there be negative? only if there is some energy in space with negative pressure what is negative pressure, well there is negative pressure inside a cylinder with a sliding piston if pulling the piston out a ways takes work if there were positive pressure then you could extract work by letting the piston be pushed out some distance. any constant energy---so and so much per cubic meter---has negative pressure because if you enlarge a volume you increase the amount of energy in it and so it must (by conservation) take work to enlarge the volume I got this argument from a cosmologist and I still think there is something tricky about it, but I dont know any better argument so I pass it along. Vacuum energy therefore has to have negative pressure! If there is a constant so and so much per cubic meter, then by that pump piston argument it must represent a constant negative pressure throughout all space and time. Indeed the equation of state for a constant vacuum energy is p = - rho the pressure is equal minus the energy density (energy density has the same units as pressure so theres no constant of proportionality, joules per cubic meter is the same as newtons per square meter) So even though dark energy is estimated currently 73% of the total rho, the energy density, and contributing in that way (with all the other forms of energy) to the slowing down of expansion, it is also by its negative pressure contributing to the speeding up of expansion And its accelerating effect dominates because of that number 3 in the equation (three comes from the number of spatial dimensions in the original GR equation) and they calculate the figure of 0.73 because it is just the right amount to produce the observed spatial flatness and the observed rate of acceleration. I'm still celebrating the arrival of LaTex. Dark energy comes out of the Friedmann equation which with LaTex we can write recognizably, so my feeling is let us say what comes out of the equations, but maybe this dark energy homily has been delivered in another thread?

Here are two good online cosmology calculators Siobahn Morgan's http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html and Ned Wright's http://www.astro.ucla.edu/~wright/CosmoCalc.html homepages for Morgan http://www.earth.uni.edu/smm.html and Wright http://www.astro.ucla.edu/~wright/intro.html To use Siobahn's calculator put Lambda = 0.73 Omega = 0.27 H = 71 (or leave her default value of H = 70, nearly the same) those are the dark energy and the matter densities as fractions of rho crit, and H is the present value of the Hubble parameter then put in any redshift z, like z =1 or 3 or 10 and it will tell you how far away the thing was when it emitted the light we are now getting from it and how far away it is now and how fast it was receding then and how fast it is receding now, at the present moment

there are a lot of great astronomy links, which other SFN posters have used some, or I have seen other places. I hope they get added. In the meantime this thread could be a collection site for other useful astronomy/astrophysics stuff. Like a copy/pasteable version of the Friedmann equations, now that we have Latex [math](\frac{a'}{a})^2 = \frac{8\pi G}{3}\rho - \frac{k}{a^2}[/math] [math]\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)[/math] 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 the Hubble parameter H is defined to be the time derivative a' of the scale parameter a, divided by a. [math]H^2 = (\frac{a'}{a})^2 [/math] In the critical density case of a spatially flat universe the first Friedmann equation boils down to [math]H^2 = \frac{8\pi G}{3}\rho_{crit}[/math] algebraically that turns into the formula for the critical density [math]\rho_{crit} = \frac{3}{8\pi G}H^2[/math]

testing [math]\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)[/math] ahhhh

[math]\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)[/math] I saw something in math forum from Dave about getting it to work

An interesting clue to current developments in HEP is the Spires HEP database at Stanford/SLAC http://www.slac.stanford.edu/library/topcites/ Every year Spires puts out a "top Forty" or "top Hundred" list of most-cited research papers and the ranking for 2003 just came out. http://www.slac.stanford.edu/library/topcites/2003/annual.shtml Here is the Spires Topcited papers in 2003, with only the recent papers showing. I want to see what kinds of recent papers are getting cited a lot, so I have eliminated everything from 1999 and earlier. (there were a lot of older papers in the Spires list which I went thru and removed by hand) the number is how many times the paper was cited by papers in the HEP database---ones that appeared in 2003---e.g. the Particle Data Group article was cited by 1702 other papers. there were 4 recent (since 1999) string papers that got 125 or more citations. to make them easy to spot they are in bold ----------------- 1702 REVIEW OF PARTICLE PHYSICS. PARTICLE DATA GROUP By Particle Data Group (K. Hagiwara et al.). Most recent version published in Phys.Rev.D66:010001,2002 0812 FIRST YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: DETERMINATION OF COSMOLOGICAL PARAMETERS By D.N. Spergel, L. Verde, Hiranya V. Peiris, E. Komatsu, M.R. Nolta, C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S.S. Meyer, L. Page, G.S. Tucker, J.L. Weiland, E. Wollack, E.L. Wright. Published in Astrophys.J.Suppl.148:175,2003 [arXiv: astro-ph/0302209] 0505 FIRST YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: PRELIMINARY MAPS AND BASIC RESULTS By C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S.S. Meyer, L. Page, D.N. Spergel, G.S. Tucker, E. Wollack, E.L. Wright, C. Barnes, M.R. Greason, R.S. Hill, E. Komatsu, M.R. Nolta, N. Odegard, Hiranya V. Peiris, L. Verde, J.L. Weiland. Published in Astrophys.J.Suppl.148:1,2003 [arXiv: astro-ph/0302207] 0351 FIRST RESULTS FROM KAMLAND: EVIDENCE FOR REACTOR ANTI-NEUTRINO DISAPPEARANCE By KamLAND Collaboration (K. Eguchi et al.). Published in Phys.Rev.Lett.90:021802,2003 [arXiv: hep-ex/0212021] 0285 DIRECT EVIDENCE FOR NEUTRINO FLAVOR TRANSFORMATION FROM NEUTRAL CURRENT INTERACTIONS IN THE SUDBURY NEUTRINO OBSERVATORY By SNO Collaboration (Q.R. Ahmad et al.). Published in Phys.Rev.Lett.89:011301,2002 [arXiv: nucl-ex/0204008] 0197 STRINGS IN FLAT SPACE AND PP WAVES FROM N=4 SUPERYANG-MILLS By David Berenstein, Juan M. Maldacena, Horatiu Nastase (Princeton, Inst. Advanced Study). Published in JHEP 0204:013,2002 [arXiv: hep-th/0202021] 0189 MEASUREMENT OF DAY AND NIGHT NEUTRINO ENERGY SPECTRA AT SNO AND CONSTRAINTS ON NEUTRINO MIXING PARAMETERS By SNO Collaboration (Q.R. Ahmad et al.). Published in Phys.Rev.Lett.89:011302,2002 [arXiv: nucl-ex/0204009] 0189 WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) FIRST YEAR OBSERVATIONS: TEMPERATURE - POLARIZATION POLARIZATION By A. Kogut, D.N. Spergel, C. Barnes, C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, M. Limon, S.S. Meyer, L. Page, G. Tucker, E. Wollack, E.L. Wright. Published in Astrophys.J.Suppl.148:161,2003 [arXiv: astro-ph/0302213] 0186 FINAL RESULTS FROM THE HUBBLE SPACE TELESCOPE KEY PROJECT TO MEASURE THE HUBBLE CONSTANT By W.L. Freedman, B.F. Madore, B.K. Gibson, L. Ferrarese, D.D. Kelson, S. Sakai, J.R. Mould, R.C. Kennicutt, H.C. Ford, J.A. Graham, J.P. Huchra, S.M.G. Hughes, G.D. Illingworth, L.M. Macri, P.B. Stetson, P.B. Stetson (Carnegie Inst. Observatories & Caltech, IPAC & Swinburne U., Ctr. Astrophys. Supercomput. & Rutgers U., Piscataway & Carnegie Inst., Wash., D.C. & NOAO, Tucson & Res. Sch. Astron. Astrophys., Weston Creek & Arizona U., Astron. Dept. - Steward Observ. & Johns Hopkins U. & Harvard-Smithsonian Ctr. Astrophys. & Cambridge U., Inst. of Astronomy & Lick Observatory & Dominion Astrophys. Obs., Victoria). Published in Astrophys.J.553:47-72,2001 [arXiv: astro-ph/0012376] 0180 MEASUREMENT OF THE RATE OF NU/E + D --> P + P + E- INTERACTIONS PRODUCED BY B-8 SOLAR NEUTRINOS AT THE SUDBURY NEUTRINO OBSERVATORY By SNO Collaboration (Q.R. Ahmad et al.). Published in Phys.Rev.Lett.87:071301,2001 [arXiv: nucl-ex/0106015] 0177 THE SLOAN DIGITAL SKY SURVEY: TECHNICAL SUMMARY By SDSS Collaboration (Donald G. York et al.). Published in Astron.J.120:1579-1587,2000 [arXiv: astro-ph/0006396] 0162 FIRST YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: IMPLICATIONS FOR INFLATION By H.V. Peiris, E. Komatsu, L. Verde, D.N. Spergel, C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S.S. Meyer, L. Page, G.S. Tucker, E. Wollack, E.L. Wright (Princeton U. & NASA, Goddard & British Columbia U. & Chicago U., EFI & CFCP, Chicago & Brown U. & UCLA). Published in Astrophys.J.Suppl.148:213,2003 [arXiv: astro-ph/0302225] 0139 THE SLOAN DIGITAL SKY SURVEY: EARLY DATA RELEASE By SDSS Collaboration (Chris Stoughton et al.). Published in Astron.J.123:485-548,2002 0135 ROLLING TACHYON By Ashoke Sen (Harish-Chandra Res. Inst. & Penn State U.). Published in JHEP 0204:048,2002 [arXiv: hep-th/0203211] 0134 A PERTURBATIVE WINDOW INTO NONPERTURBATIVE PHYSICS By Robbert Dijkgraaf (Amsterdam U. & Amsterdam U., Inst. Math.), Cumrun Vafa (Harvard U., Phys. Dept.). [arXiv: hep-th/0208048] 0133 A MEASUREMENT BY BOOMERANG OF MULTIPLE PEAKS IN THE ANGULAR POWER SPECTRUM OF THE COSMIC MICROWAVE BACKGROUND By Boomerang Collaboration (C.B. Netterfield et al.). Published in Astrophys.J.571:604-614,2002 [arXiv: astro-ph/0104460] 0130 THE COSMOLOGICAL CONSTANT AND DARK ENERGY By P.J.E. Peebles (Princeton U.), Bharat Ratra (Kansas State U.). Published in Rev.Mod.Phys.75:559-606,2003 [arXiv: astro-ph/0207347] 0126 SOLAR B-8 AND HEP NEUTRINO MEASUREMENTS FROM 1258 DAYS OF SUPER-KAMIOKANDE DATA By Super-Kamiokande Collaboration (S. Fukuda et al.). Published in Phys.Rev.Lett.86:5651-5655,2001 [arXiv: hep-ex/0103032] 0125 TYPE IIB GREEN-SCHWARZ SUPERSTRING IN PLANE WAVE RAMOND-RAMOND BACKGROUND By R.R. Metsaev (Lebedev Inst.). Published in Nucl.Phys.B625:70-96,2002 [arXiv: hep-th/0112044] 0125 INDICATIONS OF NEUTRINO OSCILLATION IN A 250 KM LONG BASELINE EXPERIMENT By K2K Collaboration (M.H. Ahn et al.). Published in Phys.Rev.Lett.90:041801,2003 [arXiv: hep-ex/0212007] 0124 NEW GENERATION OF PARTON DISTRIBUTIONS WITH UNCERTAINTIES FROM GLOBAL QCD ANALYSIS By J. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P. Nadolsky, W.K. Tung (Michigan State U.). Published in JHEP 0207:012,2002 [arXiv: hep-ph/0201195] ... ... ...

the theory of gravity (GR) that's been in use since 1915 predicts gravity waves and there is a detector that just went in to operation looking for them those would be slight temporary distortions in the geometry of spacetime, I picture them as ripples, that spread out from some source like a collapsing star or a near-collision of two very dense stars but this is not EM! EM waves are temporary disturbances in the electric field (or electric and magnetic fields treated as a single entity you are asked first to imagine a static electric field extending outwards from some charged object, the forcefield of that charged object extending out thru all space and then you are told some equations by which that field can superimposed with all the other similar fields of all the other charges, to make one electric field extending thru out the U and then you are given some rules (maxwell eqn) by which that field can be twanged and will continue vibrating, with the energy spreading out forever so that, in imagination, the field is almost a real thing, like a pondsurface or a drumhead or somesuch 3D medium of vibration but then again it isnt and that was just the classical picture, not the quantum field picture------and physics never answers any basic question, it is just a sequence of improvements in what one imagines. its all in the imagination and the amazing thing is how well it works

Great! I hope other people will add some neat links. I'll post a few I have here too. here are a couple of goodies: Ned Wright's cosmology website and FAQ http://www.astro.ucla.edu/~wright/cosmolog.htm http://www.astro.ucla.edu/~wright/cosmology_faq.html Wendy Freedman and Michael Turner's "Measuring and Understanding the Universe" http://arxiv.org/astro-ph/0308418 a lot of good astronomy links are graphic rather than verbal, such as images from the HST and computer animations, also Ned Wright has a calculator that lets you calculate from something's redshift how far away it is. I'm interested to see what links others here have found useful so I wont rush to post a lot of my favorites

this thread can be for stashing links to webpages with good explanations of astronomy stuff in Cosmology forum I just saw where aman asked about the slingshot effect (used a lot to save fuel on missions to the outer planets) and swansont gave this link: http://www.mathpages.com/home/kmath114.htm explaining clearly how the slingshot maneuver gains energy and angular momentum (taking away from the planet being used) and then Jenab confirmed having seen slingshotting in simulations he'd run http://www.scienceforums.net/forums/showthread.php?p=30823#post30823 I'm thinking of adding other good links i see to this thread, to have them handy. like link-answers to astronomy FAQ. Join in if you feel like it.

I found another review article which mentions Hawking's "euclidean quantum gravity" and compares it with loop and string. http://arxiv.org/gr-qc/9803024 "Strings, loops and others: a critical survey of the present approaches to quantum gravity" Carlo Rovelli (Plenary lecture on quantum gravity at the GR15 conference) ------------- here's a link to get recent preprints of non-string Quantum Gravity research papers: Last twelve months (e.g. 14 June 2003 to 14 June 2004): http://arXiv.org/find/nucl-ex,astro-ph,nucl-th,math-ph,hep-ex,physics,cond-mat,hep-lat,quant-ph,gr-qc,hep-ph,hep-th/1/OR+OR+abs:+AND+AND+loop+quantum+OR+cosmology+gravity+abs:+AND+AND+quantum+gravity+OR+simplicial+OR+canonical+nonperturbative+abs:+OR+AND+spin+foam+AND+dynamical+triangulation/0/1/0/past/0/1 this is designed to catch: loop quantum gravity loop quantum cosmology canonical quantum gravity simplicial quantum gravity nonperturbative quantum gravity spin foam dynamical triangulation

Looks like a tribute to the approach Hawking and collaborators pursued in the 1990s as an alternative to inflation. After a brief 4 line paragraph about inflation, it switches to talking about the alternative: "The second contender for a theory of initial conditions is quantum cosmology, the application of quantum theory to the entire universe..." Tesseract, I found a recent review paper which mentions "Euclidean quantum gravity" approach of Hawking et al, but it gives no recent research papers (most was in 1990s I think) http://arxiv.org/gr-qc/0405107 "Quantum Gravity" Enrique Alvarez

Does anyone have some QG links they want to recommend as good introductions to the subject, or surveys of current research, or particularly good for explaining one particular line of research? As for a good (popularized) intro to Loop Quantum Gravity there is Lee Smolin's January 2004 Scientific American article called "Atoms of Space and Time". The trouble being that it is not, AFAIK, available free online. here is another good popularly written article by the German science journalist Rudy Vaas http://arxiv.org/abs/physics/0403112 "The Duel: Loops versus Strings" this one is available online. Vaas writes for a German magazine similar to the Scientific American----this article is in English however