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Cosmology

Cosmology. By the end of this topic you should be able to : describe Olbers ’ paradox in Newtonian cosmology and how it is resolved; -describe the main features of the Big Bang and the expansion of the u niverse ;

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Cosmology

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  1. Cosmology Bytheend of thistopicyoushouldbeableto: describe Olbers’ paradox in Newtoniancosmology and howitis resolved; -describe themainfeatures of the Big Bang and theexpansion of theuniverse; -understandthesignificance of thecosmicbackgroundradiation; -statethemeaning of theterms open universe and closeduniverse; -outlinethetheoreticalpossibliitiesfortheevolution of theuniverse; -statethemeaning and significance of thetermcriticaldensity; -appreciatetheimportance of variousforms of darkmatter.

  2. Cosmologicalprinciple TheUniverseappearstobe full of structures. Butifwe look at itonaverylargescale, we no longerseeany. Ifwe imagine cutting up theUniverseinto cubes of side 300 Mpcacross, the interior of anyone of these cubes would look thesame as the interior of anyother cube, anywhereelse in theuniverse. Thisiscalledthehomogeneityprinciple. On a largescale, theUniverse looks uniform, i.e. the matter density of our local region, or lets say the amount of galaxies, stars, gas and dust per a certain volume is pretty much the same anywhere in the universe.

  3. Cosmologicalprinciple Similarly, ifwe look in differentdirections, weseeessentiallythesamething. No directionisspecial in comparisonwithanother. Thisiscalledtheisotropyprinciple. Thesetwoprinciples, homogeneity and isotropy, make up whatiscalledthecosmologicalprinciple. ThecosmologicalprincipleimpliesthattheUniverse has no edge (fotifitdid, thepart of theUniverseneartheedgewould look differentfrom a partfarfromtheedge, violatingthehomogeneityprinciple). Similarly, itimpliesthattheUniverse has no centre (forifitdid, observingfromthe centre would show a differentpicturefromobservingfromanyotherpoint, violatingtheprinciple of isotropy).

  4. Newton’suniverse Usingan extreme version of thecosmologicalprinciple, Newton suggestedthattheUniverseisinfinite in extent, han no beginning and isstatic, meaningit has beenuniform and isotropic at all times. Howeverserioustheoreticalproblemswereposedforthismodel.

  5. Olbers’ paradox Imagine a Universethatisinfinite and containsaninfinitenumber of stars more orlessuniformlydistributed in space. Theverydistantstarscontributeverylittle light toanobserveronEarthbutthere are varymany of them. Mathematically, letn stand forthenumberdensity of stars, thatisthenumber of stars per unitvolume of space. At a distance d from a star of luminosityL, theapparentbrightnessis Whyisthenightskydark? Thenumber of stars in a thinshell of thickness t a distance d fromtheobserverisnumberdensity x volume. Hencethereceivedenergy per area per unit of time fromallthestars in thethinshellis

  6. Olbers’ paradox Olbers’ paradoxcannotbeeliminated in Newton’suniverse. Theobviouswayto try tosolvethepuzzleistoinvokeabsorption of theradiationfromtheinterveningstars and theinterstellarmedium. Thisdoesnotwork, however, because in an eternal universetheinterstellarmediumwould, in time, beheated up bytheradiationit absorbed and wouldthenitselfradiate as muchenergy as itreceived, leadingtothesamedifficulty. Thisis a constant (i.e., itdoesnotdependonthedistancetotheshelld). Sincethereisaninfinitenumber of suchshellssurroundingtheobserver, and sinceeachcontributes a constantamount of energy, the total energyreceivedmustbeinfinite, makingthenightskyinfinitelybright, whichitisnot.

  7. Olbers’ paradox In a finite, expandingUniverse, however, theradiationreceivedbytheobserverissmall and finitefortwomainreasons: Thereis a finitenumber of stars and each has a finitelifetime. Thismeansthatstarshavenotbeenradiatingforever, norwillthegoonradiatingforever. Their total radiationisthussmall and finite. Because of thefiniteage of theUniverse, starsthat are faraway (beyondthe ‘eventhorizon’) havenotyethad time fortheir light toreachus. AnadditionalreasonthathelpsresolveOlbers’ paradoxisthefollowing: 3. Theradiationreceivedisredshifted and so containslessenergy.

  8. Hubble’sLaw Thedarklines in theabsorptionspectra of distantgalaxiescorrespondtowavelengthsthathavebeen absorbed bythechemicalelements in theouterlayers of thegalaxies. The positions of thedarklines are wellknownfromexperimentsonEarthbuttheobservedwavelengthsfromthegalaxies, whencomparedtothosemeasuredonEarth, werefoundto be a bit longer; theywereredshifted.

  9. Hubble’sLaw Hubble interpretedtheredshift of thespectrallines as evidence of a velocity of a galaxyawayfromus. The fasterthegalaxy, thelargertheredshift. Hubble’sobservationsthussuggestanexpandingUniversewithgalaxiesmovingawayfromus and fromeachother. Italsosuggeststhat in thepasttheUniversewasmuchsmaller. The Universeappearstohavestartedfrom a kind of explosionthat set mattermovingoutward. Itisimportantto realice thattheuniverseisnotexpandingintoemptyspace. The galaxiesthat are movingapartfromus are notmovingintoanother, previouslyunoccupied, part of theUniverse. Spaceisbeingcreated in betweenthegalaxies.

  10. Thecosmicbackgroundradiation In 1964, Penzias and Wilson, tworadioastronomersworking at Bell Laboratories, made a fundamental, if accidental, discovery. Theyusedanantennatheyhadjustdesignedtostudy radio signalsfromourgalaxy. Buttheantennawaspicking up a signalthatpersisted no matterwhatpart of theskytheantennawaspointing at. Thissignalturntohave a black-bodyspectrumcorrespondingto a temperature of 2.7 K. Theisotropy of thisradiationindicatedthatitwasnotcomingfromany particular spot in thesky; ratheritwasradiationthatwasfillingallspace. Thiskind of radiationhadbeenpredictedonthebasis of the Big Bangtheory 30 yearsearlierby George Gamow. Penzias and Wilson realizedthattheradiationdetectedwastheremnant of thehotexplosion at thebeginning of time. Itwastheafterglow of theenormoustemperaturethatexisted in theveryearlyuniverse. As theuniverse has expanded, thetemperature has keptfallingtoreachitspresentvalue of 2.7 K.

  11. Big bangtheory Thediscovery of theexpandinguniversebyHubbleimplies a definitebeginning of theuniverse, some 14 billionyears ago. Thesize of theuniverse at that time wasinfinitesimallysmall and thetemperature and pressureenormous. Theseconditionscreatethepicture of a giganticexplosion at t=0, which set mattermovingoutwards. Billions of yearslaterweseetheremnant of thisexplosion in therecedingmotion of thedistantgalaxies. Itisimportanttounderstandthatthe Big Bangwasnotanexplosionthattook place at a specific time in thepastsomewhere in theuniverse. At the time of the Big Bangthespace in whichthematter of theuniverse resides wascreated as well. Thus, the Big Banghappenedabout 14 billionyearsagoeverywhere in theuniverse (theuniversethenbeing a point).

  12. Big bangtheory • Themain experimental evidence in support of the Big Bangtheory: • Theexpansion of theuniverse– Theuniverseisnowobservedtoexpand. Hence in thepasttheuniversehad a smallersize. Thispointsto a picture of an ‘explosion’ that set theuniversemovingoutward. • Thecosmicbackgroundradiation– Todaywe observe thebackgroundradiation at 2.7K. Thisisconisistentwith a small, hotuniverse in thedistantpast, whichbegantocooldown as itexpanded. • Heliumabundance– Itis a prediction of the Big Bangmodelthatthereshouldbeanabundance of helium in theuniverse, of about 25% bymass. Measurements of heliumabundancetodaygive a numberthatisneverlessthan 25%. Itisverydifficulttoaccountforthislowerboundonhelium in suchdifferentmeasurementsifwe do notacceptthecosmologicalexplanation of heliumformation.

  13. Thedevelopment of theUniverse Mathematically, theexpansion of theuniverse can bedescribed in terms of a scale factor of theuniverse in thefollowingway. Ifthedistancebetweentwogalaxieswasx0 at somearbitrary time, thentheseparation of thesetwogalaxies at some time tlaterisgivenbytheexpression x(t) = R(t) x0. ThefunctionR(t)iscalledthescale factor of theuniverse and is of basicimportancetocosmology. Itissometimesreferredtoloosely as theradius of theuniverse. Note thatthisis a scalarfunction, not a vector, indicatingthestandardassumptionabouttheisotropy and homogeneity of theuniverseon a largescale.

  14. Thedevelopment of theUniverse Itis a basicproblem in cosmologytodiscoverwhatthisscale factor R(t)is. Application of thelaws of general relativityresults in threepossibilitiesforR(t). ThefirstpossibilityisthatR(t)startsfromzero, increasesto a maximumvalue and thendecreases back tozeroagain. Theuniversecollapsesafteraninitialperiod of expansion. Thisiscalled a closeduniverse.

  15. Thedevelpment of theUniverse In thesecondpossibility, thescale factor R(t) increaseswithoutlimit – theuniversecontinuestoexpandforever. Thisiscalledanopen universe. Thethirdpossibilityisthattheuniversedoesexpandforever, buttherate of expansiondecreases. Thisiscalled a flat universe.

  16. Thedevelopment of theUniverse Thethreesolutions of Einstein’sequationsfortheevolution of theuniverse. Thepresent time isindicatedby “now”. Noticethat, dependingonwhichsolutionistaken, theage of theuniverseisdifferent. In otherwords, differentsolutionsimply a differentage. Which of thethreepossibilitiesisactuallyrealizeddependsonthevalue of themassdensity of theuniverse, ρ, relativeto a criticaldensitywhosevalueisabout ρc ≈ 10-25 kg/m3.

  17. Thedeveloptment of theUniverse • Ifρ < ρc, theuniverseexpandsforever at a slowingrate. Theuniverseiscalled open. • Ifρ = ρc, theuniverseexpandsforever at a slowingratethatapproacheszero. Theuniverseiscalled flat. • Ifρ > ρc, theuniversecollapsesafter a period of expansion. Theuniverseiscalledclosed. General relativityactuallygivesanadditionalinterpretationtothethreedifferentscenariosforR(t). General relativitysaysthatthegeometry of theuniverse (i.e.the rules of geometry) dependontheamount of mass in theuniverse. Themass in theuniversebendsor curves thespace and time in theuniverse. Theamount of bendingdependsonhowmuchmassthereis. The case ρ < ρccorrespondstoan open universe of infinitevolume, whosecurvatureisanalogoustothat of thesurface of a saddle (a hyperboloid). The case ρ > ρccorrespondsto a closeduniverse, with a finitevolume and a curvature similar tothat of a sphere. Finally, ρ = ρccorrespondstoan open, infinite, but flat universe, analogoustothesurface of anordinaryplane.

  18. Darkmatter Tomeasurethemassdensity of theuniversemeansmeasuringthemass of galaxieswithin a largevolume of space and dividingthatmassbythevolume. Thereisanimmediateproblem in all of this in thatweknowthereexists “darkmatter”, matterthatwecannotsee. Thedetermination of thedensity of theuniverseisdifficult.

  19. Darkmatter Darkmattercouldbe in theform of browndwarfs and other similar coldobjects, buttheexistence of more exoticpossibilitiesisalsohypothesized. MACHOS (massive compact halo objects), forexampleblack and browndwarfs. WIMPs (weaklyinteractingmassiveparticles), forexample neutrinos (almostexcluded), neutralinos, gravitinos, axions, axinos, etc.

  20. Darkenergy Thediscussionbeforeisbasedonthestandard Big Bangmodel of theuniverse and nowisoutdated. Since 1998 it has beenknownthatdistant supernovas are movingawayfromus at muchfasterspeedsthanthoseexpectedbasedonthestandard Big Bangmodel. Basedongravitationalone, wewouldexpect a deceleration in thespeed of recession of distantobjects. The data says, instead, thatthespeedisincreasing. Whatiscausingthisacceleration?

  21. Darkenergy Itappearsthattheuniverseisfilledwith a kind of all-permeatingvacuumenergycalleddarkenergy. Thepresence of this “energy” creates a kind of repulsiveforcethatnotonlycounteractstheeffect of gravityon a largescale, butactuallydominatesit, causingacceleration in distantobjectsratherthantheexpecteddeceleration. Thedomination of theeffects of darkenergyovergravityappearstohavestartedabout 5 billionyears ago. Itthusappearsthat, eventhoughthepresentdensity of theuniverseisnowbelievedtoequatethecriticaldensity, theuniversefollowsthepatternshown in the figure. Thereisnowconvincingevidencethatρ = ρc basedondetailedradiationundertakenbytheWilkinsonMicrowaveAnisotropyProbe (WMAP)

  22. Mass-energycomposition Themass-energydensity of theuniverseisbelievedtobemadeout of approximately 73% darkenergy and only 27% matter. And of thismatter in theuniverse, 85% isestimatedtobedarkmatter (i.e. 85% of the 27% matter), leaving a minisclefraction (15% of the 27% matter) about 4% accountedforbyordinarymatter.

  23. Questions

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