Starost univerzuma — разлика између измена

(.)
</ref> U okviru njih imamo temperature najhladnijih [[beli patuljak|belih patuljaka]], koji se postepeno hlade kako stare.
 
== Kosmološki parametri ==
==Cosmological parameters==
[[Image:Mplwp universe scale evolution.svg|thumb|left|upright=1.5|TheStarost ageuniverzuma ofse themože universeodrediti can be determined by measuring themerenjem [[HubbleHablov zakon|Hablove constantkonstante]] todaydanas andi extrapolatingekstrapolacijom backunazad inu timevremenu withsa theposmatranom observedvrednošću valueparametara of density parametersgustine (<math>~\Omega~</math>). BeforePre the discovery ofotkrića [[dark energy|tamne energije]], itverovalo wasse believedda thatuniverzumom thedominira universe was matter-dominatedmaterija ([[Einstein–de Sitter universe|Ajnštajn-de Sitterov svemir]], greenzelena curvekriva). NoteTreba thatimati thena umu da [[de Sitter universe|de Siterov svemir]] hasima infinitebeskonačnu agestarost, while thedok [[Big Crunch|closedzatvoreni]] universe hasuniverzum theima leastnajmanju agestarost.]]
[[File:Age Universe Planck 2013.png|thumb|upright=1.5|TheVrednost valuefaktora ofkorekcije the age correction factorstarosti, <math>~F~,</math> isje shownprikazana askao afunkcija function of twodva [[cosmology|cosmologicalkosmološka parametersparametra]]: thetrenutna currentfrakciona fractionalgustina matter densitymaterije <math>~\Omega_\text{m}~</math> andi cosmologicalkosmološka constantkonstantna densitygustina <math>~\Omega_\Lambda~.</math> TheVrednosti ovih parametara koje su [[Lambda-CDM model|best-fit valuesnajpodesnije]], ofprikazane thesesu parametersu areokviru shownu bygornjem thelevom box in the upper leftuglu; the matter-dominateduniverzum universekojim isdominira shownmaterija byprikazan theje starzvezdom inu thedonjem lowerdesnom rightuglu.]]
 
TheProblem problemodređivanja ofstarosti determininguniverzuma theusko ageje of the universe is closely tied tovezan theza problem ofodređivanja determiningvrednosti thekosmoloških values of the cosmological parametersparametara. TodayDanas thisse isto largelyuglavnom carriedsprovodi outu in the context of thekontekstu [[Lambda -CDM model|ΛCDM]] modelmodela, wheregde these universepretpostavlja isda assumeduniverzum tosadrži contain normalnormalnu (baryonicbarionsku) mattermateriju, coldhladnu [[darkТамна matterматерија|tamnu materiju]], radiationzračenje (including bothuključujući [[photonfoton]]se andi [[neutrino|neutrine]]s), and ai [[cosmological constant|kosmološku konstantu]].
 
TheDeo fractionaldoprinosa contributionsvakog ofod eachnjih tou thetrenutnoj currentgustini energyenergije densityuniverzuma ofje the universe is given by thedat [[densityFriedmann parameterequations|parametrima gustine]]s <math>~\Omega_\text{m}~,</math> <math>~\Omega_\text{r}~,</math> andi <math>~\Omega_\Lambda~.</math> Potpuni [[ΛCDM]] model je opisan nizom drugih parametara, ali u svrhu izračunavanja njegove starosti ova tri, zajedno sa [[Hablov zakon|Hablovim parametrom]] <math>~H_0~</math>, su najvažnija.
The full [[ΛCDM]] model is described by a number of other parameters, but for the purpose of computing its age these three, along with the [[Hubble constant|Hubble parameter]] <math>~H_0~</math>, are the most important.
 
IfAko onese hasimaju accuratetačna measurementsmerenja ofovih these parametersparametara, then the age of the universeonda canse bestarost determineduniverzuma bymože usingodrediti thekorišćenjem [[Friedmann equations|FriedmannFridmanove equationjednačine]]. Ova Thisjednačina equationpovezuje relatesstopu the rate of change in thepromene [[scaleScale factor (cosmology)|scalefaktora factorrazmere]] <math>~a(t)~</math> tosa thesadržajem mattermaterije contentu of the universeuniverzumu. Preobražavajući Turning this relationovu aroundrelaciju, wemože canse calculateizračunati thepromena changevremena inpo timepromeni perfaktora changerazmere ini scaletako factorizračunati andukupna thusstarost calculate the total age of the universe byuniverzuma [[Integral|integratingintegracijom]] thisove formulaformule. The ageStarost <math>~t_0~</math> is then given by anje expressiontada ofdata theizrazom formoblika
:<math>t_0 = \frac{1}{H_0} \, F (\,\Omega_\text{r},\,\Omega_\text{m},\,\Omega_\Lambda,\,\dots\,)~</math>
 
where <math>~H_0~</math> is the [[Hubble's law|Hubble parameter]] and the function <math>~F~</math> depends only on the fractional contribution to the universe's energy content that comes from various components. The first observation that one can make from this formula is that it is the Hubble parameter that controls that age of the universe, with a correction arising from the matter and energy content. So a rough estimate of the age of the universe comes from the [[Hubble time]], the inverse of the Hubble parameter. With a value for <math>~H_0~</math> around {{val|69|u=km/s/Mpc}}, the Hubble time evaluates to <math>~1/H_0 =~</math>{{val|14.5}}&nbsp;billion years.<ref>
gde je <math>~H_0~</math> [[Hubble's law|Hablov parametar]] i funkcija <math>~F~</math> zavisi samo od frakcionog doprinosa energetskom sadržaju univerzuma koji dolazi iz različitih komponenti. Prvo zapažanje koje se može izvesti iz ove formule je da je Hablov parametar taj koji kontroliše starost univerzuma, uz korekciju koja proizilazi iz sadržaja materije i energije. Dakle, gruba procena starosti univerzuma dolazi iz [[Hablov zakon|Hablovog vremena]], inverzne vrednosti Hablovog parametra. Sa vrednošću za <math>~H_0~</math> oko {{val|69|u=km/s/Mpc}}, Hablovo vreme se procenjuje na <math>~1/H_0 =~</math>{{val|14.5}}&nbsp;milijardi godina.<ref>{{Cite book
{{Cite book
|last=Liddle |first=A. R.
|date=2003
|url-access=limited
|page=[https://archive.org/details/introductiontomo00lidd_717/page/n73 57]
}}</ref>
</ref>
 
ToDa getbi ase moredobio accuratetačniji numberbroj, themora correctionse functionizračunati funkcija korekcije <math>~F~</math> must be computed. InGeneralno, generalovo thisse mustmora beuraditi done numericallynumerički, and the results for a rangerezultati ofza cosmologicalopseg parametervrednosti valueskosmoloških areparametara shownprikazani insu thena figureslici. For theZa [[Lambda -CDM model|PlanckPlankove valuesvrednosti]] <math>~(\Omega_\text{m}, \Omega_\Lambda) =~</math>(0.,3086, 0.,6914), shownprikazane byu theokviru boxu ingornjem thelevom upperuglu leftslike, corner of the figure,ovaj thisfaktor correctionkorekcije factorje isoko about <math>~F = 0.,956 ~.</math> For aZa flatravan universeuniverzum withoutbez anyikakve cosmologicalkosmološke constantkonstante, shownprikazan byzvezdom theu stardonjem indesnom the lower right corneruglu, <math>~F = {2}/{3}~</math> isje muchmnogo smallermanji andi thussamim thetim universeje isuniverzum youngermlađi forza afiksnu fixedvrednost valueHablovog ofparametra. theDa Hubble parameter.bi Tose makedobila thisova figurecifra, <math>~\Omega_\text{r}~</math> isse heldodržava constantkonstantnim (roughlyotprilike equivalentekvivalentno tosa holding theodržavanjem [[CosmicКосмичко Microwaveпозадинско Backgroundзрачење|CMB]] temperaturetemperaturne constantkonstante) and the curvature density parameter isi fixedparametar bygustine thezakrivljenosti valueje offiksiran thevrednošću otherostala threetri.
 
ApartOsim fromPlankovog the Planck satellitesatelita, the WilkinsonWilkinsonova Microwavemikrotalasna Anisotropyanizotropna Probesonda ([[WMAP]]) wasbila instrumentalje inključna establishingu anutvrđivanju accuratetačne agestarosti of the universeuniverzuma, thoughiako otherse measurementsdruga mustmerenja bemoraju foldedsastaviti inda tobi gainse andobio accuratetačan numberbroj. [[Космичко позадинско зрачење|CMB]] measurementsmerenja aresu veryveoma gooddobra atu constrainingograničavanju thesadržaja matter contentmaterije <math>~\Omega_\text{m}~,</math><ref>{{cite web
{{cite web
|last=Hu
|first=W.
|archive-date=23 February 2008
|url-status=live
and}}</ref> curvaturei parameterparametra zakrivljenosti <math>~\Omega_\text{k}~.</math><ref name="anim3">
}}
</ref>
and curvature parameter <math>~\Omega_\text{k}~.</math><ref name="anim3">
{{cite web
|last=Hu |first=W.
|archive-date=23 February 2008
}}
</ref> To nije toliko senzitivno na <math>~\Omega_\Lambda~</math> direktno,<ref name="anim3"/> delimično zato što kosmološka konstanta postaje važna samo pri malom crvenom pomaku. Veruje se da trenutno najtačnija određivanja Hablovog parametra <math>~H_0~</math> potiču od izmerenih osvetljenosti i crvenih pomaka udaljenih [[Type Ia supernova|supernova tipa Ia]]. Kombinovanje ovih merenja dovodi do opšte prihvaćene vrednosti za starost univerzuma koja je gore citirana.
</ref>
It is not as sensitive to <math>~\Omega_\Lambda~</math> directly,<ref name="anim3"/> partly because the cosmological constant becomes important only at low redshift. The most accurate determinations of the Hubble parameter <math>~H_0~</math> are currently believed to come from measured brightnesses and redshifts of distant [[Type Ia supernova]]e. Combining these measurements leads to the generally accepted value for the age of the universe quoted above.
 
Kosmološka konstanta čini univerzum „starijim“ za fiksne vrednosti ostalih parametara. Ovo je značajno, jer pre nego što je kosmološka konstanta postala opšteprihvaćena, model Velikog praska je imao poteškoća da objasni zašto se činilo da su [[globular cluster|globularna jata]] u Mlečnom putu daleko starija od starosti univerzuma izračunatog na osnovu Hablovog parametra i univerzuma koji sadrži samo materiju.<ref>{{cite web
The cosmological constant makes the universe "older" for fixed values of the other parameters. This is significant, since before the cosmological constant became generally accepted, the Big Bang model had difficulty explaining why [[globular cluster]]s in the Milky Way appeared to be far older than the age of the universe as calculated from the Hubble parameter and a matter-only universe.<ref>
{{cite web
|title=Globular Star Clusters
|date=1 July 2011
|archive-date=6 March 2008
}}
</ref> Uvođenje kosmološke konstante omogućava univerzumu da bude stariji od ovih klastera, i daje objašnjavanje drugih karakteristika koje kosmološki model zasnovan samo na materiji nije mogao.<ref>
</ref>
Introducing the cosmological constant allows the universe to be older than these clusters, as well as explaining other features that the matter-only cosmological model could not.<ref>
{{cite arXiv
|last1=Ostriker |first1=J.P.