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Mplwp universe scale evolution

Yanvar 17, 2023

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İzah
English: Plot of the evolution of the size of the universe (scale parameter a) over time (in billion years, Gyr). Different models are shown, which are all solutions to the Friedmann equations with different parameters. The evolution is governed by the equation
.

Here is the radiation density, the matter density, the curvature parameter and the dark energy, all normalized such that represents the fact that today's expansion rate is .
Plotted parameter sets:

  • De Sitter universe: Only dark energy:
  • Lambda-CDM model: The model that fits the observations best: ,
  • An empty universe (no relevant contributions of matter, radiation, dark energy) with negative curvature:
  • Einstein–de Sitter universe: A flat universe dominated by cold matter:
  • A closed Friedmann model: ,
Tarix
Mənbə Öz işi
Müəllif Geek3
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The SVG code is valid.
 
This plot was created with mplwp, the Matplotlib extension for Wikipedia plots.
Source code
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Python code

#!/usr/bin/python # -*- coding: utf8 -*- import matplotlib.pyplot as plt import matplotlib as mpl import numpy as np from math import * code_website = 'http://commons.wikimedia.org/wiki/User:Geek3/mplwp' try: import mplwp except ImportError, er: print 'ImportError:', er print 'You need to download mplwp.py from', code_website exit(1) name = 'mplwp_universe_scale_evolution.svg' fig = mplwp.fig_standard(mpl) fig.set_size_inches(600 / 72.0, 450 / 72.0) mplwp.set_bordersize(fig, 58.5, 16.5, 16.5, 44.5) xlim = -17, 22; fig.gca().set_xlim(xlim) ylim = 0, 3; fig.gca().set_ylim(ylim) mplwp.mark_axeszero(fig.gca(), y0=1) import scipy.optimize as op from scipy.integrate import odeint tH = 978. / 68. # Hubble time in Gyr def Hubble(a, matter, rad, k, darkE): # the Friedman equation gives the relative expansion rate a = a[0] if a <= 0: return 0. r = rad / a**4 + matter / a**3 + k / a**2 + darkE if r < 0: return 0. return sqrt(r) / tH def scale(t, matter, rad, k, darkE): return odeint(lambda a, t: a*Hubble(a, matter, rad, k, darkE), 1., [0, t]) def scaled_closed_matteronly(t, m): # analytic solution for matter m > 1, rad=0, darkE=0 t0 = acos(2./m-1) * 0.5 * m / (m-1)**1.5 - 1. / (m-1) try: psi = op.brentq(lambda p: (p - sin(p))*m/2./(m-1)**1.5 - t/tH - t0, 0, 2 * pi) except Exception: psi=0 a = (1.0 - cos(psi)) * m * 0.5 / (m-1.) return a # De Sitter http://en.wikipedia.org/wiki/De_Sitter_universe matter=0; rad=0; k=0; darkE=1 t = np.linspace(xlim[0], xlim[-1], 5001) a = [scale(tt, matter, rad, k, darkE)[1,0] for tt in t] plt.plot(t, a, zorder=-2, label=ur'$\Omega_\Lambda=1$, de Sitter') # Standard Lambda-CDM https://en.wikipedia.org/wiki/Lambda-CDM_model matter=0.3; rad=0.; k=0; darkE=0.7 t0 = op.brentq(lambda t: scale(t, matter, rad, k, darkE)[1,0], -20, 0) t = np.linspace(t0, xlim[-1], 5001) a = [scale(tt, matter, rad, k, darkE)[1,0] for tt in t] plt.plot(t, a, zorder=-1, label=ur'$\Omega_m=0.\!3,\Omega_\Lambda=0.\!7$, $\Lambda$CDM') # Empty universe matter=0; rad=0; k=1; darkE=0 t0 = op.brentq(lambda t: scale(t, matter, rad, k, darkE)[1,0], -20, 0) t = np.linspace(t0, xlim[-1], 5001) a = [scale(tt, matter, rad, k, darkE)[1,0] for tt in t] plt.plot(t, a, label=ur'$\Omega_k=1$, empty universe', zorder=-3) ''' # Open Friedmann matter=0.5; rad=0.; k=0.5; darkE=0 t0 = op.brentq(lambda t: scale(t, matter, rad, k, darkE)[1,0], -20, 0) t = np.linspace(t0, xlim[-1], 5001) a = [scale(tt, matter, rad, k, darkE)[1,0] for tt in t] plt.plot(t, a, label=ur'$\Omega_m=0.\!5, \Omega_k=0.5$') ''' # Einstein de Sitter http://en.wikipedia.org/wiki/Einstein–de_Sitter_universe matter=1.; rad=0.; k=0; darkE=0 t0 = op.brentq(lambda t: scale(t, matter, rad, k, darkE)[1,0], -20, 0) t = np.linspace(t0, xlim[-1], 5001) a = [scale(tt, matter, rad, k, darkE)[1,0] for tt in t] plt.plot(t, a, label=ur'$\Omega_m=1$, Einstein de Sitter', zorder=-4) ''' # Radiation dominated matter=0; rad=1.; k=0; darkE=0 t0 = op.brentq(lambda t: scale(t, matter, rad, k, darkE)[1,0], -20, 0) t = np.linspace(t0, xlim[-1], 5001) a = [scale(tt, matter, rad, k, darkE)[1,0] for tt in t] plt.plot(t, a, label=ur'$\Omega_r=1$') ''' # Closed Friedmann matter=6; rad=0.; k=-5; darkE=0 t0 = op.brentq(lambda t: scaled_closed_matteronly(t, matter)-1e-9, -20, 0) t1 = op.brentq(lambda t: scaled_closed_matteronly(t, matter)-1e-9, 0, 20) t = np.linspace(t0, t1, 5001) a = [scaled_closed_matteronly(tt, matter) for tt in t] plt.plot(t, a, label=ur'$\Omega_m=6, \Omega_k=\u22125$, closed', zorder=-5) plt.xlabel('t [Gyr]') plt.ylabel(ur'$a/a_0$') plt.legend(loc='upper left', borderaxespad=0.6, handletextpad=0.5) plt.savefig(name) mplwp.postprocess(name)

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müəllifin qısa adı: Geek3
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indiki00:12, 17 aprel 2017600 × 450 (57 KB)Geek3validator fix
22:33, 16 aprel 2017600 × 450 (57 KB)Geek3{{Information |Description ={{en|1=Plot of the evolution of the size of the universe (scale parameter ''a'') over time (in billion years, Gyr). Different models are shown, which are all solutions to the {{W|Friedmann equations|Friedmann equations}}...

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Bu fayl aşağıdakı vikilərdə istifadə olunur:

  • Age of the universe

    • Metaməlumatlar

    Bu faylda fotoaparat və ya skanerlə əlavə olunmuş məlumatlar var. Əgər fayl sonradan redaktə olunubsa, bəzi parametrlər bu şəkildə göstərilənlərdən fərqli ola bilər.

    Yanvar 17, 2023
    fayl, mplwp, universe, scale, evolution, fayl, faylın, tarixçəsi, istifadə, edilən, səhifələr, faylın, qlobal, istifadəsi, metaməlumatlarbu, faylın, formatındakı, görünüşünün, ölçüsü, piksel, digər, ölçülər, piksel, piksel, piksel, piksel, piksel, faylın, orij. Fayl Faylin tarixcesi Istifade edilen sehifeler Faylin qlobal istifadesi MetamelumatlarBu SVG faylin PNG formatindaki bu gorunusunun olcusu 600 450 piksel Diger olculer 320 240 piksel 640 480 piksel 1 024 768 piksel 1 280 960 piksel 2 560 1 920 piksel Faylin orijinali 8206 SVG fayli nominal olaraq 600 450 piksel faylin olcusu 57 KB Bu fayl Vikimedia Commons dadirve diger layihelerde istifade edile biler Faylin tesvir sehifesine get Xulase IzahMplwp universe scale evolution svg English Plot of the evolution of the size of the universe scale parameter a over time in billion years Gyr Different models are shown which are all solutions to the Friedmann equations with different parameters The evolution is governed by the equation a a 2 H 0 2 W r a 4 W m a 3 W k a 2 W L displaystyle left frac dot a a right 2 H 0 2 left frac Omega r a 4 frac Omega m a 3 frac Omega k a 2 Omega Lambda right Here W r displaystyle Omega r is the radiation density W m displaystyle Omega m the matter density W k displaystyle Omega k the curvature parameter and W L displaystyle Omega Lambda the dark energy all normalized such that W r W m W k W L 1 displaystyle Omega r Omega m Omega k Omega Lambda 1 represents the fact that today s expansion rate is H 0 displaystyle H 0 Plotted parameter sets De Sitter universe Only dark energy W L 1 displaystyle Omega Lambda 1 Lambda CDM model The model that fits the observations best W m 0 3 displaystyle Omega m 0 3 W L 0 7 displaystyle Omega Lambda 0 7 An empty universe no relevant contributions of matter radiation dark energy with negative curvature W k 1 displaystyle Omega k 1 Einstein de Sitter universe A flat universe dominated by cold matter W m 1 displaystyle Omega m 1 A closed Friedmann model W m 6 displaystyle Omega m 6 W k 5 displaystyle Omega k 5 Tarix 17 aprel 2017Menbe Oz isiMuellif Geek3SVG genesisInfoField The SVG code is valid This plot was created with mplwp the Matplotlib extension for Wikipedia plots Source codeInfoFieldPython code usr bin python coding utf8 import matplotlib pyplot as plt import matplotlib as mpl import numpy as np from math import code website http commons wikimedia org wiki User Geek3 mplwp try import mplwp except ImportError er print ImportError er print You need to download mplwp py from code website exit 1 name mplwp universe scale evolution svg fig mplwp fig standard mpl fig set size inches 600 72 0 450 72 0 mplwp set bordersize fig 58 5 16 5 16 5 44 5 xlim 17 22 fig gca set xlim xlim ylim 0 3 fig gca set ylim ylim mplwp mark axeszero fig gca y0 1 import scipy optimize as op from scipy integrate import odeint tH 978 68 Hubble time in Gyr def Hubble a matter rad k darkE the Friedman equation gives the relative expansion rate a a 0 if a lt 0 return 0 r rad a 4 matter a 3 k a 2 darkE if r lt 0 return 0 return sqrt r tH def scale t matter rad k darkE return odeint lambda a t a Hubble a matter rad k darkE 1 0 t def scaled closed matteronly t m analytic solution for matter m gt 1 rad 0 darkE 0 t0 acos 2 m 1 0 5 m m 1 1 5 1 m 1 try psi op brentq lambda p p sin p m 2 m 1 1 5 t tH t0 0 2 pi except Exception psi 0 a 1 0 cos psi m 0 5 m 1 return a De Sitter http en wikipedia org wiki De Sitter universe matter 0 rad 0 k 0 darkE 1 t np linspace xlim 0 xlim 1 5001 a scale tt matter rad k darkE 1 0 for tt in t plt plot t a zorder 2 label ur Omega Lambda 1 de Sitter Standard Lambda CDM https en wikipedia org wiki Lambda CDM model matter 0 3 rad 0 k 0 darkE 0 7 t0 op brentq lambda t scale t matter rad k darkE 1 0 20 0 t np linspace t0 xlim 1 5001 a scale tt matter rad k darkE 1 0 for tt in t plt plot t a zorder 1 label ur Omega m 0 3 Omega Lambda 0 7 Lambda CDM Empty universe matter 0 rad 0 k 1 darkE 0 t0 op brentq lambda t scale t matter rad k darkE 1 0 20 0 t np linspace t0 xlim 1 5001 a scale tt matter rad k darkE 1 0 for tt in t plt plot t a label ur Omega k 1 empty universe zorder 3 Open Friedmann matter 0 5 rad 0 k 0 5 darkE 0 t0 op brentq lambda t scale t matter rad k darkE 1 0 20 0 t np linspace t0 xlim 1 5001 a scale tt matter rad k darkE 1 0 for tt in t plt plot t a label ur Omega m 0 5 Omega k 0 5 Einstein de Sitter http en wikipedia org wiki Einstein de Sitter universe matter 1 rad 0 k 0 darkE 0 t0 op brentq lambda t scale t matter rad k darkE 1 0 20 0 t np linspace t0 xlim 1 5001 a scale tt matter rad k darkE 1 0 for tt in t plt plot t a label ur Omega m 1 Einstein de Sitter zorder 4 Radiation dominated matter 0 rad 1 k 0 darkE 0 t0 op brentq lambda t scale t matter rad k darkE 1 0 20 0 t np linspace t0 xlim 1 5001 a scale tt matter rad k darkE 1 0 for tt in t plt plot t a label ur Omega r 1 Closed Friedmann matter 6 rad 0 k 5 darkE 0 t0 op brentq lambda t scaled closed matteronly t matter 1e 9 20 0 t1 op brentq lambda t scaled closed matteronly t matter 1e 9 0 20 t np linspace t0 t1 5001 a scaled closed matteronly tt matter for tt in t plt plot t a label ur Omega m 6 Omega k u2212 5 closed zorder 5 plt xlabel t Gyr plt ylabel ur a a 0 plt legend loc upper left borderaxespad 0 6 handletextpad 0 5 plt savefig name mplwp postprocess name Lisenziya I the copyright holder of this work hereby publish it under the following license This file is licensed under the Creative Commons Attribution Share Alike 4 0 International license Azadsiniz paylasmaq eseri kocurmek paylamaq ve oturmek ucun remiks etmek eseri adaptasiya etmek Asagidaki sertlere riayet etmekle istinad Muvafiq kredit vermelisiniz lisenziyaya bir kecid vermelisiniz ve deyisikliklerin olub olmadigini bildirmelisiniz Bunu her hansi bir aglabatan sekilde ede bilersiniz ancaq lisenziyalasdiricinin sizi ve ya istifadenizi tesdiqlemesini teklif eden bir sekilde deyil benzer paylasma Eseri remix edirsinizse deyisdirirsinizse ve ya uzerinde is aparirsinizsa oz tohfelerinizi orijinalda oldugu kimi eyni ve ya uygun lisenziya altinda yayimlamalisiniz https creativecommons org licenses by sa 4 0 CC BY SA 4 0 Creative Commons Attribution Share Alike 4 0 true trueCaptionsazerbaycancaAdd a one line explanation of what this file representsItems portrayed in this filetesvir ediryaradiciSome value without a Vikiverilenler itemmuellifin qisa adi Geek3Wikimedia username ingilis Geek3URL ingilis http commons wikimedia org wiki User Geek3copyright status ingiliscopyrighted ingilislisenziyaCreative Commons Attribution ShareAlike 4 0 International ingilisyaranma tarixi17 aprel 2017source of file ingilisoriginal creation by uploader ingilis Faylin tarixcesi Faylin evvelki versiyasini gormek ucun gun tarix bolmesindeki tarixlere klikleyin Tarix VaxtKicik sekilOlculerIstifadeciSerh indiki00 12 17 aprel 2017600 450 57 KB Geek3validator fix 22 33 16 aprel 2017600 450 57 KB Geek3 Information Description en 1 Plot of the evolution of the size of the universe scale parameter 039 039 a 039 039 over time in billion years Gyr Different models are shown which are all solutions to the W Friedmann equations Friedmann equations Istifade edilen sehifeler Bu sekile olan kecidler Lambda CDM model Faylin qlobal istifadesi Bu fayl asagidaki vikilerde istifade olunur ar wikipedia org layihesinde istifadesi عمر الكون bg wikipedia org layihesinde istifadesi Vzrast na Vselenata de wikipedia org layihesinde istifadesi Expansion des Universums en wikipedia org layihesinde istifadesi De Sitter universe Age of the universe fa wikipedia org layihesinde istifadesi سن جهان fr wikipedia org layihesinde istifadesi Age de l Univers hr wikipedia org layihesinde istifadesi Starost svemira it wikipedia org layihesinde istifadesi Universo di de Sitter it wikiquote org layihesinde istifadesi Universo di de Sitter sr wikipedia org layihesinde istifadesi Starost univerzuma ta wikipedia org layihesinde istifadesi அக லத த ன வயத vi wikipedia org layihesinde istifadesi Vũ trụ De SitterMetamelumatlar Bu faylda fotoaparat ve ya skanerle elave olunmus melumatlar var Eger fayl sonradan redakte olunubsa bezi parametrler bu sekilde gosterilenlerden ferqli ola biler Qisa basliqmplwp universe scale evolution svgSekil basligihttp commons wikimedia org wiki File mplwp universe scale evolution svg Plot created with mplwp the Matplotlib extension for Wikipedia plots Genislik600pxHundurluk450px Menbe https az wikipedia org wiki Fayl Mplwp universe scale evolution svg, wikipedia, oxu, kitab, kitabxana, axtar, tap, hersey,

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