Википедија

Датотека:Mplwp universe scale evolution.svg

Originalna datoteka ‎(SVG datoteka, nominalno 600 × 450 piksela, veličina: 57 kB)

Opis izmene

Opis
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: ,
Datum
Izvor Sopstveno delo
Autor Geek3
SVG genesis
InfoField
 
The SVG code is valid.
 
This plot was created with mplwp, the Matplotlib extension for Wikipedia plots.
Izvorni kod
InfoField

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)

Licenciranje

Ja, nosilac autorskog prava nad ovim delom, objavljujem isto pod sledećom licencom:
w:sr:Krijejtiv komons
autorstvo deliti pod istim uslovima
Ova datoteka je dostupna pod licencom Creative Commons Autorstvo-Deliti pod istim uslovima 4.0 Međunarodna.
Dozvoljeno je:
  • da delite – da umnožavate, raspodeljujete i prenosite delo
  • da prerađujete – da preradite delo
Pod sledećim uslovima:
  • autorstvo – Morate da date odgovarajuće zasluge, obezbedite vezu ka licenci i naznačite da li su izmene napravljene. Možete to uraditi na bilo koji razuman manir, ali ne na način koji predlaže da licencator odobrava vas ili vaše korišćenje.
  • deliti pod istim uslovima – Ako izmenite, preobrazite ili dogradite ovaj materijal, morate podeliti svoje doprinose pod istom ili kompatibilnom licencom kao original.

Natpisi

Dodajte objašnjenje u jednom redu o tome šta ova datoteka predstavlja

Stavke prikazane u ovoj datoteci

prikazuje

tvorac

Neka vrednost bez stavke na projektu Vikipodaci

skraćeno ime autora Serbian (transliteracija): Geek3
Vikimedija Serbian (transliteracija): Geek3
URL Serbian (transliteracija): http://commons.wikimedia.org/wiki/User:Geek3

status autorskog prava Serbian (transliteracija)

zaštićeno autorskim pravima Serbian (transliteracija)

nastanak

17. april 2017

izvor datoteke Serbian (transliteracija)

sopstveno delo Serbian (transliteracija)

Istorija datoteke

Kliknite na datum/vreme da biste videli tadašnju verziju datoteke.

Datum/vremeMinijaturaDimenzijeKorisnikKomentar
trenutna02:12, 17. april 2017.Minijatura za verziju na dan 02:12, 17. april 2017.600 × 450 (57 kB)Geek3validator fix
00:33, 17. april 2017.Minijatura za verziju na dan 00:33, 17. april 2017.600 × 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}}...

Sledeća stranica koristi ovu datoteku:

Globalna upotreba datoteke

Drugi vikiji koji koriste ovu datoteku:

Metapodaci

Ova datoteka sadrži dodatne podatke, koji verovatno dolaze od digitalnog fotoaparata ili skenera korišćenog za digitalizaciju.

Ako je prvobitno stanje datoteke promenjeno, moguće je da neki detalji ne opisuju izmenjenu datoteku u potpunosti.

Preuzeto iz „https://sr.wikipedia.org/wiki/Датотека:Mplwp_universe_scale_evolution.svg”