{"id":4364,"date":"2022-12-02T12:33:21","date_gmt":"2022-12-02T03:33:21","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=4364"},"modified":"2023-03-14T16:49:50","modified_gmt":"2023-03-14T07:49:50","slug":"planck-2018-results-%e3%81%8b%e3%82%89%e5%ae%87%e5%ae%99%e7%a9%ba%e9%96%93%e3%81%ae%e7%89%a9%e8%b3%aa%e5%af%86%e5%ba%a6%e3%82%92%e8%a8%88%e7%ae%97%e3%81%99%e3%82%8b","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4364\/","title":{"rendered":"Planck 2018 results \u304b\u3089\u5b87\u5b99\u7a7a\u9593\u306e\u7269\u8cea\u5bc6\u5ea6\u3092 Maxima \u3067\u8a08\u7b97\u3059\u308b"},"content":{"rendered":"

Maxima \u3092\u96fb\u5353\u3068\u3057\u3066\u4f7f\u3063\u3066\u5b87\u5b99\u7a7a\u9593\u306e\u7269\u8cea\u5bc6\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u4f8b\u3002Maxima \u3067\u306a\u304f\u3066\u3082\u639b\u3051\u7b97\u5272\u308a\u7b97\u304c\u3067\u304d\u308c\u3070\u306a\u3093\u3067\u3082\u3044\u3044\u3067\u3059\u3002
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Planck 2018 \u306e\u5b87\u5b99\u8ad6\u30d1\u30e9\u30e1\u30fc\u30bf<\/h3>\n

Planck 2018 results<\/a> \u306e\u5b87\u5b99\u8ad6\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n

\\begin{eqnarray}
\nH_0 &=& (67.4 \\pm 0.5) \\ \\mbox{km\/s\/Mpc} \\\\
\n\\Omega_{\\rm m} &=& 0.315 \\pm 0.007 \\\\
\n\\Omega_{\\Lambda} &=& 1 – \\Omega_{\\rm m}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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\u81e8\u754c\u5bc6\u5ea6<\/h3>\n

\u3053\u3053<\/a> \u306b\u66f8\u3044\u3066\u3044\u308b\u3088\u3046\u306b<\/p>\n

$$
\n\\rho_{\\rm cr}\\equiv \\frac{3 H_0^2}{8\\pi G}
\n$$<\/p>\n

\u7269\u8cea\u5bc6\u5ea6 $\\rho$ \u306f
\n$$\\rho = \\rho_{\\rm cr} \\Omega_{\\rm m}$$\u304b\u3089\u6c42\u3081\u308b\u3002<\/p>\n

\u4e07\u6709\u5f15\u529b\u5b9a\u6570<\/a> $G$ \u306f<\/p>\n

$$ G = 6.674 \\times 10^{-11} \\, \\frac{\\mbox{m}^3}{\\mbox{kg}\\cdot\\mbox{s}^2}$$<\/p>\n

\u307e\u305f\uff0c$H_0$ \u306f\u5225\u30da\u30fc\u30b8<\/a>\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b $s^{-1}$ \u306e\u6b21\u5143\u3092\u6301\u3064\u306e\u3067\uff0c\u9069\u5207\u306b\u5358\u4f4d\u3092\u5408\u308f\u305b\u3066\u8a08\u7b97\u3059\u308c\u3070\u78ba\u304b\u306b $\\rho_{\\rm cr}$ \u306f
\n\u8cea\u91cf\u5bc6\u5ea6 $\\mbox{kg}\/\\mbox{m}^3$ \u306e\u6b21\u5143\u3092\u3082\u3064\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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In\u00a0[1]:<\/div>\n
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\/* H0 \u306e\u7cbe\u5ea6\u306f\uff0c\u305b\u3044\u305c\u3044\u3053\u306e\u304f\u3089\u3044 *\/<\/span>\r\nfpprintprec<\/span>:<\/span> 3$\r\n\r\nau<\/span>:<\/span> 149597870700<\/span> *<\/span> m<\/span>$\r\n\/* Mpc \u3060\u304b\u3089 1E6 pc \u3067\uff0ckm \u3060\u304b\u3089 1E3 m\u3002*\/<\/span>\r\nMpc<\/span>:<\/span> 648000\/<\/span>float<\/span>(<\/span>%pi<\/span>)<\/span> *<\/span> au<\/span> *<\/span> 1E6<\/span>$\r\nkm<\/span>:<\/span> 1E3<\/span> *<\/span> m<\/span>$\r\n\r\nH0<\/span>:<\/span> 67.4<\/span> *<\/span> km<\/span>\/<\/span>(<\/span>s<\/span> *<\/span> Mpc<\/span>)<\/span>$\r\n\r\nOmega<\/span>:<\/span> 0.<\/span>315$\r\nG<\/span>:<\/span> 6.<\/span>674E<\/span>-<\/span>11<\/span> *<\/span> m<\/span>**<\/span>3<\/span> \/<\/span>(<\/span>kg<\/span> *<\/span> s<\/span>**<\/span>2<\/span>)<\/span>$\r\n\r\nrhoc<\/span>:<\/span> 3*<\/span>H0<\/span>**<\/span>2\/<\/span>(<\/span>8*<\/span>float<\/span>(<\/span>%pi<\/span>)<\/span>*<\/span>G<\/span>)<\/span>$\r\nprint<\/span>(<\/span>\"\u81e8\u754c\u5bc6\u5ea6\u306f \"<\/span>, rhoc<\/span> \/<\/span> (<\/span>kg<\/span>\/<\/span>m<\/span>^<\/span>3<\/span>)<\/span>, \"kg\/m^3\"<\/span>)<\/span>$\r\nprint<\/span>(<\/span>\"\u5b87\u5b99\u7a7a\u9593\u306e\u7269\u8cea\u5bc6\u5ea6\u306f \"<\/span>, rhoc<\/span> *<\/span> Omega<\/span> \/<\/span> (<\/span>kg<\/span>\/<\/span>m<\/span>^<\/span>3<\/span>)<\/span>, \"kg\/m^3\"<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u81e8\u754c\u5bc6\u5ea6\u306f \\(??? \\times 10^{-??}\\) kg\/m^3<\/div>\n<\/div>\n
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\u5b87\u5b99\u7a7a\u9593\u306e\u7269\u8cea\u5bc6\u5ea6\u306f \\(??? \\times 10^{-??}\\) kg\/m^3<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6f14\u7fd2<\/h3>\n
\u73fe\u5728\u306e\u5b87\u5b99\u7a7a\u9593\u306e\u7269\u8cea\u5bc6\u5ea6\u306f\u6b21\u306e\u3046\u3061\u306e\u3069\u308c\u306b\u6700\u3082\u8fd1\u3044\u304b\u3002<\/p>\n
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  1. $1\\,\\mbox{cm}^3$ \u306b\u96fb\u5b50\u304c\u6570\u500b\u7a0b\u5ea6<\/li>\n
  2. $1\\,\\mbox{cm}^3$ \u306b\u967d\u5b50\u304c\u6570\u500b\u7a0b\u5ea6<\/li>\n
  3. $1\\,\\mbox{m}^3$ \u306b\u96fb\u5b50\u304c\u6570\u500b\u7a0b\u5ea6<\/li>\n
  4. $1\\,\\mbox{m}^3$ \u306b\u967d\u5b50\u304c\u6570\u500b\u7a0b\u5ea6<\/li>\n
  5. $1\\,\\mbox{km}^3$ \u306b\u96fb\u5b50\u304c\u6570\u500b\u7a0b\u5ea6<\/li>\n
  6. $1\\,\\mbox{km}^3$ \u306b\u967d\u5b50\u304c\u6570\u500b\u7a0b\u5ea6<\/li>\n<\/ol>\n
    \u53c2\u8003<\/h4>\n