{"id":9375,"date":"2024-08-29T11:32:20","date_gmt":"2024-08-29T02:32:20","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=9375"},"modified":"2024-08-29T11:33:19","modified_gmt":"2024-08-29T02:33:19","slug":"%e5%a4%8f%e4%bc%91%e3%81%bf%e3%81%ae%e5%ae%bf%e9%a1%8c%e3%80%8c%e9%9d%9e%e4%b8%80%e6%a7%98%e5%ae%87%e5%ae%99%e3%81%ae%e8%b7%9d%e9%9b%a2%e3%80%8d","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/9375\/","title":{"rendered":"\u590f\u4f11\u307f\u306e\u5bbf\u984c\u300c\u975e\u4e00\u69d8\u5b87\u5b99\u306e\u8ddd\u96e2\u300d"},"content":{"rendered":"
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\u4e8c\u9593\u702c\u3055\u3093\u3078\u306e\u79c1\u4fe1\u3002\u590f\u4f11\u307f\u306e\u5bbf\u984c\u300c\u975e\u4e00\u69d8\u5b87\u5b99\u306e\u8ddd\u96e2\u300d\u306b\u3064\u3044\u3066\u3002<\/p>\n

$\\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408\u306e Angular Diameter Distance<\/h3>\n

\\begin{eqnarray}
\nd_A
\n&=& \\frac{2}{H_0 \\Omega_{\\rm m}^2 (1+z)^2} \\left\\{2 – \\Omega_{\\rm m} + \\Omega_{\\rm m} z – (2-\\Omega_{\\rm m}) \\sqrt{1 + \\Omega_{\\rm m} z}\\right\\}
\n\\end{eqnarray}<\/p>\n

\u4ee5\u4e0b\u3067\u306f $H_0$ \u3092\u7701\u7565\u3057\uff0c\u8868\u8a18\u306e\u90fd\u5408\u4e0a $\\Omega_{\\rm m} \\rightarrow \\Omega$<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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In\u00a0[1]:<\/div>\n
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dA<\/span>(<\/span>Omega<\/span>, z<\/span>)<\/span>:=<\/span> 2\/<\/span>(<\/span>Omega<\/span>**<\/span>2*<\/span>(<\/span>1+<\/span>z<\/span>)<\/span>**<\/span>2<\/span>)<\/span> *<\/span> \r\n             (<\/span>2-<\/span>Omega<\/span>+<\/span> Omega<\/span>*<\/span>z<\/span> -<\/span> (<\/span>2-<\/span>Omega<\/span>)<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span> +<\/span> Omega<\/span>*<\/span>z<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[1]:<\/div>\n
\\[\\tag{${\\it \\%o}_{1}$}{\\it dA}\\left(\\Omega , z\\right):=\\frac{2}{\\Omega^2\\,\\left(1+z\\right)^2}\\,\\left(2-\\Omega+\\Omega\\,z+\\left(-\\left(2-\\Omega\\right)\\right)\\,\\sqrt{1+\\Omega\\,z}\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\Omega_{\\rm m} + \\Omega_{\\Lambda} = 1$ \u306e\u5834\u5408\u306e Angular Diameter Distance<\/h3>\n
\\begin{eqnarray}
\nd_A
\n&=& \\frac{1}{H_0 (1+z)} \\int_0^z \\frac{dz}{\\sqrt{(1-\\Omega_{\\rm m}) + \\Omega_{\\rm m} (1+z)^3} }
\n\\end{eqnarray}<\/p>\n
\u89e3\u6790\u7684\u306b\u306f\u7a4d\u5206\u3067\u304d\u306a\u3044\u306e\u3067\uff0cquad_qags()<\/code> \u3067\u6570\u5024\u7a4d\u5206\u3059\u308b\u3002quad_qags()<\/code> \u306f4\u3064\u306e\u8981\u7d20<\/p>\n
[\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024, \u8fd1\u4f3c\u306e\u7d76\u5bfe\u8aa4\u5dee, \u88ab\u7a4d\u5206\u95a2\u6570\u306e\u8a55\u4fa1\u6570, \u30a8\u30e9\u30fc\u30b3\u30fc\u30c9]<\/code><\/p>\n
\u304b\u3089\u306a\u308b\u30ea\u30b9\u30c8\u3092\u8fd4\u3059\u306e\u3067\uff0c\u7a4d\u5206\u8fd1\u4f3c\u5024\u306e\u307f\u3092\u51fa\u529b\u3055\u305b\u305f\u3044\u5834\u5408\u306b\u306f [1]<\/code> \u3092\u3064\u3051\u3066\u30ea\u30b9\u30c8\u306e1\u756a\u76ee\u306e\u8981\u7d20\u306e\u307f\u3092\u51fa\u529b\u3059\u308b\u3088\u3046\u306b\u6307\u5b9a\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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\/* \u88ab\u7a4d\u5206\u95a2\u6570\u306e\u5b9a\u7fa9 *\/<\/span>\r\nf<\/span>(<\/span>Omega<\/span>, z<\/span>)<\/span>:=<\/span> 1\/<\/span>sqrt<\/span>((<\/span>1-<\/span>Omega<\/span>)<\/span> +<\/span> Omega<\/span>*<\/span>(<\/span>1+<\/span>x<\/span>)<\/span>**<\/span>3<\/span>)<\/span>;\r\n\r\ndAL<\/span>(<\/span>Omega<\/span>, z<\/span>)<\/span>:=<\/span> ((<\/span>1\/<\/span>(<\/span>1+<\/span>z<\/span>)<\/span>*<\/span>quad_qags<\/span>(<\/span>f<\/span>(<\/span>Omega<\/span>, x<\/span>)<\/span>, x<\/span>, 0<\/span>, z<\/span>))[<\/span>1])<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{2}$}f\\left(\\Omega , z\\right):=\\frac{1}{\\sqrt{1-\\Omega+\\Omega\\,\\left(1+x\\right)^3}}\\]<\/div>\n<\/div>\n
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Out[2]:<\/div>\n
\\[\\tag{${\\it \\%o}_{3}$}{\\it dAL}\\left(\\Omega , z\\right):=\\left(\\frac{1}{1+z}\\,{\\it quad\\_qags}\\left(f\\left(\\Omega , x\\right) , x , 0 , z\\right)\\right)_{1}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u975e\u4e00\u69d8\u5b87\u5b99\u306e\u8ddd\u96e2\uff1a\u30b1\u30fc\u30b91<\/h3>\n
\u8fd1\u508d\uff1a<\/p>\n
    \n
  1. $0 \\leq z \\leq 0.1$ \u306e\u8fd1\u508d\u3067\u306f\uff0clocal \u306a\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024 $\\tilde{H}_0$ \u306f global \u306a\u5024 $H_0$ \u3088\u308a $10\\%$ \u5927\u304d\u3044\u3068\u3059\u308b\u3002
    \n$$\\tilde{H}_0 = 1.1 \\, H_0$$<\/li>\n
  2. $0 \\leq z \\leq 0.1$ \u306e\u8fd1\u508d\u3067\u306f\uff0c Angular Diameter Distance \u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8a18\u8ff0\u3067\u304d\u308b\u3068\u3059\u308b\u3002
    \n\\begin{eqnarray}
    \n\\Omega_{\\Lambda} &=& 0 \\\\
    \n\\Omega_{m} &\\Rightarrow& \\Omega = 0.5 \\\\
    \nd_A(\\Omega, z) &=& \\frac{2}{\\tilde{H}_0 \\Omega^2 (1+z)^2}\\left\\{2 – \\Omega + \\Omega z – (2-\\Omega) \\sqrt{1 + \\Omega z}\\right\\} \\\\
    \n&\\simeq& \\frac{z}{\\tilde{H}_0}\\quad (z \\leq 0.1 \\ll 1)
    \n\\end{eqnarray}<\/li>\n
  3. \u8fd1\u508d\u306b\u3064\u3044\u3066\u306f Raychaudhuri equation \u3092\u89e3\u3044\u3066… \u3068\u3044\u3046\u3054\u4f9d\u983c\u3067\u3042\u3063\u305f\u304c\uff0c$z \\leq 0.1 \\ll 1$ \u3067\u3042\u308b\u305f\u3081\uff0c$\\displaystyle d_A(z) \\simeq \\frac{z}{\\tilde{H}_0}$ \u3068\u3057\u3066\u5341\u5206\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002
    \n\u3053\u308c\u306f\uff0cDyer-Roeder distance \u306e empty beam \u306e\u30b1\u30fc\u30b9\u3092\u4f7f\u3063\u3066\u3082\uff0c\u307b\u3068\u3093\u3069\u5909\u308f\u3089\u306a\u3044\u3002<\/li>\n<\/ol>\n
    \u9060\u65b9\uff1a<\/p>\n
      \n
    1. $0.1 \\leq z \\leq 1$ \u306e\u9818\u57df\u3067\u306f\uff0c\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024\u306f global \u306a\u5024 $H_0$ \u3067\u3042\u308b\u3068\u3059\u308b\u3002<\/li>\n
    2. $0.1 \\leq z \\leq 1$ \u306e\u9818\u57df\u3067\u306f\uff0cAngular Diameter Distance \u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8a18\u8ff0\u3067\u304d\u308b\u3068\u3059\u308b\u3002
      \n\\begin{eqnarray}
      \n\\Omega_{\\Lambda} &=& 0 \\\\
      \n\\Omega_{m} &\\Rightarrow& \\Omega = 1 \\\\
      \nd_A(\\Omega, z) &=& \\frac{2}{{H}_0 \\Omega^2 (1+z)^2}\\left\\{2 – \\Omega + \\Omega z – (2-\\Omega) \\sqrt{1 + \\Omega z}\\right\\} \\\\
      \n&=& \\frac{2 \\left(1+z-\\sqrt{1+z}\\right)}{H_0 (1+z)^2}
      \n\\end{eqnarray}<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
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      \u30b0\u30e9\u30d5<\/h4>\n
      \u8fd1\u508d\uff0c\u9060\u65b9\u305d\u308c\u305e\u308c\u306b\u7570\u306a\u3063\u305f\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024\u3092\u4f7f\u3063\u305f Angular Diameter Distance \u3092\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
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      In\u00a0[3]:<\/div>\n
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      \n
      localOm<\/span>:<\/span> 0.<\/span>5$\r\nglobalOm<\/span>:<\/span> 1$\r\n\r\nkeylocal<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, local H_0}\"<\/span>, localOm<\/span>)<\/span>$\r\nkeyglobal<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, global H_0}\"<\/span>, globalOm<\/span>)<\/span>$\r\n\r\ndraw2d<\/span>(<\/span>\r\n  dimensions<\/span> =<\/span> [<\/span>640<\/span>, 480]<\/span>,\r\n  user_preamble<\/span> =<\/span> [<\/span>\"set key bottom right;\"<\/span>]<\/span>,\r\n  xlabel<\/span> =<\/span> \"{\/Times z}\"<\/span>, \r\n  title<\/span> =<\/span> \"Angular Diameter Distance\"<\/span>,\r\n  \r\n  line_width<\/span> =<\/span> 2<\/span>,\r\n  key<\/span> =<\/span> keyglobal<\/span>, \r\n  color<\/span> =<\/span> red<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>globalOm<\/span>, z<\/span>)<\/span>, z<\/span>, 0.1<\/span>, 1<\/span>)<\/span>,\r\n\r\n  key<\/span> =<\/span> keylocal<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>localOm<\/span>, z<\/span>)<\/span>\/<\/span>1.1<\/span>, z<\/span>, 0<\/span>, 0.1<\/span>)<\/span> \r\n\r\n)<\/span>$<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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      \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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      \u9818\u57df\u5168\u4f53 $0 \\leq z \\leq 1$ \u3092\u4e00\u3064\u306e\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024 $\\tilde{H}_0$\uff0c\u4e00\u3064\u306e\u8ddd\u96e2\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u304b\uff0c\u8a66\u3057\u3066\u307f\u308b\u3002<\/p>\n
      \u4ee5\u4e0b\u306e\u4f8b\u3067\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u4e00\u3064\u306e\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024 $\\tilde{H}_0$\uff0c\u4e00\u3064\u306e\u8ddd\u96e2\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u306f\u305d\u3093\u306a\u306b\u3046\u307e\u304f\u306f\u3044\u304b\u306a\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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      In\u00a0[4]:<\/div>\n
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      localOm<\/span>:<\/span> 0.<\/span>5$\r\nglobalOm<\/span>:<\/span> 1$\r\ntotalOm1<\/span>:<\/span> 0.<\/span>3$\r\ntotalOm2<\/span>:<\/span> 0.<\/span>6$\r\n\r\nkeylocal<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, local H_0}\"<\/span>, localOm<\/span>)<\/span>$\r\nkeyglobal<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, global H_0}\"<\/span>, globalOm<\/span>)<\/span>$\r\nkeytotal1<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, local H_0}\"<\/span>, totalOm1<\/span>)<\/span>$\r\nkeytotal2<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \r\n    \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b=~3,f, local H_0}\"<\/span>, totalOm2<\/span>, 1-<\/span>totalOm2<\/span>)<\/span>$\r\n\r\ndraw2d<\/span>(<\/span>\r\n  dimensions<\/span> =<\/span> [<\/span>640<\/span>, 480]<\/span>,\r\n  user_preamble<\/span> =<\/span> [<\/span>\"set key bottom right;\"<\/span>]<\/span>,\r\n  xlabel<\/span> =<\/span> \"{\/Times z}\"<\/span>, \r\n  title<\/span> =<\/span> \"Angular Diameter Distance\"<\/span>,\r\n  \r\n  line_width<\/span> =<\/span> 1<\/span>,\r\n  key<\/span> =<\/span> keytotal1<\/span>, \r\n  color<\/span> =<\/span> black<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>totalOm1<\/span>, z<\/span>)<\/span>\/<\/span>1.1<\/span>, z<\/span>, 0<\/span>, 1<\/span>)<\/span>,\r\n  line_type<\/span> =<\/span> dots<\/span>,\r\n  key<\/span> =<\/span> keytotal2<\/span>, \r\n  color<\/span> =<\/span> black<\/span>,\r\n  explicit<\/span>(<\/span>dAL<\/span>(<\/span>totalOm2<\/span>, z<\/span>)<\/span>\/<\/span>1.1<\/span>, z<\/span>, 0<\/span>, 1<\/span>)<\/span>,\r\n\r\n  line_width<\/span> =<\/span> 2<\/span>,\r\n  line_type<\/span> =<\/span> solid<\/span>,\r\n  key<\/span> =<\/span> keyglobal<\/span>, \r\n  color<\/span> =<\/span> red<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>globalOm<\/span>, z<\/span>)<\/span>, z<\/span>, 0.1<\/span>, 1<\/span>)<\/span>,\r\n\r\n  key<\/span> =<\/span> keylocal<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>localOm<\/span>, z<\/span>)<\/span>\/<\/span>1.1<\/span>, z<\/span>, 0<\/span>, 0.1<\/span>)<\/span> \r\n\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
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      <\/p>\n
      \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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      \u975e\u4e00\u69d8\u5b87\u5b99\u306e\u8ddd\u96e2\uff1a\u30b1\u30fc\u30b92<\/h3>\n
      \u8fd1\u508d\uff1a<\/p>\n
        \n
      1. $0 \\leq z \\leq 0.1$ \u306e\u8fd1\u508d\u3067\u306f\uff0clocal \u306a\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024 $\\tilde{H}_0$ \u306f global \u306a\u5024 $H_0$ \u3088\u308a $10\\%$ \u5927\u304d\u3044\u3068\u3059\u308b\u3002
        \n$$\\tilde{H}_0 = 1.1 \\, H_0$$<\/li>\n
      2. $0 \\leq z \\leq 0.1$ \u306e\u8fd1\u508d\u3067\u306f\uff0c Angular Diameter Distance \u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8a18\u8ff0\u3067\u304d\u308b\u3068\u3059\u308b\u3002
        \n\\begin{eqnarray}
        \n\\Omega_{\\Lambda} &=& 0 \\\\
        \n\\Omega_{m} &\\Rightarrow& \\Omega = 0.2 \\\\
        \nd_A(\\Omega, z) &=& \\frac{2}{\\tilde{H}_0 \\Omega^2 (1+z)^2}\\left\\{2 – \\Omega + \\Omega z – (2-\\Omega) \\sqrt{1 + \\Omega z}\\right\\} \\\\
        \n&\\simeq& \\frac{z}{\\tilde{H}_0}\\quad (z \\leq 0.1 \\ll 1)
        \n\\end{eqnarray}<\/li>\n
      3. \u8fd1\u508d\u306b\u3064\u3044\u3066\u306f Raychaudhuri equation \u3092\u89e3\u3044\u3066… \u3068\u3044\u3046\u3054\u4f9d\u983c\u3067\u3042\u3063\u305f\u304c\uff0c$z \\leq 0.1 \\ll 1$ \u3067\u3042\u308b\u305f\u3081\uff0c$\\displaystyle d_A(z) \\simeq \\frac{z}{\\tilde{H}_0}$ \u3068\u3057\u3066\u5341\u5206\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002
        \n\u3053\u308c\u306f\uff0cDyer-Roeder distance \u306e empty beam \u306e\u30b1\u30fc\u30b9\u3092\u4f7f\u3063\u3066\u3082\uff0c\u307b\u3068\u3093\u3069\u5909\u308f\u3089\u306a\u3044\u3002<\/li>\n<\/ol>\n
        \u9060\u65b9\uff1a<\/p>\n
          \n
        1. $0.1 \\leq z \\leq 1$ \u306e\u9818\u57df\u3067\u306f\uff0c\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024\u306f global \u306a\u5024 $H_0$ \u3067\u3042\u308b\u3068\u3059\u308b\u3002<\/li>\n
        2. $0.1 \\leq z \\leq 1$ \u306e\u9818\u57df\u3067\u306f\uff0cAngular Diameter Distance \u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8a18\u8ff0\u3067\u304d\u308b\u3068\u3059\u308b\u3002
          \n\\begin{eqnarray}
          \n\\Omega_{\\Lambda} &=& 0 \\\\
          \n\\Omega_{m} &\\Rightarrow& \\Omega = 0.3 \\\\
          \nd_A(\\Omega, z) &=& \\frac{2}{{H}_0 \\Omega^2 (1+z)^2}\\left\\{2 – \\Omega + \\Omega z – (2-\\Omega) \\sqrt{1 + \\Omega z}\\right\\}
          \n\\end{eqnarray}<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
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          \u30b0\u30e9\u30d5<\/h4>\n
          \u8fd1\u508d\uff0c\u9060\u65b9\u305d\u308c\u305e\u308c\u306b\u7570\u306a\u3063\u305f\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024\u3092\u4f7f\u3063\u305f Angular Diameter Distance \u3092\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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          In\u00a0[5]:<\/div>\n
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          \n
          \n
          localOm<\/span>:<\/span> 0.<\/span>2$\r\nglobalOm<\/span>:<\/span> 0.<\/span>3$\r\n\r\nkeylocal<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, local H_0}\"<\/span>, localOm<\/span>)<\/span>$\r\nkeyglobal<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, global H_0}\"<\/span>, globalOm<\/span>)<\/span>$\r\n\r\ndraw2d<\/span>(<\/span>\r\n  dimensions<\/span> =<\/span> [<\/span>640<\/span>, 480]<\/span>,\r\n  user_preamble<\/span> =<\/span> [<\/span>\"set key bottom right;\"<\/span>]<\/span>,\r\n  xlabel<\/span> =<\/span> \"{\/Times z}\"<\/span>, \r\n  title<\/span> =<\/span> \"Angular Diameter Distance\"<\/span>,\r\n  \r\n  line_width<\/span> =<\/span> 2<\/span>,\r\n  key<\/span> =<\/span> keyglobal<\/span>, \r\n  color<\/span> =<\/span> red<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>globalOm<\/span>, z<\/span>)<\/span>, z<\/span>, 0.1<\/span>, 1<\/span>)<\/span>,\r\n\r\n  key<\/span> =<\/span> keylocal<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>localOm<\/span>, z<\/span>)<\/span>\/<\/span>1.1<\/span>, z<\/span>, 0<\/span>, 0.1<\/span>)<\/span> \r\n\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u9818\u57df\u5168\u4f53 $0 \\leq z \\leq 1$ \u3092\u4e00\u3064\u306e\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024 $\\tilde{H}_0$\uff0c\u4e00\u3064\u306e\u8ddd\u96e2\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u304b\uff0c\u8a66\u3057\u3066\u307f\u308b\u3002<\/p>\n
          \u4ee5\u4e0b\u306e\u4f8b\u3067\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u5b87\u5b99\u5b9a\u6570\u3092\u5c0e\u5165\u3057\u3066 $\\Omega_{m} + \\Omega_{\\Lambda} = 1$ \u3068\u3057\u305f\u5834\u5408\u306b\u306f\uff0c\u4e00\u3064\u306e\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024 $\\tilde{H}_0$\uff0c\u4e00\u3064\u306e\u8ddd\u96e2\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u306f\uff0c\u305d\u3053\u305d\u3053\u3046\u307e\u304f\u3044\u304f\u3088\u3046\u306b\u3082\u601d\u3048\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[6]:<\/div>\n
          \n
          \n
          \n
          localOm<\/span>:<\/span> 0.<\/span>2$\r\nglobalOm<\/span>:<\/span> 0.<\/span>3$\r\ntotalOm2<\/span>:<\/span> 0.<\/span>32$\r\n\r\nkeylocal<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, local H_0}\"<\/span>, localOm<\/span>)<\/span>$\r\nkeyglobal<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b= 0, global H_0}\"<\/span>, globalOm<\/span>)<\/span>$\r\nkeytotal2<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \r\n    \"{\/Times \u03a9_m =~3,f, \u03a9_\u039b=~3,f, local H_0}\"<\/span>, totalOm2<\/span>, 1-<\/span>totalOm2<\/span>)<\/span>$\r\n\r\ndraw2d<\/span>(<\/span>\r\n  dimensions<\/span> =<\/span> [<\/span>640<\/span>, 480]<\/span>,\r\n  user_preamble<\/span> =<\/span> [<\/span>\"set key bottom right;\"<\/span>]<\/span>,\r\n  xlabel<\/span> =<\/span> \"{\/Times z}\"<\/span>, \r\n  title<\/span> =<\/span> \"Angular Diameter Distance\"<\/span>,\r\n  \r\n  line_width<\/span> =<\/span> 1<\/span>,\r\n  line_type<\/span> =<\/span> dots<\/span>,\r\n  key<\/span> =<\/span> keytotal2<\/span>, \r\n  color<\/span> =<\/span> black<\/span>,\r\n  explicit<\/span>(<\/span>dAL<\/span>(<\/span>totalOm2<\/span>, z<\/span>)<\/span>\/<\/span>1.1<\/span>, z<\/span>, 0<\/span>, 1<\/span>)<\/span>,\r\n\r\n  line_width<\/span> =<\/span> 2<\/span>,\r\n  line_type<\/span> =<\/span> solid<\/span>,\r\n  key<\/span> =<\/span> keyglobal<\/span>, \r\n  color<\/span> =<\/span> red<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>globalOm<\/span>, z<\/span>)<\/span>, z<\/span>, 0.1<\/span>, 1<\/span>)<\/span>,\r\n\r\n  key<\/span> =<\/span> keylocal<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  explicit<\/span>(<\/span>dA<\/span>(<\/span>localOm<\/span>, z<\/span>)<\/span>\/<\/span>1.1<\/span>, z<\/span>, 0<\/span>, 0.1<\/span>)<\/span> \r\n\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
          \u4e8c\u9593\u702c\u3055\u3093\u3078\u306e\u79c1\u4fe1\u3002\u590f\u4f11\u307f\u306e\u5bbf\u984c\u300c\u975e\u4e00\u69d8\u5b87\u5b99\u306e\u8ddd\u96e2\u300d\u306b\u3064\u3044\u3066\u3002<\/p>
          \u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[14,20],"tags":[],"class_list":["post-9375","post","type-post","status-publish","format-standard","hentry","category-maxima","category-rel-cosmo","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/9375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=9375"}],"version-history":[{"count":2,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/9375\/revisions"}],"predecessor-version":[{"id":9381,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/9375\/revisions\/9381"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=9375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=9375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=9375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}