{"id":4362,"date":"2022-12-02T12:07:15","date_gmt":"2022-12-02T03:07:15","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=4362"},"modified":"2023-03-14T16:50:05","modified_gmt":"2023-03-14T07:50:05","slug":"planck-2018-results-%e3%81%8b%e3%82%89%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2%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\/4362\/","title":{"rendered":"Planck 2018 results \u304b\u3089 Maxima \u3067\u5b87\u5b99\u5e74\u9f62\u3092\u8a08\u7b97\u3059\u308b"},"content":{"rendered":"

Maxima \u3092\u96fb\u5353\u3068\u3057\u3066\u4f7f\u3063\u3066\u5b87\u5b99\u5e74\u9f62\u3092\u8a08\u7b97\u3059\u308b\u4f8b\u3002\u3053\u306e\u554f\u984c\u306f Maxima \u306a\u3069\u3092\u4f7f\u308f\u306a\u304f\u3066\u3082\uff0c$\\tanh^{-1} x$ \u3068 $\\sqrt{x}$ \u304c\u4f7f\u3048\u308b\u96fb\u5353\u304c\u3042\u308c\u3070\u3067\u304d\u307e\u3059\u3002<\/p>\n

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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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\u5b87\u5b99\u5e74\u9f62<\/h3>\n

$\\Omega_{\\rm m} + \\Omega_{\\Lambda} = 1$ \u3059\u306a\u308f\u3061 $k = 0$ \u306e\u5834\u5408\u306e\u5b87\u5b99\u5e74\u9f62\u306f\u3053\u3053<\/a> \u306b\u66f8\u3044\u3066\u3044\u308b\u3088\u3046\u306b<\/p>\n

$$
\nH_0 t_0 = \\frac{2}{3(\\sqrt{1-\\Omega_{\\rm m} })}\\tanh^{-1} \\sqrt{1-\\Omega_{\\rm m} } \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} < 1$$<\/p>\n

\u3088\u308a<\/p>\n

$$t_0 = \\frac{1}{H_0} \\times \\frac{2}{3(\\sqrt{1-\\Omega_{\\rm m} })}\\tanh^{-1} \\sqrt{1-\\Omega_{\\rm m} }$$<\/p>\n

\u4ee5\u4e0b\u3067\u306f\uff0cMaxima \u306e\u8868\u8a18\u306e\u90fd\u5408\u4e0a\uff0c$\\Omega_{\\rm m} \\rightarrow \\Omega$ \u3068\u3057\u3066…<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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t0<\/span>(<\/span>H0<\/span>, Omega<\/span>)<\/span>:=<\/span> 1\/<\/span>H0<\/span> *<\/span> (<\/span>2\/<\/span>(<\/span>3*<\/span>sqrt<\/span>(<\/span>1-<\/span>Omega<\/span>)))<\/span> *<\/span> atanh<\/span>(<\/span>sqrt<\/span>(<\/span>1-<\/span>Omega<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{1}$}t_{0}\\left(H_{0} , \\Omega\\right):=\\frac{1}{H_{0}}\\,\\left(\\frac{2}{3\\,\\sqrt{1-\\Omega}}\\right)\\,{\\rm atanh}\\; \\sqrt{1-\\Omega}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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kill<\/span>(<\/span>km<\/span>, s<\/span>, Mpc<\/span>)<\/span>$\r\n\r\nH0<\/span>:<\/span> 67.4<\/span> *<\/span> km<\/span>\/<\/span>s<\/span>\/<\/span>Mpc<\/span> $\r\nOmega<\/span>:<\/span> 0.315<\/span> $\r\n\r\n\/* Mpc \u3092 km \u3067 *\/<\/span>\r\nMpc<\/span>:<\/span> 3.<\/span>0856775814127E19<\/span> *<\/span> km<\/span> $\r\n\r\n\/* 1\/H0 \u306f\u79d2\u306a\u306e\u3067\u300c\u5104\u5e74\u300d\u306b\u63db\u7b97 *\/<\/span>\r\nokunen<\/span>:<\/span> 60*<\/span>60*<\/span>24*<\/span>365.<\/span>25*<\/span>1.<\/span>E8<\/span> *<\/span> s<\/span>$\r\n\r\n\/* ev(H0) \u3067 H0 \u306e\u5024\u3092\u8a55\u4fa1\u3057\u3066 s\uff08\u79d2\uff09\u306b *\/<\/span>\r\nprintf<\/span>(<\/span>true<\/span>, \"\u5b87\u5b99\u5e74\u9f62\u306f ~3,0f \u5104\u5e74\"<\/span>, t0<\/span>:<\/span>t0<\/span>(<\/span>ev<\/span>(<\/span>H0<\/span>)<\/span>, Omega<\/span>)<\/span>\/<\/span>okunen<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5b87\u5b99\u5e74\u9f62\u306f 138. \u5104\u5e74<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6f14\u7fd2<\/h3>\n
$\\pm$ \u306e\u8aa4\u5dee\u3082\u542b\u3081\u3066\u8a08\u7b97\u3057\uff0c\u5b87\u5b99\u5e74\u9f62\u3092 $138 \\ \\pm\\ ??$ \u5104\u5e74\u306e\u5f62\u306b\u6c42\u3081\u3066\u307f\u3088\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u89e3\u7b54\u4f8b<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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H0p<\/span>:<\/span> (<\/span>67.4<\/span> +<\/span> 0.5<\/span>)<\/span> *<\/span> km<\/span>\/<\/span>s<\/span>\/<\/span>Mpc<\/span> $\r\nH0m<\/span>:<\/span> (<\/span>67.4<\/span> -<\/span> 0.5<\/span>)<\/span> *<\/span> km<\/span>\/<\/span>s<\/span>\/<\/span>Mpc<\/span> $\r\nOmegap<\/span>:<\/span> 0.315<\/span> +<\/span> 0.007<\/span> $\r\nOmegam<\/span>:<\/span> 0.315<\/span> -<\/span> 0.007<\/span> $\r\n\r\n\/* t0 \u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f t0(H0m, Omegam) *\/<\/span>\r\nprintf<\/span>(<\/span>true<\/span>, \"\u6700\u5927\u5024\u306f ~3f \u5104\u5e74~%\"<\/span>, t0max<\/span>:<\/span>t0<\/span>(<\/span>ev<\/span>(<\/span>H0m<\/span>)<\/span>, Omegam<\/span>)<\/span>\/<\/span>okunen<\/span>)<\/span>$\r\n\r\n\/* t0 \u304c\u6700\u5c0f\u3068\u306a\u308b\u306e\u306f t0(H0p, Omegap) *\/<\/span>\r\nprintf<\/span>(<\/span>true<\/span>, \"\u6700\u5c0f\u5024\u306f ~3f \u5104\u5e74~%\"<\/span>, t0min<\/span>:<\/span>t0<\/span>(<\/span>ev<\/span>(<\/span>H0p<\/span>)<\/span>, Omegap<\/span>)<\/span>\/<\/span>okunen<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6700\u5927\u5024\u306f ??? \u5104\u5e74\r\n\u6700\u5c0f\u5024\u306f ??? \u5104\u5e74\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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printf<\/span>(<\/span>true<\/span>, \"\u5b87\u5b99\u5e74\u9f62\u306f ~3,0f  + ~3,0f - ~3,0f \u5104\u5e74~%\"<\/span>, \r\n              t0<\/span>, t0max<\/span> -<\/span> t0<\/span>, t0<\/span> -<\/span> t0min<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5b87\u5b99\u5e74\u9f62\u306f 138.  +  ? -  ? \u5104\u5e74\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3068\u3044\u3046\u3053\u3068\u3067\uff0c\u5b87\u5b99\u5e74\u9f62\u306f $138 \\pm ??$ \u5104\u5e74\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
Maxima \u3092\u96fb\u5353\u3068\u3057\u3066\u4f7f\u3063\u3066\u5b87\u5b99\u5e74\u9f62\u3092\u8a08\u7b97\u3059\u308b\u4f8b\u3002\u3053\u306e\u554f\u984c\u306f Maxima \u306a\u3069\u3092\u4f7f\u308f\u306a\u304f\u3066\u3082\uff0c$\\tanh^{-1} x$ \u3068 $\\sqrt{x}$ \u304c\u4f7f\u3048\u308b\u96fb\u5353\u304c\u3042\u308c\u3070\u3067\u304d\u307e\u3059\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-4362","post","type-post","status-publish","format-standard","hentry","category-maxima","category-rel-cosmo","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t