{"id":1367,"date":"2022-01-21T16:33:29","date_gmt":"2022-01-21T07:33:29","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=1367"},"modified":"2022-02-05T13:46:44","modified_gmt":"2022-02-05T04:46:44","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9a%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e3%81%ae%e9%9d%99%e6%ad%a2%e5%ae%87%e5%ae%99%e3%83%a2%e3%83%87%e3%83%ab%e3%81%a8%e3%80%8c%e4%ba%ba","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e5%ae%87%e5%ae%99%e8%ab%96\/%e8%86%a8%e5%bc%b5%e5%ae%87%e5%ae%99%e3%81%ae%e8%a8%88%e9%87%8f%e3%81%ae%e5%b0%8e%e5%87%ba%e3%81%a8%e3%83%95%e3%83%aa%e3%83%bc%e3%83%89%e3%83%9e%e3%83%b3%e6%96%b9%e7%a8%8b%e5%bc%8f\/%e8%a3%9c%e8%b6%b3%ef%bc%9a%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e3%81%ae%e9%9d%99%e6%ad%a2%e5%ae%87%e5%ae%99%e3%83%a2%e3%83%87%e3%83%ab%e3%81%a8%e3%80%8c%e4%ba%ba\/","title":{"rendered":"\u88dc\u8db3\uff1a\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u9759\u6b62\u5b87\u5b99\u30e2\u30c7\u30eb\u3068\u300c\u4eba\u751f\u6700\u5927\u306e\u904e\u3061\u300d"},"content":{"rendered":"

<\/p>\n

\u5b87\u5b99\u81a8\u5f35\u3092\u6c7a\u3081\u308b\u5f0f<\/h3>\n

\u30cb\u30e5\u30fc\u30c8\u30f3\u5b87\u5b99\u8ad6<\/strong><\/span>\u306b\u304a\u3044\u3066\u5f97\u3089\u308c\u305f\u5f0f<\/p>\n

$$\\dot{\\rho} + 3 \\frac{\\dot{a}}{a} \\rho = 0 \\tag{1}$$
\n$$\\quad \\frac{\\ddot{a}}{a} = – \\frac{4\\pi G}{3} \\rho \\tag{2}$$
\n$$\\left(\\frac{\\dot{a}}{a}\\right)^2 + \\frac{k}{a^2} = \\frac{8\\pi G}{3} \\rho \\tag{3}$$<\/p>\n

\u3053\u308c\u3089\u306e\u5f0f\u306f\u4e00\u822c\u76f8\u5bfe\u8ad6\u7684\u5b87\u5b99\u8ad6\u306b\u304a\u3044\u3066\u3082\u305d\u306e\u307e\u307e\u306e\u5f62\u3067\u6210\u308a\u7acb\u3064<\/strong><\/span>\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u9759\u6b62\u5b87\u5b99\u30e2\u30c7\u30eb<\/h3>\n

\u30cb\u30e5\u30fc\u30c8\u30f3\u540c\u69d8\uff0c\uff08\u30cf\u30c3\u30d6\u30eb\u306e\u767a\u898b\u4ee5\u524d\u306f\uff09\u5b87\u5b99\u306f\u6c38\u4e45\u4e0d\u5909\u3067\u3042\u308b\u3079\u3057\uff0c\u3068\u8003\u3048\u3066\u3044\u305f\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306f\uff0c\u5f7c\u81ea\u8eab\u306e\u63d0\u5531\u3057\u305f\u65b9\u7a0b\u5f0f\uff08\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\uff09\u304b\u3089\u5f97\u3089\u308c\u305f \\((2)\\) \u5f0f\u3092\u307f\u3066\uff0c\u3061\u3068\u56f0\u3063\u305f\uff08\u305d\u3046\u3060\uff09\u3002<\/p>\n

\u7269\u8cea\u5bc6\u5ea6\u306f \\(\\rho > 0\\) \u3060\u304b\u3089\u52a0\u901f\u5ea6\u304c\u30bc\u30ed\u306b\u306a\u3089\u306a\u3044 \\(\\ddot{a} \\neq 0\\) \uff0c\u5b87\u5b99\u306f\u3058\u3063\u3068\u3057\u3066\u3044\u3089\u308c\u306a\u3044\uff01<\/p>\n

\u5168\u80fd\u306e\u795e\u304c\u3064\u304f\u308a\u305f\u3082\u3046\u305f\uff08\u306f\u305a\u306e\uff09\u6c38\u4e45\u4e0d\u5909\u306e\u5b87\u5b99\u304c\u5f97\u3089\u308c\u306a\u3044…<\/p>\n

\u305d\u3053\u3067\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u304c\uff08\u3057\u3076\u3057\u3076\uff1f\uff09\u5c0e\u5165\u3057\u305f\u306e\u304c\uff0c\u5b87\u5b99\u5b9a\u6570<\/strong><\/span> \\({\\color{red}{\\Lambda}}\\) \u3067\u3042\u3063\u305f\u3002\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u306b\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5c0e\u5165\u3057\uff0c
\n$$\\quad \\frac{\\ddot{a}}{a} = – \\frac{4\\pi G}{3} \\rho\u00a0 {\\color{red}\\, +\\, \\frac{\\Lambda}{3}}$$<\/p>\n

\u521d\u671f\u6761\u4ef6\u3068\u3057\u3066 \\(\\displaystyle \\frac{\\ddot{a}}{a} = 0\\) \u3068\u306a\u308b\u3088\u3046\u306b \\({\\color{red}{\\Lambda}}\\) \u306e\u5024\u3092\u8abf\u7bc0\u3059\u308c\u3070\uff0c\u52a0\u901f\u5ea6\u3092\u30bc\u30ed\u306b\u3067\u304d\u308b\u3002<\/p>\n

\u5b87\u5b99\u5b9a\u6570\u306e\u5c0e\u5165\u306b\u3088\u3063\u3066 \\((3)\\) \u5f0f\u3082\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u304b\u308f\u308b\u306e\u3067
\n$$\\left(\\frac{\\dot{a}}{a}\\right)^2 + \\frac{{\\color{blue}{k}}}{a^2} = \\frac{8\\pi G}{3} \\rho {\\color{red}{ \\,+ \\,\\frac{\\Lambda}{3}}}$$<\/p>\n

\u3055\u3089\u306b\u7a4d\u5206\u5b9a\u6570 \\({\\color{blue}{k}} \\) \u306e\u5927\u304d\u3055\u3092\u3046\u307e\u304f\u8abf\u7bc0\u3059\u308c\u3070\uff0c\\(\\dot{a} = 0\\) \u3064\u307e\u308a\uff0c\u521d\u901f\u5ea6\u3082\u30bc\u30ed\u306b\u3067\u304d\uff0c\u6c38\u4e45\u4e0d\u5909\u306a\uff08\\(a\\) \u304c\u4e00\u5b9a\u3067\u3042\u308a\u3064\u3065\u3051\u308b\uff09\u9759\u6b62\u5b87\u5b99\u30e2\u30c7\u30eb\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n

\u3081\u3067\u305f\u3057\uff0c\u3081\u3067\u305f\u3057… \uff1f<\/p>\n

\u30cf\u30c3\u30d6\u30eb\u306e\u767a\u898b\u3068\u5b87\u5b99\u5b9a\u6570\u306e\u64a4\u56de<\/h3>\n

\u305d\u306e\u5f8c\uff0c\u30cf\u30c3\u30d6\u30eb\u306e\u767a\u898b\uff08\\(\\dot{a}\u00a0 > 0\\)\uff09\u3092\u805e\u3044\u305f\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306f\uff0c\u9759\u6b62\u5b87\u5b99\u30e2\u30c7\u30eb\uff08\\(\\dot{a}\u00a0 = 0\\)\uff09\u306e\u305f\u3081\uff08\u3060\u3051\uff09\u306b\u5b87\u5b99\u5b9a\u6570\u3092\u5c0e\u5165\u3057\u305f\u3053\u3068\u3092\u300c\u4eba\u751f\u6700\u5927\u306e\u904e\u3061\u300d\u3068\u3057\uff0c\u5b87\u5b99\u5b9a\u6570\u3092\u64a4\u56de\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u3053\u308c\u304c20\u4e16\u7d00\u524d\u534a\u306e\u72b6\u6cc1\u3067\u3057\u305f\u3002<\/p>\n

\u73fe\u4ee3\u5b87\u5b99\u8ad6\u306e\u300c\u30c0\u30fc\u30af\u30b5\u30a4\u30c9\u300d<\/h3>\n

\u3057\u304b\u3057\uff0c\u5b87\u5b99\u5b9a\u6570\u306e\u5c0e\u5165\u306f\uff0c\u306f\u305f\u3057\u3066\u672c\u5f53\u306b\u300c\u4eba\u751f\u6700\u5927\u306e\u904e\u3061\u300d\u3060\u3063\u305f\u306e\u304b\u3068\u3044\u3046\u3068\uff0c\u3069\u3046\u3082\u305d\u3046\u3068\u3082\u8a00\u3044\u5207\u308c\u306a\u3044\u3002<\/p>\n

20\u4e16\u7d00\u5f8c\u534a\uff0c1980\u5e74\u4ee3\u306b\u306f\u3044\u308a\uff0c\u5b87\u5b99\u306e\u3054\u304f\u521d\u671f\u306b\u6307\u6570\u95a2\u6570\u7684\u306a\u52a0\u901f\u81a8\u5f35\uff08\\(\\ddot{a}>0\\)\uff09\u306e\u6642\u671f\uff08\u3053\u308c\u3092\u5b87\u5b99\u306e\u30a4\u30f3\u30d5\u30ec\u30fc\u30b7\u30e7\u30f3<\/strong><\/span>\u3068\u3044\u3046\uff09\u304c\u3042\u3063\u305f\u3068\u3059\u308b\u8003\u3048\u304c\u63d0\u5531\u3055\u308c\u305f\u3002\u666e\u901a\u306e\u7269\u8cea\u306f \\(\\rho > 0\\) \u3067\u3042\u308b\u304b\u3089\uff0c\u3053\u306e\u3088\u3046\u306a\u52a0\u901f\u81a8\u5f35\u3092\u5f15\u304d\u8d77\u3053\u3059\u7269\u8cea\u306f\uff0c\u666e\u901a\u306e\u7269\u8cea\u3067\u306f\u3042\u308a\u3048\u305a\uff0c\u3042\u305f\u304b\u3082\uff08\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u304c\u64a4\u56de\u3057\u305f\u306f\u305a\u306e\uff09\u5b87\u5b99\u5b9a\u6570\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6301\u3064\u5fc5\u8981\u304c\u3042\u308a\uff0c\u7279\u306b\u300c\u771f\u7a7a\u306e\u30a8\u30cd\u30eb\u30ae\u30fc<\/strong><\/span>\u300d\u306a\u3069\u3068\u547c\u3070\u308c\u3066\u3044\u308b\u3002<\/p>\n

\u307e\u305f\uff0c\u4e16\u7d00\u304c\u304b\u308f\u308b\u897f\u66a6 2000\u5e74\u524d\u5f8c\u306b\uff0c\u4e3b\u306b2\u3064\u306e\u72ec\u7acb\u3057\u305f\u89b3\u6e2c\u30b0\u30eb\u30fc\u30d7\u306b\u3088\u3063\u3066\uff0c\u5b87\u5b99\u81a8\u5f35\u304c\u52a0\u901f\u3057\u3066\u3044\u308b\uff08\\(\\ddot{a}>0\\)\uff09\u3068\u3044\u3046\u7d50\u679c\u304c\u516c\u8868\u3055\u308c\u305f\u3002\u3053\u308c\u3082\u666e\u901a\u306e\u7269\u8cea\u3067\u306f\u3042\u308a\u3048\u305a\uff0c\u73fe\u5728\u306e\u5b87\u5b99\u306e\u3053\u306e\u3088\u3046\u306a\u52a0\u901f\u81a8\u5f35\u3092\u5f15\u304d\u8d77\u3053\u3059\u7269\u8cea\u306f\uff0c\u300c\u30c0\u30fc\u30af\u30a8\u30cd\u30eb\u30ae\u30fc<\/strong><\/span>\u300d\u306a\u3069\u3068\u547c\u3070\u308c\u3066\u3044\u308b\u3002<\/p>\n

\u3053\u306e\u3088\u3046\u306b\u3057\u3066\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u304c\u64a4\u56de\u3057\u305f\u306f\u305a\u306e\u5b87\u5b99\u5b9a\u6570\u306f\uff0c21\u4e16\u7d00\u306b\u304a\u3051\u308b\u73fe\u4ee3\u5b87\u5b99\u8ad6\u306b\u304a\u3044\u3066\u3082\u300c\u771f\u7a7a\u306e\u30a8\u30cd\u30eb\u30ae\u30fc<\/strong><\/span>\u300d\u3084\u300c\u30c0\u30fc\u30af\u30a8\u30cd\u30eb\u30ae\u30fc<\/strong><\/span>\u300d\u306a\u3069\u3068\u540d\u524d\u3092\u5909\u3048\u3066\u6697\u8e8d\uff1f\u5927\u6d3b\u8e8d\uff1f\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":1412,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-1367","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"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=1367"}],"version-history":[{"count":11,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1367\/revisions"}],"predecessor-version":[{"id":1756,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1367\/revisions\/1756"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1412"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=1367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}