{"id":6742,"date":"2023-10-03T12:44:57","date_gmt":"2023-10-03T03:44:57","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=6742"},"modified":"2024-08-05T10:57:00","modified_gmt":"2024-08-05T01:57:00","slug":"weinberg-%e3%81%ae%e6%95%99%e7%a7%91%e6%9b%b8%e3%81%ab%e3%81%82%e3%82%8b-cmb-%e3%81%ae%e3%80%8c%e5%8f%8c%e6%a5%b5%e7%9a%84%e7%95%b0%e6%96%b9%e6%80%a7%e3%80%8d%e3%81%ae%e5%bc%8f%e3%81%ae%e9%a3%9f","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/6742\/","title":{"rendered":"Weinberg \u306e\u6559\u79d1\u66f8\u306b\u3042\u308b CMB \u306e\u300c\u53cc\u6975\u7684\u7570\u65b9\u6027\u300d\u306e\u5f0f\u306e\u98df\u3044\u9055\u3044\uff1f"},"content":{"rendered":"<p>Weinberg \u306e2\u3064\u306e\u6559\u79d1\u66f8<\/p>\n<ul>\n<li>Gravitation and Cosmology (1972)<\/li>\n<li>Cosmology (2008) \uff08<a href=\"https:\/\/www.nippyo.co.jp\/shop\/book\/6106.html\" target=\"_blank\" rel=\"noopener\">\u65e5\u672c\u8a9e\u7248\u300c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e\u5b87\u5b99\u8ad6\u300d\u5c0f\u677e\u82f1\u4e00\u90ce \u8a33(2013)<\/a>\uff09<\/li>\n<\/ul>\n<p>\u306b\u66f8\u3044\u3066\u3042\u308b\u5b87\u5b99\u80cc\u666f\u653e\u5c04 CMB \u306e\u300c\u53cc\u6975\u7684\u7570\u65b9\u6027\u300d\u306e\u5f0f\u304c\u7570\u306a\u3063\u3066\u3044\u308b\u4ef6\u3002<\/p>\n<p><!--more--><\/p>\n<h3>Gravitation and Cosmology (1972) \u306e\u5f0f (15.5.24)<\/h3>\n<p>archive.org \u3067\u5f53\u8a72\u30da\u30fc\u30b8\uff08p.522\uff09\u3092\u307f\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/archive.org\/details\/WeinbergS.GravitationAndCosmology..PrinciplesAndApplicationsOfTheGeneralTheoryOf\/page\/n549\/mode\/1up\" target=\"_blank\" rel=\"noopener\">Weinberg S. Gravitation And Cosmology.. Principles And Applications Of The General Theory Of Relativity ( Wiley, 1972), p.522<\/a><\/li>\n<\/ul>\n<p>$$T&#8217;_{\\gamma 0} \\equiv \\left(\\frac{\\nu&#8217;}{\\nu}\\right) T_{\\gamma 0} =<br \/>\n[1 &#8211; v_{\\oplus}^2]^{-1\/2}\\,[1 &#8211; v_{\\oplus}\\,\\cos\\theta ] \\,T_{\\gamma 0} \\tag{15.5.24}$$<\/p>\n<p>\u3053\u3053\u3067\uff0c$v_{\\oplus}$ \u306fCMB \u9759\u6b62\u7cfb\u306b\u5bfe\u3059\u308b\uff08\u89b3\u6e2c\u8005\u304c\u3044\u308b\uff09\u5730\u7403\u306e\u904b\u52d5\u901f\u5ea6\u3067\u3042\u308a\uff0c$\\theta$ \u306f\u5730\u7403\u306e\u904b\u52d5\u901f\u5ea6\u3068\u5149\u5b50\u306e\u904b\u52d5\u91cf\uff08\u9032\u884c\u65b9\u5411\uff09\u3068\u306e\u306a\u3059\u89d2\uff0c$T&#8217;_{\\gamma 0} $ \u306f\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308bCMB\u306e\u6e29\u5ea6\uff0c$T_{\\gamma 0} $ \u306f CMB \u306b\u5bfe\u3057\u3066\u9759\u6b62\u3057\u3066\u3044\u308b\u89b3\u6e2c\u8005\u304c\uff08\u3082\u3057\u5b58\u5728\u3059\u308b\u306e\u3067\u3042\u308c\u3070\uff09\u89b3\u6e2c\u3059\u308bCMB\u306e\u6e29\u5ea6\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u306e\u5f0f\u3067\u306f\uff0c CMB \u306b\u5bfe\u3059\u308b\u5730\u7403\u306e\u901f\u5ea6 $v_{\\oplus}$ \u306b\u6bd4\u4f8b\u3057\u305f\u89d2\u5ea6\u4f9d\u5b58\u9805\u306f\u5206\u5b50\u306b $\\cos\\theta$ \u304c\u3042\u308b\u306e\u3067\uff0c\u53cc\u6975\u7570\u65b9\u6027 dipole anisotropy \u306e\u307f\u3002<\/p>\n<h3>\u300c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e\u5b87\u5b99\u8ad6\u300d(2013) \u306e\u5f0f (2.4.6)<\/h3>\n<p>\u300c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e\u5b87\u5b99\u8ad6\u3000\u4e0a\u300d(2013) \u306e p. 138<\/p>\n<p>$$T&#8217; = \\frac{T}{\\gamma \\left( 1 + \\beta \\cos\\theta\\right)} \\tag{2.4.6}$$<\/p>\n<p>\u3053\u3053\u3067\uff0c<\/p>\n<p>$$\\beta = \\frac{v}{c}, \\quad \\gamma = \\frac{1}{\\sqrt{1-\\beta^2}}$$<\/p>\n<p>\u3067\u3042\u308a\uff0c$v$ \u306fCMB \u9759\u6b62\u7cfb\u306b\u5bfe\u3059\u308b\u89b3\u6e2c\u8005\u304c\u3044\u308b\u5730\u7403\u306e\u904b\u52d5\u901f\u5ea6\u3067\u3042\u308a\uff0c$\\theta$ \u306f\u5730\u7403\u306e\u904b\u52d5\u901f\u5ea6\u3068\u5149\u5b50\u306e\u904b\u52d5\u91cf\uff08\u9032\u884c\u65b9\u5411\uff09\u3068\u306e\u306a\u3059\u89d2\uff0c$T&#8217; $ \u306f\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308bCMB\u306e\u6e29\u5ea6\uff0c$T$ \u306f CMB \u306b\u5bfe\u3057\u3066\u9759\u6b62\u3057\u3066\u3044\u308b\u89b3\u6e2c\u8005\u304c\uff08\u3082\u3057\u5b58\u5728\u3059\u308b\u306e\u3067\u3042\u308c\u3070\uff09\u89b3\u6e2c\u3059\u308bCMB\u306e\u6e29\u5ea6\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u306e\u5f0f\u3067\u306f\uff0c\u89d2\u5ea6\u4f9d\u5b58\u9805\u304c\u5206\u6bcd\u306b\u3042\u308b\u305f\u3081\uff0c$\\beta$ \u306e1\u6b21\u307e\u3067\u306e\u5c55\u958b\u306a\u3089\u540c\u7b49\u3060\u304c\uff0c$\\beta$ \u306e2\u6b21\u4ee5\u4e0a\u306e\u9805\u3067\u524d\u8ff0\u306e (15.5.25) \u5f0f\u3068\u7570\u306a\u3063\u3066\u304f\u308b\u3002\u3069\u3061\u3089\u304c\u6b63\u3057\u3044\u5f0f\u3067\u3042\u308d\u3046\u304b&#8230;<\/p>\n<h3>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3088\u3089\u305a\u306b\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u304a\u3088\u3073\u5149\u884c\u5dee\u306e\u5f0f\u3092\u6c42\u3081\u308b<\/h3>\n<p>\u3053\u3053\u3067\u306f\uff0c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e\u5c0e\u51fa\u6cd5\u306b\u5f93\u3046\u306e\u3067\u306f\u306a\u304f\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3088\u3089\u306a\u3044\u7d71\u4e00\u7684\u624b\u6cd5\u306b\u3088\u3063\u3066\uff0c\u81a8\u5f35\u5b87\u5b99\u3092\u542b\u3080\u4e00\u822c\u76f8\u5bfe\u8ad6\u7684\u72b6\u6cc1\u306b\u304a\u3044\u3066\u3082\u6210\u7acb\u3059\u308b\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u3068\u5149\u884c\u5dee\u306e\u5f0f\u3092\u7528\u3044\u308b\u3002<\/p>\n<p>\u8a73\u7d30\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c\/\">\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/a>\n<ul>\n<li>\u00a0<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c\/#A_B\">$A$ \u3068\u3068\u3082\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u5149\u6e90\u304b\u3089\u306e\u5149\u3092\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005 $B$ \u304c\u6e2c\u5b9a\u3059\u308b\u5834\u5408<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e8%a1%8c%e5%b7%ae\/\">\u5149\u884c\u5dee<\/a><\/li>\n<\/ul>\n<p>\u4e0a\u8a18\u306e\u30da\u30fc\u30b8\u306e\u7d50\u679c\u3092\u307e\u3068\u3081\u308b\u3068\uff0cCMB \u9759\u6b62\u7cfb\u3067\u306e\u632f\u52d5\u6570 $\\omega$ \u3092\u3042\u3089\u305f\u3081\u3066 $\\omega_0$\uff0cCMB \u9759\u6b62\u7cfb\u306b\u5bfe\u3057\uff0c\u901f\u3055 $V$ \u3067\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b\u632f\u52d5\u6570 $\\bar{\\omega}$ \u3092\u3042\u3089\u305f\u3081\u3066 $\\omega_{\\rm obs}$ \u3068\u3059\u308b\u3068\uff0c<\/p>\n<p>$$\\omega_{\\rm obs} = \\omega_0 \\frac{\\sqrt{1-V^2}}{1+V \\cos\\bar{\\theta}}$$<\/p>\n<p>\u3067\u3042\u308a\uff0c\u3053\u3053\u3067 $\\bar{\\theta}$ \u306f\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306e\u901f\u5ea6\u3068\u5149\u306e\u9032\u884c\u65b9\u5411\u3068\u306e\u306a\u3059\u89d2\u3092\uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3057\u305f\u89d2\u5ea6\u3067\u3042\u308b\u3002\u8ab0\u304c\u6e2c\u5b9a\u3057\u305f\u89d2\u5ea6\u304b\uff0c\u306f\u3063\u304d\u308a\u3055\u305b\u308b\u3053\u3068\u306f\u91cd\u8981\u3067\u3042\u308b\u3002\u306a\u305c\u306a\u3089\u3070&#8230;<\/p>\n<p>\u5149\u306e\u9032\u884c\u65b9\u5411\u306f\uff0c\u89b3\u6e2c\u8005\u306e\u904b\u52d5\u306b\u3088\u3063\u3066\u5909\u308f\u308b\u3002\u3053\u306e\u73fe\u8c61\u306f\u300c\u5149\u884c\u5dee\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u308b\u3002\u540c\u3058\u5149\u3092\u89b3\u6e2c\u3057\u3066\u3044\u3066\u3082\uff0c\u305d\u306e\u9032\u884c\u65b9\u5411\u3092\u8868\u3059\u89d2\u5ea6\u306f\u89b3\u6e2c\u8005\u306e\u904b\u52d5\u901f\u5ea6\u306b\u3088\u3063\u3066\u5909\u308f\u308b\u3002\u9759\u6b62\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b\u9032\u884c\u65b9\u5411\u3092\u8868\u3059\u89d2\u5ea6\u3092 $\\theta$ \u3068\u3059\u308b\u3068\uff0c<\/p>\n<p>$$\\cos \\bar{\\theta} = \\frac{\\cos\\theta -V}{1 \u2013 V\\cos\\theta}$$<\/p>\n<p>\u8ab0\u304c\u89b3\u6e2c\u3059\u308b\u89d2\u5ea6\u306a\u306e\u304b\uff08\u9759\u6b62\u89b3\u6e2c\u8005\u306a\u306e\u304b\uff0c\u904b\u52d5\u89b3\u6e2c\u8005\u306a\u306e\u304b\uff09\u3092\u306f\u3063\u304d\u308a\u3055\u305b\u3066\uff0c\u305d\u308c\u306b\u5fdc\u3058\u3066\u89d2\u5ea6\u306e\u8868\u8a18\u3082\u533a\u5225\u3057\u3048\u304a\u304f\u3053\u3068\u304c\u809d\u5fc3\u3067\u3042\u308b\u3002<\/p>\n<h3>\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306b\u3088\u308bCMB\u306e\u7570\u65b9\u6027\u306e\u5f0f<\/h3>\n<p>CMB \u306e\u6e29\u5ea6 $T$ \u306f\u5149\u306e\u632f\u52d5\u6570\u3068\u540c\u3058\u3088\u3046\u306b\u5b87\u5b99\u8ad6\u7684\u8d64\u65b9\u504f\u79fb\u3084\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u3092\u53d7\u3051\u308b\u3002\u3064\u307e\u308a\uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b CMB \u306e\u6e29\u5ea6 $\\bar{T}$ \u3068\u9759\u6b62\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b\u6e29\u5ea6 $T$ \u3068\u306e\u95a2\u4fc2\u306f\uff0c<\/p>\n<p>$$\\bar{T} = \\frac{\\omega_{\\rm obs}}{\\omega_0} T = T \\frac{\\sqrt{1-V^2}}{1+V \\cos\\bar{\\theta}}$$<\/p>\n<p>\u3053\u308c\u304c\uff0c\u6211\u3005\u304c\u4e3b\u5f35\u3059\u308b\u3068\u3053\u308d\u306e\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3088\u3089\u306a\u3044\u7d71\u4e00\u7684\u624b\u6cd5\u306b\u3088\u3063\u3066\u5c0e\u304d\u51fa\u3057\u305f\uff0c\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u52b9\u679c\u306b\u3088\u308b CMB \u306e\u7570\u65b9\u6027\u306e\u5f0f\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u308c\u3092\u3064\u3089\u3064\u3089\u3068\u773a\u3081\u3066\u307f\u308b\u3068\uff0c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e 2013:(2.4.6) \u5f0f\u306b\u304d\u308f\u3081\u3066\u3088\u304f\u4f3c\u3066\u3044\u308b\u3053\u3068\u306b\u6c17\u3065\u304f\u3002\u3053\u3053\u3067\u306f\uff0c\u672c\u30b5\u30a4\u30c8\u306e\u57fa\u672c\u65b9\u91dd\u306b\u3057\u305f\u304c\u3063\u3066\uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306e\u91cf\u306b\u306f\u30d0\u30fc ($\\bar{\\ }$) \u3092\u3064\u3051\u3066\u3042\u3089\u308f\u3057\u305f\u5f0f\u3092\u305d\u306e\u307e\u307e\u5f15\u7528\u3057\u305f\u3002\u4ee5\u4e0b\u3067\u306f\uff0c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e\u65b9\u91dd\u306b\u3057\u305f\u304c\u3044\uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306e\u91cf\u306b\u306f\u30c0\u30c3\u30b7\u30e5 (${}&#8217;$) \u3092\u3064\u3051\u308b\u3053\u3068\u306b\u3057\u3066\u8a71\u3092\u7d9a\u3051\u3088\u3046\u3002<\/p>\n<p>&nbsp;<\/p>\n<h3>\u5149\u884c\u5dee\u306e\u5f0f\u3067\u89e3\u6c7a\uff01<\/h3>\n<p>\u3053\u306e\u4e00\u898b\u7570\u306a\u308b2\u3064\u306e\u5f0f 1972:(15.5.24) \u3068 2013:(2.4.6) \u306f\uff0c\u89d2\u5ea6 $\\theta$ \u306e\u610f\u5473\u3092\u304d\u3061\u3093\u3068\u533a\u5225\u3057\u3066\uff0c\u5149\u884c\u5dee\u306e\u5f0f\u3092\u4f7f\u3046\u3068\u540c\u7b49\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u3002<\/p>\n<p>\u307e\u305a\uff0c\u6bd4\u8f03\u3057\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u306b 1972:(15.5.24) \u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a18\u53f7\u8868\u8a18\u3092\u305d\u308d\u3048\u3066\u66f8\u304d\u76f4\u3059\u3002<\/p>\n<p>$$T&#8217; = \\frac{1 &#8211; \\beta \\cos\\theta}{\\sqrt{1 &#8211; \\beta^2}} T\u00a0 \\tag{$A$}$$<\/p>\n<p>\u3053\u3053\u3067\uff0c$\\theta$ \u306f\u539f\u8457 p.522 \u306b\u66f8\u3044\u3066\u3042\u308b\u3088\u3046\u306b<\/p>\n<blockquote><p>where $\\theta$ is now the angle between the velocity of the earth and photon.<\/p><\/blockquote>\n<p>&nbsp;<\/p>\n<p>\u3060\u304c\uff0cCMB \u306b\u5bfe\u3057\u3066\u9759\u6b62\u3057\u3066\u3044\u308b\u7cfb\u3067\u306e\u89d2\u5ea6\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002<\/p>\n<p>\u6b21\u306b\uff0c2013:(2.4.6) \u5f0f\u3082\u5c11\u3057\u3060\u3051\u8a18\u53f7\u8868\u8a18\u3092\u5909\u3048\u3066\u66f8\u304d\u76f4\u3059\u3002<\/p>\n<p>$$T&#8217; = \\frac{\\sqrt{1 &#8211; \\beta^2}}{\\left( 1 + \\beta \\cos\\theta&#8217; \\right)} T \\tag{$B$} $$<\/p>\n<p>\u3053\u3053\u3067 $\\theta&#8217;$ \u306f\uff0c\u5730\u7403\u306e\u904b\u52d5\u65b9\u5411\u3068\u5149\u5b50\u306e\u904b\u52d5\u65b9\u5411\u3068\u306e\u306a\u3059\u89d2\u3067\u3042\u308b\u304c\uff0c\u3010<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u3053\u3053\u304c\u5927\u4e8b<\/strong><\/span>\u3011<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u904b\u52d5\u3057\u3066\u3044\u308b\u5730\u7403\u304b\u3089\u307f\u305f\u89d2\u5ea6<\/strong><\/span>\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002<\/p>\n<p>$\\theta$ \u3068 $\\theta&#8217;$ \u306f\u4ee5\u4e0b\u306e<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e8%a1%8c%e5%b7%ae\/\">\u5149\u884c\u5dee<\/a>\u306e\u5f0f\u3067\u95a2\u4fc2\u3065\u3051\u3089\u308c\u308b\u3002<\/p>\n<p>$$\\cos \\theta&#8217; = \\frac{\\cos\\theta &#8211; \\beta}{1 &#8211; \\beta \\cos\\theta}$$<\/p>\n<p>\u3053\u308c\u3092\u4f7f\u3046\u3068\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n1 + \\beta \\cos\\theta&#8217; &amp;=&amp; 1 + \\frac{\\beta\\cos\\theta &#8211; \\beta^2}{1 &#8211; \\beta \\cos\\theta} \\\\<br \/>\n&amp;=&amp; \\frac{1 &#8211; \\beta^2}{1 &#8211; \\beta \\cos\\theta} \\\\<br \/>\n\\therefore\\ \\ \\frac{\\sqrt{1 &#8211; \\beta^2}}{\\left( 1 + \\beta \\cos\\theta&#8217; \\right)} T &amp;=&amp; \\frac{1 &#8211; \\beta \\cos\\theta}{\\sqrt{1 &#8211; \\beta^2}} T<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\uff0c$(A)$ \u5f0f\u3068 $(B)$ \u5f0f\u306f\u7b49\u3057\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u3064\u307e\u308a\uff0cWeinberg \u306f\uff08\u672c\u4eba\u306f\u533a\u5225\u3067\u304d\u3066\u3044\u308b\u306e\u3060\u308d\u3046\u304c\uff09CMB \u9759\u6b62\u7cfb\u3067\u307f\u305f\u89d2\u5ea6 $\\theta$\u00a0 \u3068\uff0c\u5730\u7403\u9759\u6b62\u7cfb\u3067\u307f\u305f\u89d2\u5ea6 $\\theta&#8217;$ \u3092\u533a\u5225\u305b\u305a\u306b $\\theta$ \u3068\u8868\u8a18\u3057\u305f\u305f\u3081\u306b\uff0c\u3044\u3089\u306c\u6df7\u4e71\u3092\u307e\u306d\u3044\u305f\u3060\u3051\u3067\u3042\u308a\uff0c$(B)$ \u5f0f\u306e\u3088\u3046\u306b\uff0c\u5730\u7403\u9759\u6b62\u7cfb\u3067\u307f\u305f\u89d2\u5ea6\u306f\u3061\u3083\u3093\u3068 $\\theta&#8217;$\u00a0 \u3068\u66f8\u304d\u5206\u3051\u308b\u3068\uff0c\u6df7\u4e71\u306f\u306a\u304f\uff0c2\u3064\u306e\u5f0f\u304c\u540c\u7b49\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067\u3042\u308b\u3002<\/p>\n<p>\u307e\u305f\uff0c\u3053\u308c\u3089\u306e\u89d2\u5ea6\u306f\u5730\u7403\u306e\u904b\u52d5\u65b9\u5411\u3068\u5149\u5b50\u306e\u904b\u52d5\u65b9\u5411\u3068\u306e\u306a\u3059\u89d2\u3067\u3042\u308b\u304b\u3089\uff0c\u5730\u7403\u306e\u904b\u52d5\u65b9\u5411\u304b\u3089\u304f\u308b\u5149\u306b\u3064\u3044\u3066\u306f\uff0c$\\theta$ \u307e\u305f\u306f $\\theta&#8217;$ \u304c\uff08$0$ \u3067\u306f\u306a\u304f\uff09$\\pi$ \u30e9\u30b8\u30a2\u30f3\u3068\u306a\u308a\uff0c\u7e26\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f<\/p>\n<p>\\begin{eqnarray}<br \/>\nT&#8217; &amp;=&amp; \\frac{\\sqrt{1 &#8211; \\beta^2}}{\\left( 1 + \\beta \\cos\\pi \\right)} T \\\\<br \/>\n&amp;=&amp; \\frac{1 &#8211; \\beta \\cos\\pi}{\\sqrt{1 &#8211; \\beta^2}} T \\\\<br \/>\n&amp;=&amp; \\sqrt{\\frac{1 + \\beta}{1 &#8211; \\beta}} T &gt; T<br \/>\n\\end{eqnarray}<\/p>\n<p>\u304c\u5f97\u3089\u308c\u308b\u3002\u9032\u884c\u65b9\u5411\u306e\u6e29\u5ea6\u304c\u9ad8\u3044\uff01<\/p>\n<p>\u307e\u305f\uff0c\u89b3\u6e2c\u8005\u304b\u3089\u307f\u3066\u771f\u6a2a $\\displaystyle \\theta&#8217; = \\frac{\\pi}{2}$ $\\displaystyle\\left( \\theta \\neq \\frac{\\pi}{2}\\right)$\u306e\u3068\u304d\uff0c\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f<\/p>\n<p>\\begin{eqnarray}<br \/>\nT&#8217; &amp;=&amp; {\\sqrt{1 &#8211; \\beta^2}}\u00a0 \\,T &lt;\u00a0 T<br \/>\n\\end{eqnarray}<\/p>\n<p>\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n<h3>\u307e\u3068\u3081<\/h3>\n<p>\u89b3\u6e2c\u8005\u306e\u904b\u52d5\u306b\u8d77\u56e0\u3059\u308b\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306b\u3088\u308b CMB \u306e\u53cc\u6975\u7570\u65b9\u6027\u3092\u8868\u3059\u5f0f\u306b\u3064\u3044\u3066\uff0c\u540c\u3058\u8457\u8005\uff0c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u304c\u66f8\u3044\u305f2\u518a\u306e\u30c6\u30ad\u30b9\u30c8\u306b\u66f8\u304b\u308c\u3066\u3044\u308b\u5f0f\u304c\u7570\u306a\u308b\u3053\u3068\u3092\u767a\u898b\u3057\uff0c\u3069\u3061\u3089\u304c\u6b63\u3057\u3044\u5f0f\u304b\u3092\u78ba\u304b\u3081\u308b\u305f\u3081\uff0c\u6211\u3005\u306e\u7814\u7a76\u5ba4\u3067\u69cb\u7bc9\u3057\u3066\u304d\u305f\u300c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3088\u3089\u306a\u3044\u7d71\u4e00\u7684\u624b\u6cd5\u300d\u306b\u3088\u3063\u3066\uff0c\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u3092\u5c0e\u3044\u305f\u3002<\/p>\n<p>\u305d\u306e\u7d50\u679c\u306f\uff0c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e 2013:(2.4.6) \u5f0f\u3068\u3088\u304f\u4f3c\u3066\u304a\u308a\uff0c\u5b9f\u969b\uff0c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e\u5f0f\u306b\u73fe\u308c\u308b\u5149\u306e\u9032\u884c\u65b9\u5411\u3092\u3042\u3089\u308f\u3059\u89d2\u5ea6 $\\theta$ \u3092\uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u89d2\u5ea6 $\\theta&#8217;$ \u306b\u5909\u66f4\u3059\u308b\u3053\u3068\u3067\uff0c\u6211\u3005\u306e\u5c0e\u3044\u305f\uff08\u6b63\u3057\u3044\uff09\u5f0f\u3068\u5168\u304f\u540c\u3058\u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n<p>\u3064\u307e\u308a\uff0cCMB \u9759\u6b62\u7cfb\u3067\u307f\u305f\u89d2\u5ea6 $\\theta$\u00a0 \u3068\uff0c\u5730\u7403\u9759\u6b62\u7cfb\u3067\u307f\u305f\u89d2\u5ea6 $\\theta&#8217;$ \u3092\u533a\u5225\u305b\u305a\u306b $\\theta$ \u3068\u8868\u8a18\u3057\u305f\u3057\u305f\u3053\u3068\u304c\u6df7\u4e71\u3092\u62db\u3044\u305f\u539f\u56e0\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u306e\u3067\u3042\u308b\u3002<\/p>\n<p>\u307e\u305f\uff0c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u3082\u8ff0\u3079\u3066\u3044\u308b\u3088\u3046\u306b\uff0c<\/p>\n<p>$$T&#8217; = \\frac{\\sqrt{1 &#8211; \\beta^2}}{\\left( 1 + \\beta \\cos\\theta&#8217; \\right)} T \\tag{$B$} $$<\/p>\n<p>\u304c\u6b63\u3057\u3044\u5f0f\u3067\u3042\u308b\u306e\u3067\uff0c$\\beta$ \u306b\u95a2\u3059\u308b\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3092\u884c\u3048\u3070\uff0c$\\beta$ \u306e1\u6b21\u3067\u306f\u78ba\u304b\u306b $\\cos\\theta&#8217;$ \u306b\u6bd4\u4f8b\u3059\u308b\u53cc\u6975\u7570\u65b9\u6027\u306e\u9805\u304c\u3042\u3089\u308f\u308c\u308b\u304c\uff0c\u5024\u306f\u5c0f\u3055\u304f\u306a\u308b\u3082\u306e\u306e\uff0c$\\beta$ \u306e2\u6b21\u4ee5\u4e0a\u3067\u306f\u53cc\u6975\u7570\u65b9\u6027\u4ee5\u5916\u306e\u9ad8\u6b21\u306e\u591a\u91cd\u6975\u7570\u65b9\u6027\u3082\u307e\u305f\u81ea\u7136\u306b\u3042\u3089\u308f\u308c\u308b\u3053\u3068\u3082\uff0c\u6211\u3005\u306e\u5c0e\u51fa\u3057\u305f\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u304b\u3089\u8a00\u3048\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<p>\u306a\u304a\uff0c\u5b9f\u969b\u306e CMB \u306e\u89b3\u6e2c\u304b\u3089\u53cc\u6975\u7570\u65b9\u6027\u306e\u7a0b\u5ea6\u306f $10^{-3}$ \u3064\u307e\u308a\uff0c$\\beta \\sim 10^{-3}$ \u3067\u3042\u308b\u3002$\\beta^2$ \u306e\u9805\u306f\u3069\u306e\u304f\u3089\u3044\u306e\u5927\u304d\u3055\u3067\u3059\u304b\uff1f\u3068\u3044\u3046\u60f3\u5b9a\u8cea\u554f\u306b\u3082\u3061\u3083\u3093\u3068\u7b54\u3048\u3089\u308c\u308b\u3088\u3046\u306b\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E5%AE%87%E5%AE%99%E3%83%9E%E3%82%A4%E3%82%AF%E3%83%AD%E6%B3%A2%E8%83%8C%E6%99%AF%E6%94%BE%E5%B0%84\">\u5b87\u5b99\u30de\u30a4\u30af\u30ed\u6ce2\u80cc\u666f\u653e\u5c04 &#8211; Wikipedia<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Weinberg \u306e2\u3064\u306e\u6559\u79d1\u66f8<\/p>\n<ul>\n<li>Gravitation and Cosmology (1972)<\/li>\n<li>Cosmology (2008) \uff08\u65e5\u672c\u8a9e\u7248\u300c\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\u306e\u5b87\u5b99\u8ad6\u300d\u5c0f\u677e\u82f1\u4e00\u90ce \u8a33(2013)\uff09<\/li>\n<\/ul>\n<p>\u306b\u66f8\u3044\u3066\u3042\u308b\u5b87\u5b99\u80cc\u666f\u653e\u5c04 CMB \u306e\u300c\u53cc\u6975\u7684\u7570\u65b9\u6027\u300d\u306e\u5f0f\u304c\u7570\u306a\u3063\u3066\u3044\u308b\u4ef6\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/6742\/\">\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":[20],"tags":[],"class_list":["post-6742","post","type-post","status-publish","format-standard","hentry","category-rel-cosmo","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6742","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=6742"}],"version-history":[{"count":31,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6742\/revisions"}],"predecessor-version":[{"id":9329,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6742\/revisions\/9329"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=6742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=6742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=6742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}