{"id":92149,"date":"2024-04-26T19:03:38","date_gmt":"2024-04-26T19:03:38","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%AB%E3%83%A1%E3%83%BC%E3%83%88%E3%83%AB%E3%83%BB%E3%83%AD%E3%83%90%E3%83%BC%E3%83%88%E3%82%BD%E3%83%B3%E3%83%BB%E3%82%A6%E3%82%A9\/"},"modified":"2024-04-26T19:03:38","modified_gmt":"2024-04-26T19:03:38","slug":"%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%AB%E3%83%A1%E3%83%BC%E3%83%88%E3%83%AB%E3%83%BB%E3%83%AD%E3%83%90%E3%83%BC%E3%83%88%E3%82%BD%E3%83%B3%E3%83%BB%E3%82%A6%E3%82%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=92149","title":{"rendered":"\u30d5\u30ea\u30fc\u30c9\u30de\u30f3\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u30fb\u30ed\u30d0\u30fc\u30c8\u30bd\u30f3\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc\u6307\u6a19 – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>

\u5b87\u5b99\u8ad6\u3067\u306f\u3001\u30ed\u30d0\u30fc\u30c8\u30bd\u30f3\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc<\/b>\u8a08\u91cf\u306f\u3001\u81a8\u5f35\u30d1\u30e9\u30e1\u30fc\u30bf R(t) \u306e\u30d5\u30ea\u30fc\u30c9\u30de\u30f3\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb<\/b>\u65b9\u7a0b\u5f0f (\u4e00\u822c\u306bFLRW<\/b>\u30e2\u30c7\u30eb\u3068\u7565\u3055\u308c\u308b) \u3068\u7d44\u307f\u5408\u308f\u3055\u308c\u308b\u3053\u3068\u304c\u591a\u304f\u3001\u81a8\u5f35\u306b\u304a\u3044\u3066\u5c40\u6240\u7684\u306b\u5747\u8cea\u3067\u5c40\u6240\u7684\u306b\u7b49\u65b9\u6027\u306e\u5b87\u5b99<\/a><\/span>\u3092\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u8a08\u91cf\u3067\u3059\u3002\u307e\u305f\u306f\u53ce\u7e2e\u3002\u3053\u306e\u30e2\u30c7\u30eb\u306f\u3001\u5b87\u5b99\u306e\u6a19\u6e96\u5b87\u5b99\u30e2\u30c7\u30eb<\/a><\/span>\u3067\u3042\u308b\u30d3\u30c3\u30b0\u30d0\u30f3<\/a><\/span>\u3078\u306e\u6700\u521d\u306e\u8fd1\u4f3c<\/a><\/span>\u3068\u3057\u3066\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>

\u5730\u7406\u7684\u307e\u305f\u306f\u6b74\u53f2\u7684\u306a\u597d\u307f\u306b\u5fdc\u3058\u3066\u3001FLRW \u30e2\u30c7\u30eb\u306f\u3001\u30a2\u30ec\u30af\u30b5\u30f3\u30c0\u30fc \u30d5\u30ea\u30fc\u30c9\u30de\u30f3\u3001\u30b8\u30e7\u30eb\u30b8\u30e5 \u30eb\u30e1\u30fc\u30c8\u30eb<\/a><\/span>\u3001\u30cf\u30ef\u30fc\u30c9 \u30d1\u30fc\u30b7\u30fc \u30ed\u30d0\u30fc\u30c8\u30bd\u30f3\u3001\u30a2\u30fc\u30b5\u30fc \u30b8\u30a7\u30d5\u30ea\u30fc \u30a6\u30a9\u30fc\u30ab\u30fc\u306e 4 \u4eba\u306e\u79d1\u5b66\u8005\u306e\u540d\u524d\u3067\u547c\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u4f8b:\u30d5\u30ea\u30fc\u30c9\u30de\u30f3-\u30ed\u30d0\u30fc\u30c8\u30bd\u30f3-\u30a6\u30a9\u30fc\u30ab\u30fc<\/i>(FRW) \u307e\u305f\u306f\u30ed\u30d0\u30fc\u30c8\u30bd\u30f3-\u30a6\u30a9\u30fc\u30ab\u30fc<\/i>(RW)\u3002<\/p>

\n\"\u30d5\u30ea\u30fc\u30c9\u30de\u30f3\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u30fb\u30ed\u30d0\u30fc\u30c8\u30bd\u30f3\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc\u6307\u6a19<\/figure>

FLRW \u30e1\u30c8\u30ea\u30af\u30b9\u3092\u4f7f\u7528\u3057\u3066\u5b87\u5b99\u3092\u8aac\u660e\u3059\u308b<\/h2>

FLRW \u30e2\u30c7\u30eb\u306f\u5b87\u5b99\u304c\u5747\u8cea\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u30d3\u30c3\u30b0\u30d0\u30f3 \u30e2\u30c7\u30eb\u3067\u306f\u5b87\u5b99\u306b\u5b58\u5728\u3059\u308b\u5bc6\u5ea6<\/a><\/span>\u5909\u52d5\u3092\u8aac\u660e\u3067\u304d\u306a\u3044\u3068\u7d50\u8ad6\u4ed8\u3051\u308b\u4eba\u3082\u3044\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u5b9f\u969b\u3001\u53b3\u5bc6\u306a FLRW \u30e2\u30c7\u30eb\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u5929\u4f53\u306f\u5e73\u5747<\/a><\/span>\u3057\u3066\u5b87\u5b99\u3088\u308a\u306f\u308b\u304b\u306b\u5bc6\u5ea6\u304c\u9ad8\u3044\u305f\u3081\u3001\u9280\u6cb3\u56e3<\/a><\/span>\u3001\u661f<\/a><\/span>\u3001\u60d1\u661f<\/a><\/span>\u3001\u751f\u7269\u7684\u5b58\u5728\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\u3002<\/p>

\u5b9f\u969b\u306b\u306f\u3001FLRW \u30e2\u30c7\u30eb\u306f\u8a08\u7b97\u304c\u7c21\u5358\u3067\u3042\u308b\u305f\u3081\u3001\u6700\u521d\u306e\u8fd1\u4f3c\u3068\u3057\u3066\u306e\u307f\u4f7f\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u3053\u308c\u306f\u5f53\u3066\u306f\u307e\u308a\u307e\u305b\u3093\u3002\u6b21\u306b\u3001\u5bc6\u5ea6\u5909\u52d5\u3092\u8003\u616e\u3057\u305f\u30e2\u30c7\u30eb\u304c FLRW \u30e2\u30c7\u30eb\u306b\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002\u307b\u3068\u3093\u3069\u306e\u5b87\u5b99\u5b66\u8005\u306f\u3001\u5b87\u5b99\u306e\u89b3\u6e2c\u53ef\u80fd\u306a\u90e8\u5206\u304c<\/a><\/span>FLRW \u306b\u8fd1\u3044<\/i>\u30e2\u30c7\u30eb\u3001\u3064\u307e\u308a\u539f\u59cb\u5bc6\u5ea6\u5909\u52d5\u3092\u9664\u3044\u3066 FLRW \u8a08\u91cf\u306b\u5f93\u3046\u30e2\u30c7\u30eb\u306b\u3088\u3063\u3066\u3088\u304f\u8fd1\u4f3c\u3055\u308c\u308b\u3053\u3068\u306b\u540c\u610f\u3057\u3066\u3044\u307e\u3059\u3002 2003 \u5e74\u306b\u306f\u3001\u3053\u308c\u3089\u306e\u3055\u307e\u3056\u307e\u306a\u62e1\u5f35\u6a5f\u80fd\u306e\u7406\u8ad6\u7684\u610f\u5473\u306f\u5341\u5206\u306b\u7406\u89e3\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u3067\u3042\u308a\u3001\u305d\u306e\u76ee\u6a19\u306f\u3001\u305d\u308c\u3089\u3092 COBE \u304a\u3088\u3073 WMAP\u885b\u661f<\/a><\/span>\u306b\u3088\u3063\u3066\u884c\u308f\u308c\u305f\u89b3\u6e2c<\/span>\u3068\u4e00\u81f4\u3055\u305b\u308b\u3053\u3068\u3067\u3059\u3002<\/p>

\u305f\u3060\u3057\u3001\u5b8c\u5168\u306a FLRW \u30e2\u30c7\u30eb\u3068\u6442\u52d5\u30e2\u30c7\u30eb\u306e\u9055\u3044\u3092\u5fd8\u308c\u308b\u5371\u967a\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u307b\u307c FLRW<\/i>\u30e2\u30c7\u30eb\u306f\u901a\u5e38\u3001\u5358\u306bFLRW’<\/i>\u30e2\u30c7\u30eb\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>

\u66f2\u7387\u5024\u306b\u57fa\u3065\u304f FLRW \u30e1\u30c8\u30ea\u30c3\u30af<\/h2>
\n\"\u30d5\u30ea\u30fc\u30c9\u30de\u30f3\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u30fb\u30ed\u30d0\u30fc\u30c8\u30bd\u30f3\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc\u6307\u6a19<\/figure>

\u5e73\u9762\u7a7a\u9593\u306b\u304a\u3051\u308b FLRW \u30e1\u30fc\u30c8\u30eb\u6cd5<\/span><\/h3>

\u4e07\u4e00\u306b\u5099\u3048\u3066

$$ {k = 0 \\;} $$<\/div> \u3001\u30e1\u30c8\u30ea\u30af\u30b9\u3092\u66f8\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>
$$ {{\\rm d}s^2 = c^2 {\\rm d}t^2 – a(t)^2 ( {\\rm d}r^2 + r^2 {\\rm d} \\Omega^2 ) \\;} $$<\/div><\/dd><\/dl><\/center>

\u3053\u3053\u3067\u306f\u3001\u534a\u5f84\u5ea7\u6a19\u3067\u8868\u73fe\u3055\u308c\u305f\u3001\u30b9\u30b1\u30fc\u30eb\u4fc2\u6570\u3092\u5099\u3048\u305f\u901a\u5e38\u306e\u7a7a\u9593\u306e\u8a08\u91cf\u306e\u53e4\u5178\u7684\u306a\u5024\u3092\u898b\u3064\u3051\u307e\u3059\u3002

$$ {(r, \\theta, \\phi) \\;} $$<\/div><\/p>

\u6b63\u306e\u66f2\u7387\u7a7a\u9593\u306b\u304a\u3051\u308b FLRW \u8a08\u91cf<\/span><\/h3>

\u3082\u3057

$$ {k = +1 \\;} $$<\/div> \u3001 \u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059<\/p>
$$ {{\\rm d}s^2 = c^2 {\\rm d}t^2 – R(t)^2 \\left (\\frac{{\\rm d}r^2}{1 – r^2} + r^2 {\\rm d} \\Omega^2 \\right )} $$<\/div><\/dd><\/dl>

r<\/i> = 1<\/span>\u306b\u7279\u7570\u70b9\u304c\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u533a\u9593\u4e0a\u306e\u5ea7\u6a19\u306e\u5909\u5316\u3092\u63a2\u3057\u307e\u3059\u3002

$$ {]-1;1[ \\;} $$<\/div>\u8d70\u884c\u8ddd\u96e2\u3092\u7c21\u5358\u306b\u8868\u793a\u3057\u307e\u3059\u3002\u305d\u308c\u306b\u6c17\u3065\u3044\u3066
$$ {\\int \\frac{{\\rm d}r}{\\sqrt{1 – r^2}} = \\arcsin r} $$<\/div> \u3001\u79c1\u305f\u3061\u304c\u9078\u629e\u3057\u307e\u3059
$$ {\\chi \\;} $$<\/div>\u306e\u3088\u3046\u306a
$$ {R_0 r = \\sin(\\chi) \\;} $$<\/div> \u3002\u6b21\u306b\u3001\u65b0\u3057\u3044\u5f62\u5f0f\u306e\u30e1\u30c8\u30ea\u30af\u30b9\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <\/p>
$$ {{\\rm d}s^2 = c^2 {\\rm d}t^2 – a(t)^2 ( {\\rm d} \\chi^2 + \\sin^2 \\chi \\; {\\rm d} \\Omega^2 ) \\;} $$<\/div><\/dd><\/dl><\/center>
\n\"\u30d5\u30ea\u30fc\u30c9\u30de\u30f3\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u30fb\u30ed\u30d0\u30fc\u30c8\u30bd\u30f3\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc\u6307\u6a19<\/figure>

\u8ca0\u306e\u66f2\u7387\u7a7a\u9593\u306b\u304a\u3051\u308b FLRW \u8a08\u91cf<\/span><\/h3>

\u3082\u3057

$$ {k = -1 \\;} $$<\/div> \u3001 \u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059<\/p>
$$ {{\\rm d}s^2 = c^2 {\\rm d}t^2 – a(t)^2 \\left (\\frac{{\\rm d}r^2}{1 + r^2} + r^2 {\\rm d} \\Omega^2 \\right )} $$<\/div><\/dd><\/dl>

\u305d\u308c\u306b\u6c17\u3065\u3044\u3066

$$ {\\int \\frac{{\\rm d}r}{\\sqrt{1 + r^2}} = \\operatorname{arcsinh}\\ r} $$<\/div> \u3001\u30b3\u30fc\u30c7\u30a3\u30cd\u30fc\u30c8\u306e\u5909\u66f4\u3068\u3057\u3066\u9078\u629e\u3057\u307e\u3059
$$ {\\chi \\;} $$<\/div>\u306e\u3088\u3046\u306a
$$ {r = \\sinh(\\chi) \\;} $$<\/div> \u3002\u6b21\u306b\u3001\u65b0\u3057\u3044\u5f62\u5f0f\u306e\u30e1\u30c8\u30ea\u30af\u30b9\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <\/p>
$$ {{\\rm d}s^2 = c^2 {\\rm d}t^2 – a(t)^2 ( {\\rm d} \\chi^2 + \\sinh^2 \\chi \\; {\\rm d} \\Omega^2 ) \\;} $$<\/div><\/dd><\/dl><\/center>
\n\"\u30d5\u30ea\u30fc\u30c9\u30de\u30f3\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u30fb\u30ed\u30d0\u30fc\u30c8\u30bd\u30f3\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc\u6307\u6a19<\/figure>

\u6570\u5b66\u7684\u5b9a\u5f0f\u5316<\/h2>

\u6975\u5ea7\u6a19<\/a><\/span>\u3067

$$ {(r, \\theta, \\phi) \\;} $$<\/div> \u3001\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>
<\/center>

\u307e\u305f\u306f\u3001\u5ea7\u6a19\u306e\u5909\u66f4\u3092\u4f7f\u7528\u3057\u3066\u79fb\u52d5\u8ddd\u96e2\u3092\u8868\u793a\u3057\u307e\u3059\u3002

$$ {\\chi \\;} $$<\/div> :<\/p>
<\/center>

\u307e\u305f\u306f<\/p>