\u5225\u30da\u30fc\u30b8<\/a>\u3067\u793a\u3057\u305f\u3088\u3046\u306b\uff0c<\/p>\n$\\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408<\/h4>\n$\\Omega_{\\Lambda} = 0, \\Omega_{\\rm m} > 1$ \u3059\u306a\u308f\u3061 $k > 0$ \u306e\u5834\u5408<\/h5>\n
\u30b9\u30b1\u30fc\u30eb\u56e0\u5b50 $a(t)$ \u306f\u5171\u5f62\u6642\u9593 $\\eta$ \u3092\u5a92\u4ecb\u5909\u6570\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n
\\begin{eqnarray}
\n\\frac{a}{a_0}
\n&=& \\frac{\\Omega_{\\rm m}}{2 (\\Omega_{\\rm m} -1)}
\n\\left(1 -\\cos\\left(\\sqrt{k} \\eta\\right)\\right)
\n\\end{eqnarray}<\/p>\n
\\begin{eqnarray}
\nH_0 t &=& \\frac{\\Omega_{\\rm m}}{2 (\\Omega_{\\rm m} -1)^{\\frac{3}{2}} }
\n\\left(\\sqrt{k} \\eta -\\sin\\left(\\sqrt{k} \\eta\\right)\\right)
\n\\end{eqnarray}<\/p>\n
$\\Omega_{\\Lambda} = 0, \\Omega_{\\rm m} < 1$ \u3059\u306a\u308f\u3061 $k < 0$ \u306e\u5834\u5408<\/h5>\n
\\begin{eqnarray}
\n\\frac{a}{a_0}
\n&=&\\frac{\\Omega_{\\rm m}}{2 (1-\\Omega_{\\rm m} )}
\n\\left(\\cosh\\left(\\sqrt{|k|} \\eta\\right) -1\\right)
\n\\end{eqnarray}<\/p>\n
\\begin{eqnarray}
\nH_0 t &=& \\frac{\\Omega_{\\rm m}}{2 (1-\\Omega_{\\rm m})^{\\frac{3}{2}} }
\n\\left(\\sinh\\left(\\sqrt{|k|} \\eta\\right) -\\sqrt{|k|} \\eta\\right)
\n\\end{eqnarray}<\/p>\n
$k=0$ \u306e\u5834\u5408<\/h4>\n$k = 0, \\ 1<\\Omega_{\\rm m} $ \u3064\u307e\u308a $\\Omega_{\\Lambda} < 0$\u306e\u5834\u5408<\/h5>\n
\\begin{eqnarray}
\n\\frac{a}{a_0}
\n&=& \\left\\{\\sqrt{\\frac{\\Omega_{\\rm m}}{\\Omega_{\\rm m}-1}}
\n\\sin\\left(\\frac{3\\sqrt{\\Omega_{\\rm m}-1}}{2} H_0 t\\right)\\right\\}^{\\frac{2}{3}}
\n\\end{eqnarray}<\/p>\n
$k = 0, \\ 0<\\Omega_{\\rm m} < 1$ \u3064\u307e\u308a $\\Omega_{\\Lambda} > 0$ \u306e\u5834\u5408<\/h5>\n
\\begin{eqnarray}
\n\\frac{a}{a_0} &=& \\left\\{\\sqrt{\\frac{\\Omega_{\\rm m}}{1-\\Omega_{\\rm m}}}
\n\\sinh\\left(\\frac{3\\sqrt{1-\\Omega_{\\rm m}}}{2} H_0 t\\right)\\right\\}^{\\frac{2}{3}}
\n\\end{eqnarray}<\/p>\n
<\/p>\n
$H_0 t$ \u3092\u30b9\u30b1\u30fc\u30eb\u56e0\u5b50\u306e\u95a2\u6570\u3068\u3057\u3066\u8868\u3059<\/h3>\n$\\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408<\/h4>\n$\\Omega_{\\Lambda} = 0, \\Omega_{\\rm m} > 1$ \u3059\u306a\u308f\u3061 $k > 0$ \u306e\u5834\u5408<\/h5>\n
\\begin{eqnarray}
\n\\frac{a}{a_0}
\n&=& \\frac{\\Omega_{\\rm m}}{2 (\\Omega_{\\rm m} -1)}
\n\\left(1 -\\cos\\left(\\sqrt{k} \\eta\\right)\\right)
\n\\end{eqnarray}<\/p>\n
\u3088\u308a<\/p>\n
$$\\cos\\left(\\sqrt{k} \\eta\\right) = 1 -\\frac{2 (\\Omega_{\\rm m} -1)}{\\Omega_{\\rm m}}\\frac{a}{a_0}$$
\n$$\\sqrt{k} \\eta = \\cos^{-1} \\left(1 -\\frac{2 (\\Omega_{\\rm m} -1)}{\\Omega_{\\rm m}}\\frac{a}{a_0} \\right)$$<\/p>\n
\\begin{eqnarray}
\n\\therefore\\ \\ H_0 t &=& \\frac{\\Omega_{\\rm m}}{2 (\\Omega_{\\rm m} -1)^{\\frac{3}{2}} }
\n\\left(\\sqrt{k} \\eta -\\sin\\left(\\sqrt{k} \\eta\\right) \\right) \\\\
\n&=& \\frac{\\Omega_{\\rm m}}{2 (\\Omega_{\\rm m} -1)^{\\frac{3}{2}} }
\n\\left(\\cos^{-1} \\left(1 -\\frac{2 (\\Omega_{\\rm m} -1)}{\\Omega_{\\rm m}} \\frac{a}{a_0} \\right)
\n-\\sqrt{1 -\\left(1 -\\frac{2 (\\Omega_{\\rm m} -1)}{\\Omega_{\\rm m}} \\frac{a}{a_0} \\right)^2} \\right)
\n\\end{eqnarray}<\/p>\n
$a = a_0$ \u3068\u306a\u308b\u5b87\u5b99\u5e74\u9f62 $t_0$ \u306f<\/p>\n
\\begin{eqnarray}
\n\\therefore\\ \\ H_0 t_0
\n&=& \\frac{\\Omega_{\\rm m}}{2 (\\Omega_{\\rm m} -1)^{\\frac{3}{2}} }
\n\\left(\\cos^{-1} \\left(1 -\\frac{2 (\\Omega_{\\rm m} -1)}{\\Omega_{\\rm m}}\u00a0 \\right)
\n-\\sqrt{1 -\\left(1 -\\frac{2 (\\Omega_{\\rm m} -1)}{\\Omega_{\\rm m}}\\right)^2} \\right) \\\\
\n&=& \\frac{\\Omega_{\\rm m}}{2 (\\Omega_{\\rm m} -1)^{\\frac{3}{2}} }
\n\\cos^{-1} \\left(\\frac{2-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}\\right) -\\frac{1}{\\Omega_{\\rm m} -1}
\n\\end{eqnarray}<\/p>\n
\u3057\u305f\u304c\u3063\u3066\uff0c$(1)$ \u5f0f\u3068\u4e00\u81f4\u3059\u308b\u305f\u3081\u306b\u306f<\/p>\n
$$2 \\tan^{-1} \\sqrt{\\Omega_{\\rm m} -1} = \\cos^{-1} \\left(\\frac{2-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}\\right) $$
\n\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b\u304c\uff0c\u3053\u308c\u306f\u4e00\u822c\u306b\u4ee5\u4e0b\u306e\u516c\u5f0f<\/p>\n
$$2 \\tan^{-1} x = \\cos^{-1}\\frac{1 -x^2}{1 + x^2}$$<\/p>\n
\u3092\u8a3c\u660e\u3059\u308c\u3070\u3088\u3044\u3002<\/p>\n
\\begin{eqnarray}
\n\\cos (2 \\theta) &=& \\cos^2 \\theta -\\sin^2 \\theta \\\\
\n&=& \\cos^2 \\theta \\left( 1 -\\tan^2 \\theta\\right)\\\\
\n&=& \\frac{1 -\\tan^2 \\theta}{1 + \\tan^2 \\theta}\\\\
\n\\therefore\\ \\ 2 \\theta & = & \\cos^{-1}\\frac{1 -\\tan^2 \\theta}{1 + \\tan^2 \\theta}
\n\\end{eqnarray}<\/p>\n
\u3042\u3068\u306f\uff0c$\\theta = \\tan^{-1} x$\u00a0 \u3068\u304a\u3051\u3070
\n$$2 \\tan^{-1} x = \\cos^{-1}\\frac{1 -x^2}{1 + x^2}$$
\n\u304c\u793a\u3055\u308c\u305f\u3002<\/p>\n
\u3053\u3053\u3067\uff0c$x = \\sqrt{\\Omega_{\\rm m} -1}$ \u3068\u304a\u304f\u3068\uff0c<\/p>\n
$$\\frac{1 -x^2}{1 + x^2} = \\frac{1 -(\\Omega_{\\rm m} -1)}{1 +(\\Omega_{\\rm m} -1)} = \\frac{2-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}$$<\/p>\n
$$\\therefore\\ \\ \\cos^{-1} \\left(\\frac{2-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}\\right) = 2 \\tan^{-1} \\sqrt{\\Omega_{\\rm m} -1}$$<\/p>\n
\u3068\u306a\u308a\uff0c\u5b87\u5b99\u5e74\u9f62\u306e\u8868\u5f0f\u304c $(1)$ \u5f0f\u3068\u66f8\u3044\u3066\u3082\u3088\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n
$\\Omega_{\\Lambda} = 0, \\Omega_{\\rm m} < 1$ \u3059\u306a\u308f\u3061 $k < 0$ \u306e\u5834\u5408<\/h5>\n
\\begin{eqnarray}
\n\\frac{a}{a_0}
\n&=&\\frac{\\Omega_{\\rm m}}{2 (1-\\Omega_{\\rm m} )}
\n\\left(\\cosh\\left(\\sqrt{|k|} \\eta\\right) -1\\right)
\n\\end{eqnarray}<\/p>\n
\u3088\u308a<\/p>\n
$$\\cosh\\left(\\sqrt{|k|} \\eta\\right) = 1 + \\frac{2 (1-\\Omega_{\\rm m})}{\\Omega_{\\rm m}}\\frac{a}{a_0} $$
\n$$\\sqrt{|k|} \\eta= \\cosh^{-1} \\left(1 + \\frac{2 (1-\\Omega_{\\rm m})}{\\Omega_{\\rm m}}\\frac{a}{a_0} \\right)$$<\/p>\n
\\begin{eqnarray}
\n\\therefore\\ \\ H_0 t &=& \\frac{\\Omega_{\\rm m}}{2 (1-\\Omega_{\\rm m})^{\\frac{3}{2}} }
\n\\left(\\sinh\\left(\\sqrt{|k|} \\eta\\right) -\\sqrt{|k|} \\eta\\right) \\\\
\n&=& \\frac{\\Omega_{\\rm m}}{2 (1-\\Omega_{\\rm m})^{\\frac{3}{2}} }
\n\\left(\\sqrt{\\left(1 + \\frac{2 (1-\\Omega_{\\rm m})}{\\Omega_{\\rm m}}\\frac{a}{a_0} \\right)^2 -1}
\n-\\cosh^{-1} \\left(1 + \\frac{2 (1-\\Omega_{\\rm m})}{\\Omega_{\\rm m}}\\frac{a}{a_0}\\right) \\right)
\n\\end{eqnarray}<\/p>\n
$a = a_0$ \u3068\u306a\u308b\u5b87\u5b99\u5e74\u9f62 $t_0$ \u306f<\/p>\n
\\begin{eqnarray}
\nH_0 t_0
\n&=& \\frac{\\Omega_{\\rm m}}{2 (1-\\Omega_{\\rm m})^{\\frac{3}{2}} }
\n\\left(\\sqrt{\\left(1 + \\frac{2 (1-\\Omega_{\\rm m})}{\\Omega_{\\rm m}}\\right)^2 -1}
\n-\\cosh^{-1} \\left(1 + \\frac{2 (1-\\Omega_{\\rm m})}{\\Omega_{\\rm m}}\\right) \\right)\\\\
\n&=& \\frac{1}{1 -\\Omega_{\\rm m} } -\\frac{\\Omega_{\\rm m}}{2 (1-\\Omega_{\\rm m} )^{\\frac{3}{2}} }
\n\\cosh^{-1} \\left(\\frac{2-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}\\right)
\n\\end{eqnarray}<\/p>\n
\u3057\u305f\u304c\u3063\u3066\uff0c$(2)$ \u5f0f\u3068\u4e00\u81f4\u3059\u308b\u305f\u3081\u306b\u306f<\/p>\n
$$2 \\tanh^{-1} \\sqrt{1-\\Omega_{\\rm m} } = \\cosh^{-1} \\left(\\frac{2-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}\\right)$$
\n\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b\u304c\uff0c\u3053\u308c\u306f\u4e00\u822c\u306b\u4ee5\u4e0b\u306e\u516c\u5f0f<\/p>\n
$$2 \\tanh^{-1} x = \\cosh^{-1}\\frac{1 + x^2}{1 -x^2}$$<\/p>\n
\u3092\u8a3c\u660e\u3059\u308c\u3070\u3088\u3044\u3002\u76f4\u63a5\u8a08\u7b97\u3057\u3066\u3082\u5bb9\u6613\u3060\u304c\uff0c\u3053\u3053\u3067\u306f\u4e0a\u3067\u793a\u3057\u305f<\/p>\n
\\begin{eqnarray}
\n\\cos (2 \\theta)
\n&=& \\frac{1 -\\tan^2 \\theta}{1 + \\tan^2 \\theta}
\n\\end{eqnarray}<\/p>\n
\u3067\uff0c$\\theta \\rightarrow i y$ \u3068\u7f6e\u304d\u63db\u3048\u3066 $\\cos (2 i y) = \\cosh 2 y, \\tan (i y) = i \\tanh y$ \u3092\u4f7f\u3046\u3068<\/p>\n
\\begin{eqnarray}
\n\\cosh (2 y)
\n&=& \\frac{1 + \\tanh^2 y}{1 -\\tanh^2 y} \\\\
\n\\therefore\\ \\ 2 y &=& \\cosh^{-1} \\frac{1 + \\tanh^2 y}{1 -\\tanh^2 y}
\n\\end{eqnarray}<\/p>\n
\u3042\u3068\u306f $y = \\tanh^{-1} x$ \u3068\u304a\u3051\u3070$$2 \\tanh^{-1} x = \\cosh^{-1}\\frac{1 + x^2}{1 -x^2}$$<\/p>\n
\u304c\u793a\u3055\u308c\u305f\u3002\u3053\u3053\u3067 $x = \\sqrt{1-\\Omega_{\\rm m}}$ \u3068\u304a\u3051\u3070\uff0c<\/p>\n
$$\\frac{1 + x^2}{1 -x^2} = \\frac{1 + (1-\\Omega_{\\rm m})}{1 -(1-\\Omega_{\\rm m})} = \\frac{2 -\\Omega_{\\rm m}}{\\Omega_{\\rm m}}$$<\/p>\n
$$\\therefore\\ \\ \\cosh^{-1} \\left(\\frac{2-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}\\right) = 2 \\tanh^{-1} \\sqrt{1-\\Omega_{\\rm m} }$$<\/p>\n
\u3068\u306a\u308a\uff0c\u5b87\u5b99\u5e74\u9f62\u306e\u8868\u5f0f\u304c $(2)$ \u5f0f\u3068\u66f8\u3044\u3066\u3082\u3088\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n
<\/p>\n
$k=0$ \u306e\u5834\u5408<\/h4>\n$k = 0, \\ 1<\\Omega_{\\rm m} $ \u3064\u307e\u308a $\\Omega_{\\Lambda} < 0$\u306e\u5834\u5408<\/h5>\n
\\begin{eqnarray}
\n\\frac{a}{a_0}
\n&=& \\left\\{\\sqrt{\\frac{\\Omega_{\\rm m}}{\\Omega_{\\rm m}-1}}
\n\\sin\\left(\\frac{3\\sqrt{\\Omega_{\\rm m}-1}}{2} H_0 t\\right)\\right\\}^{\\frac{2}{3}}
\n\\end{eqnarray}<\/p>\n
\u3088\u308a<\/p>\n
$$H_0 t = \\frac{2}{3\\sqrt{\\Omega_{\\rm m}-1}} \\sin^{-1} \\left(\\sqrt{\\frac{\\Omega_{\\rm m}-1}{\\Omega_{\\rm m}}} \\left(\\frac{a}{a_0}\\right)^{\\frac{3}{2}}\\right)$$<\/p>\n
$a = a_0$ \u3068\u306a\u308b\u5b87\u5b99\u5e74\u9f62 $t_0$ \u306f<\/p>\n
$$H_0 t_0 = \\frac{2}{3\\sqrt{\\Omega_{\\rm m}-1}} \\sin^{-1} \\left(\\sqrt{\\frac{\\Omega_{\\rm m}-1}{\\Omega_{\\rm m}}}\\right)$$<\/p>\n
\u3057\u305f\u304c\u3063\u3066\uff0c$(3)$ \u5f0f\u3068\u4e00\u81f4\u3059\u308b\u305f\u3081\u306b\u306f<\/p>\n
$$ \\tan^{-1} \\sqrt{\\Omega_{\\rm m} -1} = \\sin^{-1} \\left(\\sqrt{\\frac{\\Omega_{\\rm m}-1}{\\Omega_{\\rm m}}}\\right)$$<\/p>\n
\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b\u304c\uff0c\u3053\u308c\u306f\u4e00\u822c\u306b\u4ee5\u4e0b\u306e\u516c\u5f0f<\/p>\n
$$\\tan^{-1} x = \\sin^{-1}\\frac{ x}{\\sqrt{1 + x^2}}$$<\/p>\n
\u3092\u8a3c\u660e\u3059\u308c\u3070\u3088\u3044\u3002<\/p>\n
\\begin{eqnarray}
\n\\sin\\theta &=& \\tan\\theta\\, \\cos\\theta = \\frac{\\tan\\theta}{\\sqrt{1 + \\tan^2\\theta}} \\\\
\n\\therefore\\ \\\u00a0 \\theta &=& \\sin^{-1} \\frac{\\tan\\theta}{\\sqrt{1 + \\tan^2\\theta}}
\n\\end{eqnarray}<\/p>\n
$\\theta = \\tan^{-1} x$\u00a0 \u3068\u304a\u3051\u3070<\/p>\n
\\begin{eqnarray}
\n\\tan^{-1} x &=& \\sin^{-1} \\frac{x}{\\sqrt{1 + x^2}}
\n\\end{eqnarray}<\/p>\n
\u304c\u793a\u3055\u308c\u305f\u3002\u3053\u3053\u3067 $x = \\sqrt{\\Omega_{\\rm m}-1}$ \u3068\u304a\u3051\u3070\uff0c<\/p>\n
$$\\frac{x}{\\sqrt{1 + x^2}} = \\frac{\\sqrt{\\Omega_{\\rm m}-1}}{\\sqrt{\\Omega_{\\rm m}}}$$\u3068\u306a\u308a\uff0c\u5b87\u5b99\u5e74\u9f62\u306e\u8868\u5f0f\u304c $(3)$ \u5f0f\u3068\u66f8\u3044\u3066\u3082\u3088\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n
$k = 0, \\ 0<\\Omega_{\\rm m} < 1$ \u3064\u307e\u308a $\\Omega_{\\Lambda} > 0$ \u306e\u5834\u5408<\/h5>\n
\\begin{eqnarray}
\n\\frac{a}{a_0} &=& \\left\\{\\sqrt{\\frac{\\Omega_{\\rm m}}{1-\\Omega_{\\rm m}}}
\n\\sinh\\left(\\frac{3\\sqrt{1-\\Omega_{\\rm m}}}{2} H_0 t\\right)\\right\\}^{\\frac{2}{3}}
\n\\end{eqnarray}<\/p>\n
\u3088\u308a
\n$$H_0 t = \\frac{2}{3\\sqrt{1-\\Omega_{\\rm m}}}
\n\\sinh^{-1} \\left( \\sqrt{\\frac{1-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}} \\left(\\frac{a}{a_0}\\right)^{\\frac{3}{2}}\\right)$$<\/p>\n
$a = a_0$ \u3068\u306a\u308b\u5b87\u5b99\u5e74\u9f62 $t_0$ \u306f<\/p>\n
$$H_0 t_0 = \\frac{2}{3\\sqrt{1-\\Omega_{\\rm m}}}
\n\\sinh^{-1} \\left( \\sqrt{\\frac{1-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}} \\right)$$<\/p>\n
\u3057\u305f\u304c\u3063\u3066\uff0c$(4)$ \u5f0f\u3068\u4e00\u81f4\u3059\u308b\u305f\u3081\u306b\u306f<\/p>\n
$$ \\tanh^{-1} \\sqrt{1-\\Omega_{\\rm m} } = \\sinh^{-1} \\left(\\sqrt{\\frac{1-\\Omega_{\\rm m}}{\\Omega_{\\rm m}}}\\right)$$<\/p>\n
\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b\u304c\uff0c\u3053\u308c\u306f\u4e00\u822c\u306b\u4ee5\u4e0b\u306e\u516c\u5f0f<\/p>\n
$$\\tanh^{-1} x = \\sinh^{-1}\\frac{ x}{\\sqrt{1 -x^2}}$$<\/p>\n
\u3092\u8a3c\u660e\u3059\u308c\u3070\u3088\u3044\u3002\u76f4\u63a5\u8a08\u7b97\u3057\u3066\u3082\u3088\u3044\u304c\uff0c$\\theta \\rightarrow i y$\u00a0 \u3068\u7f6e\u304d\u63db\u3048\u308b\u3068<\/p>\n
\\begin{eqnarray}
\n\\sin\\theta &=&\u00a0 \\frac{\\tan\\theta}{\\sqrt{1 + \\tan^2\\theta}} \\\\
\n\\sin(i y) &=&\u00a0 \\frac{\\tan(i y)}{\\sqrt{1 + \\tan^2(i y)}} \\\\
\ni \\sinh(y) &=&\u00a0 \\frac{i \\tanh(y)}{\\sqrt{1 -\\tanh^2(y)}} \\\\
\n\\sinh(y) &=&\u00a0 \\frac{\\tanh(y)}{\\sqrt{1 -\\tanh^2(y)}} \\\\
\n\\therefore\\ \\ y &=& \\sinh^{-1} \\frac{\\tanh(y)}{\\sqrt{1 -\\tanh^2(y)}}
\n\\end{eqnarray}<\/p>\n
$y = \\tanh^{-1} x$\u00a0 \u3068\u304a\u3051\u3070$$\\tanh^{-1} x = \\sinh^{-1}\\frac{ x}{\\sqrt{1 -x^2}}$$<\/p>\n
\u304c\u793a\u3055\u308c\u305f\u3002\u3053\u3053\u3067 $x = \\sqrt{1-\\Omega_{\\rm m}}$ \u3068\u304a\u3051\u3070<\/p>\n
$$\\frac{ x}{\\sqrt{1 -x^2}} = \\frac{\\sqrt{1-\\Omega_{\\rm m}}}{\\sqrt{\\Omega_{\\rm m}}}$$\u3068\u306a\u308a\uff0c\u5b87\u5b99\u5e74\u9f62\u306e\u8868\u5f0f\u304c $(4)$ \u5f0f\u3068\u66f8\u3044\u3066\u3082\u3088\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":1483,"menu_order":15,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-1706","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\/1706","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=1706"}],"version-history":[{"count":29,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1706\/revisions"}],"predecessor-version":[{"id":1712,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1706\/revisions\/1712"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1483"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=1706"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}