de Sitter space and Holography
de Sitter space and Holography
de Sitter space and Holography
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Planer (Inflationary) coordinates: t, x i , i = 1, · · · ,d − 1Consi<strong>de</strong>r the constraint <strong>and</strong> <strong>de</strong>compose into two parts(−X0 2 + Xd) 2 + (X1 2 + · · · + Xd−1) 2 = l 2One may also consi<strong>de</strong>r a situation−X0 2 + Xd 2 = l 2 − x 2 e −2t/lX1 2 + · · · + Xd−1 2 = x 2 e −2t/l (x 2 = x i x i )which may solve as followsX 0X 0X i= l sinh t l − x22 e−t/l= l cosh t l − x22 e−t/l= x i e −t/lfor −∞ < x i < ∞ <strong>and</strong> −∞ < t < ∞.13
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