Higher (second) order gauge invariant perturbation theory - RESCEU

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Perturbations of the Klein-Gordon equation • Klein-Gordon equation ( ) • Perturbative expansion of the Klein-Gordon equation : • We can show that each order perturbation of this Klein-Gordon equation is decomposed into the gauge-invariant and gauge-variant parts as : gauge invariant part : gauge variant part 12
IV. Einstein eqs. and Klein-Gordon eq. We impose the Einstein equation of each order, Then, the Einstein equation of each order is automatically given in terms of gauge invariant variables : linear order : second order : Further, each order perturbation of the Klein-Gordon equation is also automatically given in the gauge invariant form : • Background : • Linear order : • Second order : We do not have to care about gauge degree of freedom at least in the level where we concentrate only on the equations. 13 .
Page 1 and 2: Second-order gauge-invariant cosmol
Page 3 and 4: The first order approximation of ou
Page 5 and 6: In this poster, ... • I will give
Page 7 and 8: Gauge transformation rules of each
Page 9 and 10: Second order : Since the above assu
Page 11: Perturbations of Einstein tensor an
Page 15 and 16: Second order Klein-Gordon equation
Page 17 and 18: VI. Summary Based on the general fr

Higher (second) order gauge invariant perturbation theory - RESCEU

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