16.13 For the line element ds² = (1+20) di² - (1−20) R²(1)(dx² +dy² +dz²), show that, to first order in , the perturbed

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16 13 For The Line Element Ds 1 20 Di 1 20 R 1 Dx Dy Dz Show That To First Order In The Perturbed 1 (94.2 KiB) Viewed 15 times

16.13 For the line element ds² = (1+20) di² - (1−20) R²(1)(dx² +dy² +dz²), show that, to first order in , the perturbed parts of the connection coefficients take the form 81μ = d. Ope ST-R²(+4HD), ii = 1 00 R20D, SI -a. ipe where no sum over repeated i indices is implied and and the remaining perturbed coefficients either follow from symmetry or are zero. Hence show that the perturbed part of the Einstein tensor is given by 8G = -28, (+HD), SG = -2(7²0-3H-3H²D), SG = 2[+4H+ (2H+ 3H²)Þ],| where again no sum over repeated i indices is implied and the remaining entries either follow from symmetry or are zero. containing a growing -field increases by a factor ~ 10 after every time interval At = H-¹. Note: This is the mechanism underlying stochastic inflation.