Q2[13.0pt]: In class, we have shown that the luminosity distance can be expanded as the following...

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Q2[13.0pt]: In class, we have shown that the luminosity distance can be expanded as the following Taylor series when z. < < < 1 d CZ [1 1 + 1 - % -] +0(z) 2 In this exercise, we will compute the (z) corrections to the luminosity distance. (a) [1.0pt]: The deceleration and jerk parameters are defined as 1_d(a) | Hao di 1 d(a) and jo Hao dt Show that we can Taylor expand the scale factor to the third order in powers of (1-10) as a(t) 1+ 1+ Ho(t to) 90H - - ao 2 -(1-10). JOH -(1-10) 6 From now on, we will assume that a = 1. Q2[13.0pt]: In class, we have shown that the luminosity distance can be expanded as the following Taylor series when z. < < < 1 d CZ [1 1 + 1 - % -] +0(z) 2 In this exercise, we will compute the (z) corrections to the luminosity distance. (a) [1.0pt]: The deceleration and jerk parameters are defined as 1_d(a) | Hao di 1 d(a) and jo Hao dt Show that we can Taylor expand the scale factor to the third order in powers of (1-10) as a(t) 1+ 1+ Ho(t to) 90H - - ao 2 -(1-10). JOH -(1-10) 6 From now on, we will assume that a = 1.