Kindly solve the cosmology problem 16.6 and 16.7. The problem is under the concept of Inflation cosmology. We are lookin

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Kindly solve the cosmology problem 16.6 and 16.7.

Kindly Solve The Cosmology Problem 16 6 And 16 7 The Problem Is Under The Concept Of Inflation Cosmology We Are Lookin 1 (177.44 KiB) Viewed 42 times

The problem is under the concept of Inflation cosmology. We are looking to the rate of change of the hubble parameter is proportional to the rate of the square of the cosmological scalar field.
In which we try to prove the Hamilton-Jacobi formalism using that.
ome://external-file 19 16.6 Show that, in general, of 592 R = R(H + H²). < Show that H > 0 only if p < -p, which is forbidden by the weak energy condition (see Exercise 8.8). Hence show that, for inflation to occur, one requires н <1, H2 and thus that the first slow-roll parameter must obey € < 1. 16.7 In the slow-roll approximation, show that Н -102 Assuming that º varies monotonically with t throughout the period of inflation, show that = -2H'() where H is now considered as a function of o, and hence that we may write the cosmological field equation as [H'(0)]? - H²(0=-V(o). This is known as the Hamilton-Jacobi formalism for inflation.