When Did the Universe Start Accelerating?

June_cosmo
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Homework Statement


Assume the cosmological model with H0=72,Omega_M=1-Omega_lamda=0.3,(so dark energy with w = − 1) and a flat universe.)
a) Find the redshift z at which the universe starts accelerating (that is, when it transitions from decelerating to accelerating).
b) How long ago did this happen?

Homework Equations

The Attempt at a Solution


I don't quite understand the accelerating here. Does it mean that the expanding rate begins to accelerate? How should I start this problem?
 
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Accelerating expansion means that the second derivative of the scale factor ##a(t)## is positive.
 
Orodruin said:
Accelerating expansion means that the second derivative of the scale factor ##a(t)## is positive.
Orodruin said:
Accelerating expansion means that the second derivative of the scale factor ##a(t)## is positive.
I see. Should I use the deceleration formula?
 
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The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
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