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unscientific
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Homework Statement
[/B]
(a) Find the value of A and ##\Omega(\eta)## and plot them.
(b) Find ##a_{max}##, lifetime of universe and deceleration parameter ##q_0##.
Homework Equations
Unsolved problems: Finding lifetime of universe.
The Attempt at a Solution
Part(a)[/B]
FRW equation is given by
[tex]\left( \frac{\dot a}{a}\right)^2 = H_0^2 \Omega_{m,0} a^{-3} - \frac{kc^2}{a^2} [/tex]
Subsituting and using ##dt = a d\eta##, I find that ##A = \frac{H_0^2}{c^2}\Omega_{m,0}##.
Using ##\\Omega_m = \Omega_{m,0}a^{-3}##, I find that ##\Omega_m = \frac{kc^2}{H_0^2 sin^2(\frac{\sqrt{k} c \eta}{2})}##.
Part(b)
Maximum value of normalized scale factor is
[tex]a_{max} = \frac{A}{k} = \frac{H_0^2}{kc^2}\Omega_{m,0}[/tex]
Deceleration parameter is given by
[tex]q_0 = -\frac{\ddot a_0 a_0}{\dot a_0^2}[/tex]
This can be found by using ##\sqrt {k} c \eta = sin (\sqrt {k} c \eta)##.
How do I find the lifetime of the universe? Is it simply ## \int_0^\infty t d\eta##? If I can solve for the lifetime, I can compare it to its current age and see if that is feasible.