Suppose, as was once thought to be the case, that the universe today is flat and dominated by cold (pressure free) matter (a) Show that a t 2 3 and evaluate the age of the universe assuming the Hubble constant given in Sec 28 2 3 H 0 67 7 km s 1 Mpc 1 (b) Evaluate an expression for the angular diameter distance as a function of a and find its maximum value (c) Calculate the comoving volume within the universe back to very early times Data from Sec 28 2 3 Hubble constant Hubble constant 18 H 0 H(t 0 ) is the contemporary value of H and is one of the key parameters of observational cosmology It measures the age and size of the universe We now know that the universe is accelerating q 0 q(t 0 ) 0 and j 0 j (t 0 ) 0

Question: Suppose, as was once thought to be the case, that the universe today is flat and dominated by cold (pressure-free) matter. (a) Show that a

Suppose, as was once thought to be the case, that the universe today is flat and dominated by cold (pressure-free) matter.

(a) Show that a ∝ t ^2/3 and evaluate the age of the universe assuming the Hubble constant given in Sec. 28.2.3: H₀ = 67.7 km s⁻¹ Mpc⁻¹.

(b) Evaluate an expression for the angular diameter distance as a function of a and find its maximum value.

Data from Sec. 28.2.3. Hubble constant

Hubble constant¹⁸ H₀ ≡ H(t₀) is the contemporary value of H and is one of the key parameters of observational cosmology. It measures the age and size of the universe. We now know that the universe is accelerating q₀ ≡ q(t₀) < 0 and j₀ ≡ j (t₀) > 0.

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a To show that a t23 for a flat universe dominated by cold matter we start with the Friedmann equation for a flat universe H a2 8G3 where H is the Hubble parameter a is the scale factor of the univers... View full answer

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