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Unformatted text preview: COSMOLOGY Problem Set 4 April 19, 2010 Problem 1 : k-Matter Assume that the Universe is flat ( k = 0) and that the energy density is dominated by a field ( X ) whose equation of state is: w X =- 1 / 3. a) For this model find ρ X as a function of the scale factor (or, of x ≡ a/a ) and also as a function of the redshift.  b) For this model find x versus t in terms of H and/or t .  c) For this model find the present age ( t ) in terms of the Hubble age H- 1 . Also, find the deceleration parameter q for this model.  d) For this model find the lookback time (Δ t ≡ t- t e ), in units of the Hubble time, versus redshift.  e) For this model find the distance modulus ( m- M ) as a function of redshift and evaluate it for z = 0 . 04 and for z = 0 . 4. You may assume that H = 70 km/s/Mpc.  Problem 2 : Dark Energy Assume that the Universe (near the present epoch) consists of two components, “or- dinary” (non-relativistic) matter ( w M = 0) and “dark energy” ( X ) with an equation...
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