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Unformatted text preview: COSMOLOGY Problem Set 4 April 19, 2010 Problem 1 : kMatter 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. [5] b) For this model find x versus t in terms of H and/or t . [5] 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. [5] d) For this model find the lookback time (Δ t ≡ t t e ), in units of the Hubble time, versus redshift. [5] 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. [10] Problem 2 : Dark Energy Assume that the Universe (near the present epoch) consists of two components, “or dinary” (nonrelativistic) matter ( w M = 0) and “dark energy” ( X ) with an equation...
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 Spring '10
 STEIGMAN
 Energy

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