In: Physics
Using these data, calculate the following quantities. Express your answers in SI units (unless the quantity is dimensionless) and to an appropriate number of significant figures.
Quantity | Value* |
---|---|
Hubble parameter at current time | 72 km s–1 Mpc–1 |
Curvature parameter | 0 |
Density parameter of matter at current time | 0.32 |
Density parameter of cosmological constant at current time | 0.68 |
* Note that the uncertainties associated with these
measurements are not given.
given :
Hubble parameter (H0 ) = 72 km s–1 Mpc–1 = 72 x 103/ 3.09 x1016 x 106 s–1 = 2.33 x 10-18 s–1
curvature parameter (k) = 0
density parameter of matter at current time =
0.32
Density parameter of cosmological constant at current time
= 0.68
gravitational constant = 6.67408 × 10-11 m3 kg-1 s-2
a) the critical density is given by c = 3
H02 / 8
G = 3 * ( 2.33 x
10-18) 2 / (8
x 6.67408 ×
10-11)= 9.7104 x 10-27
kg/m3
b) density of matter at current time =
=
/
c
=
c x
=
9.7104 x 10-27 x 0.32 = 3.1073
x 10-27 kg/m3
c) energy density of matter at current time (Um) =
c2 =
(3.1073 x 10-27 ) x (3 x
108)2 = 2.7966 x 10-10
J/m3
d) energy density (uΛ) due to the cosmological constant
=
uΛ /
c
therefore, uΛ =
x
c
=0.68 x 9.7104 x 10-27 =
6.6031 x 10-27 J/m3