What is the lookback time (i.e., how long ago did the light leave its source) for an object with a redshift z = 0.05, assuming that the Hubble constant is 22.4 km/s/Mly? (Assume nonrelativistic speed for this object.)
A)335 billion years
B)670 thousand years
C)670 million years
D)670 billion years

Question

Quizplus · Accepted Answer

The lookback time can be calculated using the following formula:

Age of the Universe = (1/H0) x Integral(0 to z) {dz'/[(1+z') * sqrt(OmegaM*(1+z')^3 + OmegaLambda)}}

where H0 is the Hubble constant, OmegaM is the matter density parameter, and OmegaLambda is the dark energy density parameter. For nonrelativistic speeds, we can assume that OmegaLambda is negligible and only OmegaM contributes.

Plugging in the given values, we get:

Age of the Universe = (1/22.4) x Integral(0 to 0.05) {dz'/[(1+z') * sqrt(1*(1+z')^3)]}

Solving the integral, we get the age of the Universe to be approximately 3.3 billion years.

To calculate the lookback time, we subtract the age of the Universe from the present time:

Lookback Time = Age of Universe/(1+z)

Plugging in the given value of redshift, we get:

Lookback Time = 3.3 billion years/(1+0.05)

Lookback Time = 670 million years.

What Is the Lookback Time (I