CQW is an educational resource for theoretical physics and astrophysics, field theory, relativity and cosmology. we post a new question every wednesday for students to get and for teachers to stay in shape.

Wednesday, January 6, 2016

redshift drift

welcome back to CQW in 2016 with a question about redshifting:

can you construct a cosmological model in which the redshift of distant objects stays constant? would that mean that the last-scattering surface of the CMB has a constant distance?

The Friedmann-Lemaitre model with Omega=0, lambda=0 has no redshift drift. This is sometimes known as the Milne model, since this Friedmann-Lemaitre model is dual to Milne's model. This Friedmann-Lemaitre model, though, is empty, so strictly speaking there is no redshift since there are no objects. Thinking of it as a limit and looking at the redshift of a test particle, there is no redshift drift. In this model, H(z) = H_0(1+z). There is no acceleration, no deceleration, so the rate of expansion is constant. H is just the rate of expansion divided by the scale factor, which leads to the equation above.

One can calculate the distance by the standard formula and finds that it is not constant in time. However, there is an easier way to see this: at the time of the big bang, the distance between any two objects is zero (even though the universe has infinite spatial extent, even at the time of the big bang), or at least arbitrarily small. After the big bang, this is obviously not the case, so the distance does change as a function of time.

The Friedmann-Lemaitre model with Omega=0, lambda=0 has no redshift drift. This is sometimes known as the Milne model, since this Friedmann-Lemaitre model is dual to Milne's model. This Friedmann-Lemaitre model, though, is empty, so strictly speaking there is no redshift since there are no objects. Thinking of it as a limit and looking at the redshift of a test particle, there is no redshift drift. In this model, H(z) = H_0(1+z). There is no acceleration, no deceleration, so the rate of expansion is constant. H is just the rate of expansion divided by the scale factor, which leads to the equation above.

ReplyDeleteOne can calculate the distance by the standard formula and finds that it is not constant in time. However, there is an easier way to see this: at the time of the big bang, the distance between any two objects is zero (even though the universe has infinite spatial extent, even at the time of the big bang), or at least arbitrarily small. After the big bang, this is obviously not the case, so the distance does change as a function of time.

Yes. No.

ReplyDelete