Redshift for Proton-Antiproton Pair Creation in Early Universe

[ppyadof]

Homework Statement

The question:
Explain why pair creation is expected to occur in the early universe, and estimate the redshift at which proton-antiproton pairs are created.

Homework Equations

The Attempt at a Solution

My logic for the reason is that the process requires high energy gamma photons to create the proton-antiproton pair. As for the second part, I don't really have a clue, although this is my guess:

For the process to occur, u need a photon to have around $2m_p c^2$ of energy, so:
[tex] 2m_pc^2 = \frac{hc}{\lambda_e} [/itex]
where the mass is the rest mass of the proton and the lambda is the wavelength of the original photon which made the pair.

Since
$$1+Z = \frac{\delta \lambda}{\lambda_e}$$
$$Z = \frac{2 \delta \lambda m_p c}{h} - 1$$

But I don't have any values, so where am I suppose to go from here?

 

[Jhero]

Your reasoning for the first part is correct. In the early universe, there were high energy gamma photons present due to the high temperatures and densities. These high energy photons had enough energy to create pairs of particles like protons and antiprotons through pair creation.

As for the second part, your approach is on the right track. The equation you have used is the energy-momentum conservation equation for pair creation, and it can be rearranged to solve for the redshift Z. However, as you mentioned, you do not have any values to plug into the equation. In order to estimate the redshift at which proton-antiproton pairs are created, you would need to know the energy of the photons present in the early universe, which is dependent on the temperature and density at that time. Unfortunately, these values are not precisely known, so it is not possible to give a specific estimate for the redshift. However, it is generally accepted that pair creation would have occurred at a very high redshift, possibly as high as z~10^12 or even higher. This is because the early universe was extremely hot and dense, providing the necessary conditions for high energy photons to exist. So, while we cannot give a precise estimate, we can say that pair creation most likely occurred at a very high redshift in the early universe.