Consequences of a fourth neutrino type

[szcsongor]

Homework Statement

If there was a fourth neutrino type it would have affected Universe's development the following way...

Relevant Equations

none

Hi,

I got this question on a recent astronomy course but can't really find the right answer (rough translation from Swedish):

If there was a fourth neutrino type it would have affected Universe's development the following way:
a. more photons and more He-4 generated
b. less photons and less He-4
c. more neutrons and more He-4
d. more protons and more He-4

My guess would be answer (a) but I'm not sure.

 

[mfb]

Relevant Equations
none

Are you sure you don't have equations describing the evolution of the early universe? How does its temperature change over time? How does that depend on neutrinos?

My guess would be answer (a) but I'm not sure.

Why do you guess (a)?

 

[szcsongor]

Hi,

Thanks for the quick reply. I was on holiday, so couldn't answer sooner.
I was thinking about this question but unfortunately I don't know how to start solving it. I guess there are some relations (equations?) to use here but I'm unable to see it :(

The temperature of the universe is decreasing constantly, but I don't see the relation with neutrinos.
My guess was a) because I was thinking that neutrinos are produced in the process of H-1 -> He-4 alongside with photons, so another type of neutrinos could be a consequence of more He-4 and photons produced. But it might be true only in stars... Or might be that I'm wrong completely :)

 

[mfb]

Think earlier. How did neutrinos influence the temperature evolution?
Electron neutrinos were important for the neutron to proton ratio, but a fourth generation neutrino shouldn't affect that directly as it doesn't couple to electrons.

If you prefer you can also look up how Planck measured the number of neutrino generations in the early universe. Their result was 3...

 

[szcsongor]

Thanks for trying to help.
I think I see now how I should proceed with this. I also found clues in the course material now when I read through it:

If we "put in" an other type of neutrino into the universe there should be less baryonic matter to comply with the principle of conservation of mass. But since neutrinos do not interact with matter (and also almost massless), the universe would have expanded faster. The consequence would have been more neutrons (higher neutron / proton ratio) because there would have been less time for the n -> p + e + v reaction. And more neutrons mean more He-4 generated. Therefore answer (c) seem to be the right one.
Am I right? :)

 

[mfb]

Sounds plausible.