Calculating the Maximum total neutrino mass by using cosmological boun

In summary, the conversation discusses the derivation of the value for the total neutrino mass density, with the source article being referenced. The individual is struggling to understand the factor of 3 in the equation and eventually realizes their mistake in not considering the number density and average mass properly. It is also mentioned that the individual may not have a strong enough foundation in physics to fully comprehend the topic being discussed.
  • #1
Arman777
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In an article its written,

$$\Omega_{\nu} = \frac{\rho_{\nu}}{\rho_{crit}}=\frac{\sum m_{i,\nu}n_{i,\nu}}{\rho_{crit}} = \frac{\sum m_{\nu}}{93.14h^2eV}$$

Now I am trying to derive this for myself but I could not. Can someone help me ?

So the values are,

##\rho_{crit} = 1.053 75 \times 10^{-5}h^2 GeV/c^2~~cm^{-3}##

Total neutrino average number density today : ##n_{\nu} = 339.5~cm^{-3}##

I tried to write it like,

$$\frac{n_{\nu}\sum m_{\nu}}{\rho_{crit}} = \frac{\sum m_{\nu}}{93.14h^2eV}$$

$$\frac{n_{\nu}}{\rho_{cric}} = \frac{339.5cm^{-3}}{1.05375 \times 10^{-5}h^2 GeV/c^2~~cm^{-3}} = \frac{1}{3.103h^2 \times 10^{-8} GeV} = \frac{1}{31.0382916 h^2eV}$$

Which I am missing additional ##1/3##.

I guess its a simple question but I couldn't see the answer.
 
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  • #2
Arman777 said:
In an article its written

By now you should know this is not an acceptable PF reference. Point us to where you are having trouble and don't make us guess!

Arman777 said:
31.0382916

Is innumerate nonsense. Please use proper rounding.

I strongly suspect, given the factor of 3, it's a difference between one neutrino flavor and all neutrino flavors, but since you didn't say what your sources are I can't say for sure.
 
  • #3
Vanadium 50 said:
By now you should know this is not an acceptable PF reference. Point us to where you are having trouble and don't make us guess!
Is innumerate nonsense. Please use proper rounding.

I strongly suspect, given the factor of 3, it's a difference between one neutrino flavor and all neutrino flavors, but since you didn't say what your sources are I can't say for sure.
Yes sorry
https://www.google.com/url?sa=t&sou...Vaw0oNgNCVyC98o9jzCu867SY&cshid=1577529872455

I am thinking kind of the same buts its strange.. Umm equation 25.2
 
  • #4
Since [itex]\sum m_\nu = m_1 +m_2 + m_3[/itex] (bottom of page 3), why do you want [itex]n_\nu \sum m_\nu[/itex] ?
 
  • #5
Vanadium 50 said:
Since [itex]\sum m_\nu = m_1 +m_2 + m_3[/itex] (bottom of page 3), why do you want [itex]n_\nu \sum m_\nu[/itex] ?
I thought I can pull out the number density from the sum and obtain the similar format w.r.t to the paper.
 
  • #6
Getting any information out of you is a slow and painful process. If you want people to find your mistake, you need to clearly explain what you are doing, and not let it slowly ooze out.

I also think you are in way over your head trying to study cosmology without having the prerequisites down cold. That's why you need to start a new thread every 3-4 days. Nobody is benefiting from this - you don't really learn cosmology, you just think you do, and people who are trying to help just get cross. You have to start at the beginning, not the middle.

If n is a number density, n * the average mass is a mass density. True or false?
If there are three species of neutrinos, m1 + m2 + m3 is:
A. The average mass
B. Three times the average mass.
C. One third the average mass.
D. None of the above.
 
  • #7
It's B... I understand it now. I should try to read things more carefully.
Vanadium 50 said:
I also think you are in way over your head trying to study cosmology without having the prerequisites down cold.
you are right yes, but I cannot re-take physics courses. I am trying my best to learn.
 

FAQ: Calculating the Maximum total neutrino mass by using cosmological boun

1. What is the significance of calculating the maximum total neutrino mass using cosmological bounds?

The maximum total neutrino mass is an important parameter in cosmology as it can provide insights into the composition and evolution of the universe. Neutrinos are one of the fundamental particles in the standard model of particle physics and their mass has been a topic of interest for many years. By calculating the maximum total neutrino mass using cosmological bounds, we can better understand the role of neutrinos in the structure and dynamics of the universe.

2. How is the maximum total neutrino mass calculated using cosmological bounds?

The maximum total neutrino mass is typically calculated by combining cosmological observations with theoretical models and simulations. This involves studying the effects of neutrino mass on the large-scale structure of the universe, such as the distribution of galaxies and the cosmic microwave background, and comparing it to observational data. The maximum total neutrino mass can then be constrained by setting upper limits on the amount of mass that can be contributed by neutrinos.

3. What are the current constraints on the maximum total neutrino mass from cosmological bounds?

The current constraints on the maximum total neutrino mass vary depending on the specific cosmological model and observational data used. However, recent studies have found that the maximum total neutrino mass is likely to be less than 0.12 eV, with some models placing even tighter constraints. These constraints are expected to improve with future observations and advancements in theoretical models.

4. How does the maximum total neutrino mass affect the evolution of the universe?

The maximum total neutrino mass can have significant implications for the evolution of the universe. Neutrinos are known to have a small but non-zero mass, and this mass can impact the growth of large-scale structures in the universe. In particular, the presence of massive neutrinos can suppress the growth of structures and alter the expansion rate of the universe. Therefore, understanding the maximum total neutrino mass is crucial for accurately modeling the evolution of our universe.

5. What are the potential implications of a higher maximum total neutrino mass?

If the maximum total neutrino mass is found to be higher than current constraints, it could have significant implications for our understanding of the universe. For example, it could challenge our current models of structure formation and require new theories to explain the observed data. It could also have implications for other areas of physics, such as particle physics and the properties of dark matter. Further research and observations are needed to fully understand the potential implications of a higher maximum total neutrino mass.

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