Hot dark matter constrained by the CMB

[fhenryco]

Hello,

I often read that hot dark matter is constrained by structure formation issues. But I'm now wondering why it is not constrained by the CMB data itself because such hot dark matter should belong to radiation (with density evolving as 1/a^4 rather than 1/a^3) so for instance when we replace cold dark matter by hot dark matter we should also shift the redshift of matter(baryons+CDM: 1/a^3)--radiation(photons and HDM : 1/a^4) equatlity ... so shouldn't this disturb the expansion rate history H(z) and then many observables in the CMB but also at Big-Bang nucleosynthesis ?

thanks in advance

 

[kimbyd]

Hello,

I often read that hot dark matter is constrained by structure formation issues. But I'm now wondering why it is not constrained by the CMB data itself because such hot dark matter should belong to radiation (with density evolving as 1/a^4 rather than 1/a^3) so for instance when we replace cold dark matter by hot dark matter we should also shift the redshift of matter(baryons+CDM: 1/a^3)--radiation(photons and HDM : 1/a^4) equatlity ... so shouldn't this disturb the expansion rate history H(z) and then many observables in the CMB but also at Big-Bang nucleosynthesis ?

thanks in advance

Yes, basically. It was ruled out by the COBE observations, apparently:
http://w.astro.berkeley.edu/~mwhite/darkmatter/hdm.html

According to the above link, COBE was able to measure the large-scale inhomogeneities in the CMB. In order for us to have lots of galaxy clusters, those large-scale inhomogeneities would have had to have been huge for the hot dark matter case. They weren't very large, which ruled out the model.

If you're really interested in this, and know a bit about programming, you could possibly download a CMB code and mess around with the parameters to see what hot dark matter would look like in the power spectrum.

 

[fhenryco]

OK but this is again the same argument i have already seen about the formation of structures. what I'm wondering about is that if our universe had been dominated by hot dark matter up to now it would therefore have remained radiation dominated up to now (because hot dark matter density evolves as 1/a^4) . And then the scale factor history, age of the universe and so on ... would have been very different : the scale of sound horizon would have been at a different angle than ~ 1 degree.
I'm wondering because even now there are models with mixed cold and hot or warm dark matter which also should lead to a very different history of the scale factor evolution and therefore should be completely excluded by all geometrical tests (BAO or again the angle of first CMB peak ) or what did i miss? why do people still work on such models ? If those models were only making possible a better understanding of the growth of structure without changing everything in the expansion history of the universe then i would understand but according to my understanding they should change everything and then would be ruled out by many other observables ! or else what did i miss ?

 

[kimbyd]

OK but this is again the same argument i have already seen about the formation of structures. what I'm wondering about is that if our universe had been dominated by hot dark matter up to now it would therefore have remained radiation dominated up to now (because hot dark matter density evolves as 1/a^4) . And then the scale factor history, age of the universe and so on ... would have been very different : the scale of sound horizon would have been at a different angle than ~ 1 degree.
I'm wondering because even now there are models with mixed cold and hot or warm dark matter which also should lead to a very different history of the scale factor evolution and therefore should be completely excluded by all geometrical tests (BAO or again the angle of first CMB peak ) or what did i miss? why do people still work on such models ? If those models were only making possible a better understanding of the growth of structure without changing everything in the expansion history of the universe then i would understand but according to my understanding they should change everything and then would be ruled out by many other observables ! or else what did i miss ?

I think what you have to understand is that back when COBE was released, in the early 90's, cosmological data was incredibly limited. We didn't know much about the spatial curvature. The rate of expansion had huge error bars. We had little understanding of the overall matter density. There was no experimental data which pointed to dark energy.

I think you're absolutely right that hot dark matter would have resulted in massive differences in a lot of ways, but our cosmological data before COBE really was that limited. The scale of the sound horizon, for example, was not known at all before COBE.

It wasn't really until the late 90's, far after COBE, that things gelled.

 

[fhenryco]

OK thank you but then what about modern models with mixed cold and hot dark matter. even a small percentage of hot dark matter at z=10 is going to dominate the cold dark matter somewhere between z=10 and z=1100 (because it runs as 1/a^4 rather than 1/a^3) and then significantly shift the reshift of matter radiation equality to much lower z than in the standard LCDM model ... is that correct? can all the observable of cosmology support this scenario ? or else what did i miss?

 

[kimbyd]

OK thank you but then what about modern models with mixed cold and hot dark matter. even a small percentage of hot dark matter at z=10 is going to dominate the cold dark matter somewhere between z=10 and z=1100 (because it runs as 1/a^4 rather than 1/a^3) and then significantly shift the reshift of matter radiation equality to much lower z than in the standard LCDM model ... is that correct? can all the observable of cosmology support this scenario ? or else what did i miss?

I think a lot of things would be impacted by any significant fraction of hot dark matter.

I suspect that the strongest constraints on hot dark matter would come directly from the CMB data. If you're familiar with running software like that (it's not at all user-friendly, but doesn't require a huge amount of expertise either), you could probably run some tests yourself to see what the modern constraints are.

Of course, there would be other constraints from nearby measurements, but I suspect the CMB constraints will probably be the strongest ones (and the easiest ones to check yourself). Plus it's probably the easiest to do yourself.

What is your overall motivation for this question, by the way? What are you trying to accomplish?

 

[fhenryco]

What is your overall motivation for this question, by the way? What are you trying to accomplish?

In the model I'm working on the first Friedman equation (for a flat universe k=0) is modified with an additional term :

H²=8πGρ/3+K/a⁴

where K is an integration constant which could just be zero but i was wondering if such term could lead to interesting new predictions
as it behaves as a radiation term which would shift the matter-radiation equality.
At first i believed that this should be very constrained to be very small but then i remembered that there are still mixed cold and hot dark matter
models actively studied ... i don't know much about them but if hot dark matter is introduced to produce significant effects at relatively low redshift (upt to z=10)
then this hot dark matter as it is a radiation component evolving as 1/a^4 may become dominant at higher redshift and have a big effect on the redshift of matter-radiation equality. So may be such big effects would not be ruled out.

BTW my term being a pure integration term is purely homogeneous : it can't fluctuate and play this way a role in the formation of structures at the contrary to genuine HDM

well i would just need to find some good paper on the subject ...

 

[kimbyd]

In the model I'm working on the first Friedman equation (for a flat universe k=0) is modified with an additional term :

H²=8πGρ/3+K/a⁴

where K is an integration constant which could just be zero but i was wondering if such term could lead to interesting new predictions
as it behaves as a radiation term which would shift the matter-radiation equality.
At first i believed that this should be very constrained to be very small but then i remembered that there are still mixed cold and hot dark matter
models actively studied ... i don't know much about them but if hot dark matter is introduced to produce significant effects at relatively low redshift (upt to z=10)
then this hot dark matter as it is a radiation component evolving as 1/a^4 may become dominant at higher redshift and have a big effect on the redshift of matter-radiation equality. So may be such big effects would not be ruled out.

BTW my term being a pure integration term is purely homogeneous : it can't fluctuate and play this way a role in the formation of structures at the contrary to genuine HDM

well i would just need to find some good paper on the subject ...

Sounds reasonable. I definitely don't know what the constraints are off-hand. But I'd start with CMB data for sure. Here's a recent paper which looked into HDM with Planck and other data:
https://www.sciencedirect.com/science/article/pii/S0370269315008734

I don't think their parameterization is what you need for it to be directly useful, but it's a place to start at least.

Edit: Also make sure to check up on constraints from Big Bang Nucleosynthesis. If you can prove this $K/a^4$ term would have been small at that time, then you may be able to skip this check.