An interesting model is the curvaton model. 

K. Enqvist, D. G. Figueroa and R. N. Lerner, JCAP, 1301, 040 (2013) [arXiv:1211.5028]

Curvaton can cause primordial density fluctuations in CMBR. If it is a dark matter candidate it cannot decay, however, there are alternative mechanisms through which standard model particles are created. 

Dear Dr. Sanjeev Kumar Verma, 

Allow me to pay your attention at our (together with Elena Kadyshevich) PFO-CFO Theory of Solar System Formation, namely, at its cosmological portion. The publications are available at our pages of the ResearchGate site and some additional consideration is available in my answers to cosmological questions by Elena Kadyshevich at this site. There is no saying, isn't it time to remember about the fantasies of 100-years' prescription? How long does it take to understand that it is impossible to seek the thing that doesn't exist and existed never? 

An alternative approach to theories of dark matter is that it is an increase in the gravitational field. Einstein actually predicted this  by increase in gravity produced  needed for the extra bending of light, advance in the perihelion of Mercury etc.etc .

Einstein therefore can be translated into an increase in the gravitational field and in extremes this can increase by a factor of 6.25, at the black hole event horizon and the Cosmological event horizon. The exact ratio of ordinary matter to dark matter is 6.25 (see Link)

Article The formulation of Dynamic Newtonian advanced gravity, DNAg

Dear Dr.Andrew Worsley,

The fact of the matter is that the problem of black holes exists as not an isolated problem but in the context of the general cosmology, but the prior cosmology foll into decay by different causes about which a lot of issues was written here and in other RG pages.    

Approaches to resolving the dark matter question using modified gravity are very difficult when structure growth prior to recombination is considered since there were no gravitationally bound structures at that time.

A second problem for such approaches is dwarf galaxies or globular clusters with very high mass-to-light ratios. Worsley above gives an upper limit of 6.25 but for example the object known as Segue 1 has a mass to light ratio of 3400.

https://en.wikipedia.org/wiki/Segue_1

@Goerge Dishman

Thank you for your insight into mass to light ratios. However the ratio of 6.25 applies to the ordinary (baryonic) matter to dark matter ratio.

I understand that Andrew, in Segue 1 the ratio of dark matter to the baryonic mass (determined from the luminosity) is 3400. There is roughly 3400 times as much dark matter as baryonic matter (the figures have a significant spread).

@George

Let me explain in further- at the event horizon of a black hole and at the cosmological event horizon the factor is exactly 6.25. The ratio of dark matter to baryonic matter.

Now if we have an old globular cluster there is a larger central black hole and there are more black holes and binary black holes. In the latter case the increase in dark matter goes up by a factor of 39 ( using the below paper) so it is feasible that individual globular cluster the ratio of dark matter to ordinary matter can go up much further- even up to a factor of 3400

Article The formulation of Dynamic Newtonian advanced gravity, DNAg

In Segue 1, the total luminosity is only about 300 times that of the Sun and there are estimated to be only about 1000 stars altogether. It is unlikely that there are many black holes in it, if any. The distributed mass however is more than half a million times that of the Sun.

The MACHO studies of the 2000 an 2001 purportedly found only small amounts  of dark matter in the galactic halo.

In fact  they actually found significant amounts, but because they excluded binary systems a significant amount of that dark matter was excluded. And as binary black hole systems exert 39 times their mass, that helps account for all the dark  matter in the galactic halo.

Importantly most of those dark matter objects in the galactic halo were between 0.5-1 solar masses and yet they were not visible - the principal conclusion is that they were primordial black holes

This may explain your Segue 1 data.

Specifically that this globular cluster  is a large collection of primordial black holes

Article Advances in Black Hole Physics and Dark Matter Modelling of ...

I thought only stars with a mass >4 solar mass could form black holes when they collapse.   What is the lifetime of a black hole of < 1 solar mass assuming only Hawking radiation would fuel its evaporation?  If it's  < 13 billion years .........?

Agreed, for stellar black holes the minimum solar mass is 4 solar masses with the result that minimum black hole is 3 solar masses. Although the majority of black holes the mass is more then this .

For primordial black holes the minimum mass black hole is however far lower.

As regards Hawking  radiation,  a 0.5-1.0 solar masses primordial black hole  would take a lot lot more time to evaporate, than the apparent life of the Universe.

Thanks!

What is the limiting population density of black holes and the maximum size of any member, that avoids the collapse of most/all of them into a single black hole?

Dear All, 

Your fathers searched for dark matter, your grandfathers searched for dark matter, and you again search for dark matter. Stop the search for a black cat in the dark room where no cat exists. 

The fantasies which were born by the biggest fantasy about Big Bang were possible when no another cosmological theory was available. Today the PFO-CFO Theory contains no holes. 

As for  black holes, this question is not about them. Forty years ago, Dr. Stephen Hawking wrote on the basis of his calculations that the black holes are reality. Recently, he wrote clearly and round that he was mistaken and that no black holes exist. You return again to the idea on black holes. But do you think that it is possible to be holier than the Pope?  

@Stephen

I guess your question is on  earliest galaxy formation

Not yet calculated- but within calculable bounds given the gravitational physics of multiple black holes.

Collaboration?

Dear All,

The present cosmology is in the crisis state. I think that each reasonable person, if he personally didn't participate in the formulation of the today disgracefulness, cannot be dissenting with this statement. Just therefore, numerous particular hypotheses trying to explain any unit phenomenon in isolation from an all-inclusive cosmological theory flourish.

At present, only one comprehensive intrinsically-noncontradictory cosmological theory exists, and this is the PFO-CFO Theory. In its ground, the principle "everything - from something" and Einstein’s conclusion on the common essence of the mass and energy are laid as its basis instead of the fantastic principle "everything - from nothing", which is in the basis of the today cosmology. 

Everybody, who is really interested in the creation and development of a new theory, which is capable of giving new explanations for the Universal processes and phenomena from the "Beginning" up to the future of the Solar System and including simple explanations of stars formation, elements formation, formation of the Solar System, nature of the protuberances and solar wind, nature of the 11-year cycles of solar activity, transformation of the solar magnetic moments, etc., I advice to familiarize yourselves with the PFO-CFO Theory , beginning from my answers to the question by Elena Kadyshevich at the ResearchGate site by the address https://www.researchgate.net/post/Einsteins_relativity_what_is_eternal_questionable_and_erroneous_in_the_starting_points_of_the_theory_and_in_the_subsequent_conclusions_from_it  ) and then to read our publications on different aspects of the theory from publications of 2015 to earlier ones at my or Elena Kadyshevich RG pages. I call you to discuss and develop new theories rather than to mend and repair the aged 100-year-old theory, which is based on arbitrary fictions.

Andrew Worsley · 9.72 · 99.62 · University of London

Dark matter can be reconstructed from models of gravitation.

First you have to deconstruct General relativity and reformulate it to get rid of the nasty singularities that you get at the event horizon of a black hole.

Having done this you can explain both black holes and dark matter by using the same gravitation - and solve a lot of problems that GR generates

Yes GR works in the weak fields of the the solar system, and Intermediate

fields of neutron stars. But

1). It produces infinite density singularities in the very strong fields

such as in black holes.

2).It does not necessarily explain dark matter in galaxy cores where we

know super-massive black holes exist and the galactic dark matter

therein,

3). It does not explain dark mater present in galactic halo's,and galactic

clusters such as the bullet cluster,

4).It does not explain the presence of cosmological dark matter as a whole.

5). It has not yet been fully corroborated by the studies of neutron stars

and in black holes.

6). It does not easily explain the presence of dark energy and cannot be

translated in quantum gravity.

Here I enclose a number of publications which explain all of these

phenomena, whilst agreeing with the results of GR where it has been

thoroughly tested.

1).First to obviate the infinite density singularities.

1a)

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub

1b)

https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub

2).Secondly we explain the presence of dark matter at the centre of the

galaxy.

2a)

https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter

3) Thirdly it is possible to explain the presence of dark matter in the

galactic halo.

3a)

https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub

4). It is able to explain the presence of cosmological dark matter

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity

5). It is corroborated in neutron stars (including Data from radiation

damping ) and is corroborated by black hole studies.

5a)

https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation

5b).

https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1

6) it explains dark energy and translates into quantum gravity

https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity

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Article: An advanced modification of dynamic gravitation

Article An advanced dynamic adaptation of Newtonian equations of gravity

Article The formulation of Dynamic Newtonian advanced gravity, DNAg

Article Advances in Black Hole Gravitational Physics and Cold Dark M...

Article Advances in Black Hole Physics and Dark Matter Modelling of ...

Article An advanced modification of dynamic gravitation

Article Corroboration of Dynamic Black Hole Gravitational Physics fr...

Article String quintessence and the formulation of advanced quantum gravity