Mordred

The problem can easily get compounded when using AI to study physics. One example is having AI look up a specific equation. One example being if you were to look for relations specific to a metric or methodology. AI could very well return a relation specific to say a canonical treatment as opposed to a conformal treatment. With the FLRW metric it often confuses conformal coordinates as opposed to commoving coordinates. If the AI user isnt aware of these distinctions to recognize the AI mistakes they could easily get confused as well as get frustrated when they try to apply those equations. As AI looks through literature Ive seen it throw in cosmographic metrics as well and mix them with commoving metrics. (LOL the above can also be used to recognize someone relying too heavily on AI)

Forgot to add I don't see anything particularly wrong in your treatment above at the moment. In so far as the math relations involved. I would be curious though if you agree that direction would be an inherent degree of freedom of any underlying state/system being described. Where one state resides in relation to another obviously is related.

Thank you for the above, its a tremendous help in understanding the purpose of your article. Sorry I was being a bit of a stickler on material needed being presented here. I do have good reasons for that, lol lets just say I've come across one poster in the past that although his ideas were sound. He had dozens of different papers and articles he kept referring to and you literally had to go through them to get any sense of what he was doing in the first place.... That's not the reason of course but its a good extreme example. In the above you have a statement of avoiding any unnecessary complexity. Obviously scalar relations does indeed simplify the mathematics I would argue that requiring "direction of kinematic relations is a necessary complexity". Which direction an interaction (whatever that kinematic interaction represents) is just as important as the scalar relations. Obviously we all know any " Field treatment requires geometry" particularly for any mappings of particle or measured quantity distributions". Depending on what your after those mappings will also give a necessary complexity. Those are two aspects I would consider as being necessary ( for what I do in physics absolutely necessary) So the question of what is "necessary complexity" is something I think should be looked into in greater detail. Side note I will often post added Mainstream relations relating to a thread. I've found in the past this habit is an aid to other readers not involved in the conversation better understand what is being discussed as well as useful for comparisons between methodologies etc

agreed though propogators cannot be directly measured and include probability currents which are mathematical as well

Your list above is fairly accurate though some of the list is fairly broad. Light path deflection for example would include spectography redshifting. For example integrated Sache Wolfe effect as signals pass through the mass variation of DM halos as one example. If I think of anything not already covered on that list I will post it As far as the fine structure constant your methodology from what you described here sounds remarkably similar to whats done in BSBM model (Berkenstein Model ) a version of TeVeS MOND. The problem with coupling the fine structure constant is that you may find you would require a varying fine structure constant as per BSBM as well as the Hubble constant also varies over time. ( it's only constant everywhere at a given time slice. Ie today. If you would like to test it at different Z ranges I can give you the Hubble constant value at any given redshift value. The cosmocalc in my signature which I was involved with developing has the correct second order terms for when the recessive velocity exceeds c for redshift beyond 1.49 ( Hubble Horizon) to the particle horizon. the following below is for other readers to keep others at the same speed. The second order formula I'm referring to is the last formula on the list. The previous formulas is the mathematical proof using the equations of state and how they evolve over the universe expansion history. FLRW Metric equations \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] setting \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] \[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\] which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0. the related GR solution the the above will be the Newton approximation. \[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] Thermodynamics Tds=DU+pDV Adiabatic and isentropic fluid (closed system) equation of state \[w=\frac{\rho}{p}\sim p=\omega\rho\] \[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\] as radiation equation of state is \[p_R=\rho_R/3\equiv \omega=1/3 \] radiation density in thermal equilibrium is therefore \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \] \[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\] temperature scales inversely to the scale factor giving \[T=T_O(1+z)\] with the density evolution of radiation, matter and Lambda given as a function of z \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] its other purpose was more my work testing the accuracy of the inverse relation to blackbody temperature. I rarely trust literature on any verbatim basis so often like to see how a statement such as temperature being the inverse of the scale factor is determined as being accurate. Sides its good practice lol ( above i had done previously in my Nucleosynthesis thread. ) the last formula the cosmocalc employs though has from version 1 of the cosmocalc well over a decade ago . specifically this formula will provide the Hubble constant value as a function of redshift \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] should note for others as well the GR statements are for the Newton approximation which the FLRW metric falls under just a side note the FLRW metric is not maximally symmetric where the Minkowskii metric under SR is. The use of the scale factor is one of the key issues with maximal symmetry (You can see this via the Christoffels for the FLRW metric ) or another way to learn this is through the Rayleigh equations.

In Feymann integrals the propogator ( a propogator propagates an operator) with the propogator being the internal lines and operator being the external solid lines ( observables ) ie real particles with internal often associated with virtual particles though its more accurate to just treat the propogator as field. You require one quanta of effective progator action to affect an operator . Thats about the only way one can potentially denotes some form of minimal threshold that I myself am aware of.

The writeup was likely using a Hilbert space common in QM treatments. A Hilbert space being defined from the inner product of a vector field. Its not the only class of wavefunctions. You can have wavefunctions that do not require a Hilbert space nor the inner product. Scalar field spaces being one example. You have no need for vectors nor inner or cross product. However you can still have a wavefunction relating to number density of photons as one example based on the amplitude of the probability current. Just an FYI. Lol one solid clue to keep track of the distinction. A function is a mathematical set of operations. The prefix of wave is simply naming the type of function. Same applies to correlation function for entanglement.

Lets straighten out the wavefunction being not physical. You develop the wavefunction using known properties of the particles state and apply it to the Schrodinger equation or Klein Gordon etc. You can also take into consideration the experimental apparatus, error margins etc. In QFT you can employ a probability current just a side note. Its simply our formulas employed with previous well tested studies of the particle properties, application of the appropriate formulas. Strictly determined via mathematics. Mathematics are not physical even though they may describe a physical state etc. Physical is what you have measured. You measure physical properties the mathematics only describe or predict what you will measure. That's a very important distinction

Well it may help to consider that its not necessarily the galaxy rotation curves themselves that provide the strongest support of DM being a particle. Consider the following if you take the FLRW metric and use the equations of state and apply the FLRW metric acceleration equations. Then remove the DM component and just apply baryonic matter of just 3% then there would never be enough matter in our universe for matter to become the dominant contributor to expansion. Instead of radiation era, matter era the Lambda era. You would only go from radiation directly to Lambda dominant. The Hubble constant would not have the value it does today. Matter radiation equality would never occur ( roughly when the universe is 7 Glyrs old.) Expansion rates themselves and it how it evolves over time would be completely different. Now as expansion occurs radiation diffuses more readily in an increased volume than matter so their densities evolve at different rates. Matter having an equation of state w=0 meaning it exerts no equivalent pressure term. This one can construe as being the primary evidence that influences the research more in favor of a particle constituent. Coupled with the detail that DM halos do cause gravitational lensing helps us confirm the density distributions. In point of detail Hubble telescope often makes use of these DM halos lenses to extend its range. Hope that helps if you like some of the related mathematics I can post them here. Lol wouldn't take any real effort as I have em handy in another thread. Edit correction on above the time frame was for matter lambda equality radiation/equality is sometime prior to Z=1150 depending on dataset used I would have to check later on. Zeq 3387 using Planck 2018+BAO dataset.

Bingo the one point all the crackpots miss lmao. Not stating anyone here is one lol.

Easy way is to consider a classic example if you determine some probability function for simplicity lets just use coin tosses but dropping a collection of coins in a given time frame. This forms a time or time independent wavefunction depending on drop rate. Once you make measurements ie number of coins with heads up as opposed to heads down. The original wavefunction isn't needed you have made determinations through observation and measurement you now have a determined wavefunction as opposed to a probability wave function. Some often refer to the latter as simply waveform to avoid confusion with the probability characteristic of a wavefunction.

Interesting article and proposal will be interesting what future findings on this will present itself for those wanting to look through the arxiv article itself https://arxiv.org/abs/2510.19087

This post had nothing to do with your article. I simply thought it was an idea you could make use of. Good luck. You want thinking outside the box its simple any mathematical methodology that can accurately describe a system or state has validity. You dont need tensors to do GR its simply another handy mathematical tool. You dont need to use 4 parameters to describe spacetime you can use parametric equations to reduce them. Thats my view point

Whatever as I mentioned before the rules state that there is no requirement to visit other sites or links and all pertinent information should be here. Im sorry you do not get that policy but its your full pdf on your opening page I have absolutely zero interest in opening up any other of your website links. So good luck with your work . Im done I have better things to do

Here's an interesting trick for you then take the equation of motion for a mechanical spring. If you compare the equation for the quantum harmonic oscillator you will find the precise same relations albeit a change in variables applied. The ratios of change are identical. If you study deep enough you will find a great deal of similarities between the seemingly complex equations have similar relations to many classical physics formulas commonly used in engineering. This is quite a bit more complex first and foremost the conservation rules require a closed system or a closed group. To go into greater detail would be more suitable to a seperate thread and such a discussion can get extensively lengthy. In some treatments involving spacetime one can define a conserved system usually ties into innvariance of a quantity. This is often done under local geometry in some mathematical space or manifolds. Anyways best left for a different thread

When I first started physics one of my earlier goals was to solve DE as an optical illusion. I realized early enough that doing so required mathematics and a good understanding of the FLRW metric and GR. In those studies I learned a valuable lesson. Simply because something doesn't make sense to you doesn't mean its incorrect. Its a lesson I carry on to this very day. More enough enough if one studies why the physics professional community states what they state there is always numerous supportive as well as counter arguments or methodologies supporting one theory or another. To a layman this unfortunately gives a rather daunting task of sorting through. Though the effort of doing so with an open mind can lead one to learn a great deal. The biggest challenge is avoiding any personal bias. Once you form a solid opinion of I feel it should be this way. One tends to close the book on examine other possibilities. This goes for any physics theory or model. The effort to understanding why physics describes something a certain way always has very strong reasoning behind it and those reasons are typically best understood by studying the related mathematical proofs. Its one reason I study not just mainstream models and physics but study numerous potential models or theories. You would be amazed that with enough studying how much something that originally sounded ridiculous starts to make sense. One also discovers how truly interconnected one theory is to numerous others. A simple change in one theory can often have numerous ramifications of dozens of others. Something many of our typical crackpot dont fully recognize. There's a simple consideration no theory or model ever becomes considered mainstream physics without years of rigorous testing and years of sorting the best fit to observational evidence. Eureka moments are typically something that only exists in movies. Theory and model building for a robust theory takes an incredible amount of work and whats often forgotten. One of the most valuable practices is that a good theorist should spend far more time proving his own theory wrong than he/she did in developing it. Little hint here if one studies statistics and statistical mechanics. One discovers that a great deal of the more difficult terminology used in QM and QFT actually originates from classical statistics. Examples being superposition, correlation functions the list goes on. It does help pull a lot of the mystery out of QM.

There is a handy simplification related to the non linearity of the relativistic addition of velocities where the Lorentz transformations matrix comes in handy. Rapidity using rapidity velocity is replaced by rapidity and becomes linearly additive. The method applies the hyperbolic spacetime diagram of the Minkowskii metric its also useful for a constant accelerating object. Not sure if that would interest you or not but its a useful simplification on calculations with regards to Lorentz transformations.

Great so where is the difference between using a unitary basis under GR. Normalization I fully recognize and relate to same goes for dimensionless values. Still doesn't address where dimensionless values isn't appropriate for specific relations. Oh Ive read your article its mannerism of writing is rather scattered but that's another issue so dont call me a liar on that. One of the reasons I had to reread it was I initially thought you declared the Gamna factor being the inverse of the beta function which would be incorrect but your B_y isn't identical to the normal beta function relation. Not that I saw you employing Gamma factor so it was irrelevant to mention. What Im suppose to be convinced by your graphic ? Simply because you employed dimensionless replacements or using normalized units ? Its fairly rudementary to normalize or make some relation dimensionless. Ive come across numerous articles that make \{8 \pi G \} normalized to one good example is the critical density formula nothing new or exciting about that. Do you not want to expand on your article for example The Kerr metric isn't a static solution. Perfect arena for testing your method on a rotating frame. You didn't really go into alot of detail in that section of your article. If you feel your article is a done deal then it amounts to just advertising in which case I lose all interest. Correct me if Im wrong but you assigned E_0 as invariant energy with M_0 being the invariant mass with E being total energy so explain why you have \{E=m_0\} and not \{E_0=m_0\} ? Correct me if Im wrong but your thread title does state testing. So add tests you haven't already done. Solving twin paradox with your methodology might prove a useful challenge as another example. However then you will have to deviate from the symmetry relations of constant velocity to include the rotations involved for acceleration

In so far as a particle origin for DM it would be easier to apply the virial theorem to DM with regards to galaxy rotation curves the weakly interactive characteristics for example well suits neutrinos. Or any other particle that is weakly interactive. When you study the NFW profile which utilizes Virial theorem for galaxy rotation curves you find that its power law relations show that in order to obtain the measured galaxy rotation curves instead of the Keplar decline you need a greater amount of mass in fairly uniform distribution surrounding the galaxy. The DM halo distribution while being weakly interactive DM is still subject to gravity. One of the primary reasons its expected to drop out of thermal equilibrium early is that its also considered responsible for initializing mass density anistropy for early large scale structure formation. Obviously we cannot measure directly DM but we can certainly infer its existence in some form or another as a pressureless ( matter) component via the equations of state in cosmology. Some of these articles describe secondary effects that can be measured involving DM. Example below. The double beta decay in the above articles should also allow for some interactions that we can hopefully measure https://arxiv.org/pdf/1402.4119

If your going to attempt to do that then perhaps some consistency might be in order. Take for example your statement there is no momentum later on in your article yet your B_y which you describe as the inverse of the gamma factor includes velocity terms. Mass for example is resistance to inertia change. It is a kinematic property. You also claim no need for any geometry yet you discuss two manifolds S_1 and S_2. Which are geometric objects. Your use of a circle and sphere are both geometric objects. Now consider this any invariant quantity in physics does not rely on a metric one can arbitrarily choose any metric without changing the value of that invariant quantity. Ive read your paper several times over and I see no clear purpose or ontology view in its written format. However that's just my opinion. The inherent problem of ontology views trying to dictate how physics is done is that they often forget one of our primary jobs is to interpret datasets and graphs produced by experimental apparatus. You need geometry to accomplish that. Yes physics uses mathematics it is a fundamental tool for describing what we measure. Do not be fooled into thinking I believe in any fundamental realism I am well aware that terms such as mass, energy, fields, time etc Are abstract. Ive read countless ontology papers over the past 40 years. I am well aware of the difference between mathematical objects or descriptives vs fundamental realism. None of that changes the job of a physicist which requires those mathematics you dont feel important in order for that physicist to secure jobs etc. As far as that last link how did you program it without applying some form of geometry.. can you honestly state no geometry was used. I can readily accomplish the same using the standard methods with all those geometric relations. Do you honestly believe that simply because you can plot a 2d orbital that this encompasses all possible observer from other angles ? That was why I mentioned those little challenges. Lets see how well your mathematics work when you have multiple reference frames at any random 3d coordinate. Not just simply a simple case of a 2d plane. By the way you and I are both aware that link describes a Maximally symmetric spacetime. Lets see how well your calculations work without having a Maximally symmetric spacetime. ( Marcus Hanke already mentioned the relevant killing vectors). Im choosing to ignore the scalar quantity E as being in any regards a suitable replacement for spacetime geometry.

Read the forum rules material needs to presented here Im not about to go through a bunch of different links. This requirement has already been mentioned. I did the one exception by reading your main article. I will stick to that. From that main article I do not believe you can give the proper seperation distance between two inertial reference frames ds^2 without being able to curve trace the worldline between the two events. Particularly when the Lorentz transformations include not just time dilation but also length contractions. Try this without considering geometry try more than two events say 3 different reference frames and what each observer sees relative to each observer at 3 different coordinate locations. Then try it in a non Maximally symmetric spacetime such as one in rotation...ie Sagnac effect.

What's ridiculous is whenever I mention something in textbooks Im met with scorn. There is good reasons the stuff I mentioned exist in textbooks. Its a known methodology proven to work... For example you could take a constant accelerating twin and plot the curve after following the rextbook methodology and fully describe the curve by \{\frac{g^4€{c^2}\} which will return the hyperbolic geometry produced via a spacetime graph of the travelling twins worldline... I won't waste my time showing how that equation is the resultant see Lewis Ryders General relativity textbook

No thank you I don't visit forums to deal with attitude I read your paper that was enough for me. Take my opinion or not couldn't care one way or another Just reading through this thread its obvious your lacking in areas that others have pointed out as well. Of course you could have instead shown where your applying the vectors etc but you chose attitude instead of showing where my statement is in error. ( hint tangent vectors for slope curve fitting) commonly used for SR and GR... how is your methodology replacing them and giving the same detail ya know basic calculus curve fitting.... After all not all spacetimes are Maximally symmetric like Euclidean or Cartesian.

I must admit this is the first time Ive heard of this particular possibility. Thank you for bringing it up. Lol knowing me I will dig considerably deeper into related articles to get a better feel for the status of Strangeness as DM +1 They would certainly drop out of thermal equilibrium early enough to form DM seeding for large scale structure formation

Lately I have been seeing numerous articles on right hand neutrinos contributing to dark matter. There are several different proposals. Those proposals involve whether or not neutrinos follow the terms of Dirac mass or Majorana mass https://arxiv.org/abs/2008.02110 here is a breakdown into singlets and doublets SU(2) \[{\small\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline Field & \ell_L& \ell_R &v_L&U_L&d_L&U_R &D_R&\phi^+&\phi^0\\\hline T_3&- \frac{1}{2}&0&\frac{1}{2}&\frac{1}{2}&-\frac{1}{2}&0&0&\frac{1}{2}&-\frac{1}{2} \\\hline Y&-\frac{1}{2}&-1&-\frac{1}{2}&\frac{1}{6}&\frac{1}{6}& \frac{2}{3}&-\frac{1}{3}&\frac{1}{2}&\frac{1}{2}\\\hline Q&-1&-1&0&\frac{2}{3}&-\frac{1}{3}&\frac{2}{3}&-\frac{1}{3}&1&0\\\hline\end{array}}\] \(\psi_L\) doublet \[D_\mu\psi_L=[\partial_\mu-i\frac{g}{\sqrt{2}}(\tau^+W_\mu^+\tau^-W_\mu^-)-i\frac{g}{2}\tau^3W^3_\mu+i\acute{g}YB_\mu]\psi_L=\]\[\partial_\mu-i\frac{g}{\sqrt{2}}(\tau^+W_\mu^-)+ieQA_\mu-i\frac{g}{cos\theta_W}(\frac{t_3}{2}-Qsin^2\theta_W)Z_\mu]\psi_L\] \(\psi_R\) singlet \[D_\mu\psi_R=[\partial\mu+i\acute{g}YB_\mu]\psi_R=\partial_\mu+ieQA_\mu+i\frac{g}{cos\theta_W}Qsin^2\theta_WZ_\mu]\psi_W\] with \[\tau\pm=i\frac{\tau_1\pm\tau_2}{2}\] and charge operator defined as \[Q=\begin{pmatrix}\frac{1}{2}+Y&0\\0&-\frac{1}{2}+Y\end{pmatrix}\] \[e=g.sin\theta_W=g.cos\theta_W\] \[W_\mu\pm=\frac{W^1_\mu\pm iW_\mu^2}{\sqrt{2}}\] \[V_{ckm}=V^\dagger_{\mu L} V_{dL}\] The gauge group of electroweak interactions is \[SU(2)_L\otimes U(1)_Y\] where left handed quarks are in doublets of \[ SU(2)_L\] while right handed quarks are in singlets the electroweak interaction is given by the Langrangian \[\mathcal{L}=-\frac{1}{4}W^a_{\mu\nu}W^{\mu\nu}_a-\frac{1}{4}B_{\mu\nu}B^{\mu\nu}+\overline{\Psi}i\gamma_\mu D^\mu \Psi\] where \[W^{1,2,3},B_\mu\] are the four spin 1 boson fields associated to the generators of the gauge transformation \[\Psi\] The 3 generators of the \[SU(2)_L\] transformation are the three isospin operator components \[t^a=\frac{1}{2} \tau^a \] with \[\tau^a \] being the Pauli matrix and the generator of \[U(1)_\gamma\] being the weak hypercharge operator. The weak isospin "I" and hyper charge \[\gamma\] are related to the electric charge Q and given as \[Q+I^3+\frac{\gamma}{2}\] with quarks and lepton fields organized in left-handed doublets and right-handed singlets: For neutrinos involving Majorana mass an overview of the related mathematics is below including links to relevant papers \[m\overline{\Psi}\Psi=(m\overline{\Psi_l}\Psi_r+\overline{\Psi_r}\Psi)\] \[\mathcal{L}=(D_\mu\Phi^\dagger)(D_\mu\Phi)-V(\Phi^\dagger\Phi)\] 4 effective degrees of freedom doublet complex scalar field. with \[D_\mu\Phi=(\partial_\mu+igW_\mu-\frac{i}{2}\acute{g}B_\mu)\Phi\]\ \[V(\Phi^\dagger\Phi)=-\mu^2\Phi^\dagger\Phi+\frac{1}{2}\lambda(\Phi^\dagger\Phi)^2,\mu^2>0\] in Unitary gauge \[\mathcal{L}=\frac{\lambda}{4}v^4\] \[+\frac{1}{2}\partial_\mu H \partial^\mu H-\lambda v^2H^2+\frac{\lambda}{\sqrt{2}}vH^3+\frac{\lambda}{8}H^4\] \[+\frac{1}{4}(v+(\frac{1}{2}H)^2(W_mu^1W_\mu^2W_\mu^3B_\mu)\begin{pmatrix}g^2&0&0&0\\0&g^2&0&0\\0&0&g^2&g\acute{g}\\0&0&\acute{g}g&\acute{g}^2 \end{pmatrix}\begin{pmatrix}W^{1\mu}\\W^{2\mu}\\W^{3\mu}\\B^\mu\end{pmatrix}\] Right hand neutrino singlet needs charge conjugate for Majorana mass term (singlet requirement) \[\Psi^c=C\overline{\Psi}^T\] charge conjugate spinor \[C=i\gamma^2\gamma^0\] Chirality \[P_L\Psi_R^C=\Psi_R\] mass term requires \[\overline\Psi^C\Psi\] grants gauge invariance for singlets only. \[\mathcal{L}_{v.mass}=hv_{ij}\overline{I}_{Li}V_{Rj}\Phi+\frac{1}{2}M_{ij}\overline{V_{ri}}V_{rj}+h.c\] Higgs expectation value turns the Higgs coupling matrix into the Dirac mass matrix. Majorana mass matrix eugenvalues can be much higher than the Dirac mass. diagonal of \[\Psi^L,\Psi_R\] leads to three light modes v_i with mass matrix \[m_v=-MD^{-1}M_D^T\] MajorN mass in typical GUT \[M\propto10^{15},,GeV\] further details on Majorana mass matrix https://arxiv.org/pdf/1307.0988.pdf https://arxiv.org/pdf/hep-ph/9702253.pdf Now in order to account for the mass terms of DM the mass terms must be in or above the Kev range. Below are some related articles involving DESI. The Kev range would readily fall under the mentioned warm dm models. However there is also papers that place right hand neutrinos being in the GeV range through double beta decay. DESI constraints https://www.osti.gov/servlets/purl/3011043 Has a particular section to follow up on massive neutrinos behaving as dark matter described in above link. https://arxiv.org/abs/2507.01380 double beta decay primer https://arxiv.org/abs/2108.09364 In a nutshell the possibility is there so I started this thread to explore various examinations and starting a discussion on the the pros and cons of such a proposal. Naturally I would be interested in any related papers including counter arguments. This is not my own model proposal but a discussion on models presented by others. It doesn't suit a mainstream forum not yet anyways lol. As for myself I see the potential but I question whether or not the mass terms will meet the required DM mass distribution. There was a fairly recent study that placed constraints on any simple Dirac mass term for right hand neutrinos in that examinations of the energy sector did not have any relevant findings. Still digging up that study hopefully I can find it however if I recall it constrained 5 KeV or less if memory serves. other related papers https://arxiv.org/pdf/1911.05092.pdf https://arxiv.org/pdf/1901.00151.pdf https://arxiv.org/pdf/2109.00767v2.pdf https://arxiv.org/abs/1402.2301 https://arxiv.org/pdf/0708.1033 Located the light neutrino constraint paper via MicroBoone https://arxiv.org/abs/2512.07159