Farnes, cosmology involving negative mass I came across a paper recently which seems to be getting a lot of popular press, and a student also emailed me to ask about it: --
Farnes, "A Unifying Theory of Dark Energy and Dark Matter: Negative Masses and Matter Creation within a Modified ΛCDM Framework," https://arxiv.org/abs/1712.07962
After replying to her with some vague impressions, I thought I would edit my email and recycle it as a question here. After spending some time looking at the paper, I wasn't really able to tell much about whether it was any good -- I'm only kind of a dilettante at general relativity. It seemed pretty similar to the steady state model, or to some of the more recent kookish attempts to revive the steady state. But the surface similarity to disproven or kookish models doesn't necessarily mean it's not good work. It wasn't clear to me whether it suffered from the same problems as the steady state model: inconsistency with the CMB (he gets an oscillating universe), and breaking of Lorentz invariance (which is probably the most extensively and precisely tested scientific theory in history).
Is this idea any good? Consistent with observation? Does it solve a problem that actually is a problem?
 A: I went to Lubos log and checked for negative masses, to see whether they are compatible with quantum field theory. I am copying from an article related to masses of antiparticles

But can you imagine a genuinely negative matter? Can it exist? Can there be a repulsive gravity between two localized objects?
The answer is almost certainly "No" in any viable world, too. Why? To get a negative energy/mass, the original starting point (the space without matter, i.e. the vacuum) has to fail to be the lowest-energy state. So it becomes unstable.
You may imagine a non-vacuum where the Dirac sea is not occupied and where you can add genuinely negative-energy electrons. However, it is not just a "label" when we say that the vacuum isn't the lowest-energy state. Such a situation has dramatic physical consequences. This kind of space will spontaneously decay, creating pairs of electrons with negative and positive energies out of nothing - because it violates no conservation laws. Such a non-vacuum would behave very differently than our peaceful vacuum.

As effective field theories of gravity are quite successfully used in cosmological models it seems to me too big a hurdle to overcome . Of course the author leaves open the possibility his model is an emergent one from some other , but I do not see how to overcome the instability of the QFT vacuum. Lubos goes on to discuss tachyons, (cannot exist in our world and are a problem due to negative squared masses) and tachyonic string theory, which may neutralize the tachyons. Maybe a corresponding string theory for this proposal would exist.
A: My naive interpretation is that gravitational lensing due to dark matter haloes behaves as if the halo were composed of positive mass. Were the halo to be composed of negative mass (as Farnes hypothesises), then lensing behaviour would display inverted spacetime curvature from that which is actually observed. It is unclear to me how Farnes explains that away.
A: Different forms of explanation based on criteria(Force, Motion, Active Mass). Due to the
negative inertial mass, the direction of force and motion changes.

Mainstream researchers have misconceptions about negative mass. Because of this misconceptions, the negative mass model is not under fair scientific review.
[ False claims or misconceptions about negative mass ]
1)Vacuum instability problem 2)Runaway motion problem 3)Wheel problem with negative and positive mass 4)Spin-2 field problem
1. False claims or misconceptions about negative mass
1) The vacuum instability problem is wrong.

When negative mass exists within potential with maximal and minimal points, different directions of force and acceleration should be considered for negative mass.
F = - m_a (m_>0)
a = - F/m_
The acceleration of negative mass is opposite to the direction of force. Therefore, the negative mass has harmonic oscillation at the maximum point and it is also stable at the maximum point.
In the case of positive mass, it was stable at the minimum point at which energy is the low. However, in case of negative mass, stable equilibrium is a point of maximum value, not a point of minimum value.
For positive mass to enter the domain of (total energy is negative) negative energy level, energy should have negative value, and this means that it should have the characteristics of negative mass.
When considering the process of entering into the domain of negative energy levels from positive energy levels, it must pass through the domain between 0^- (Approach from negative direction to '0') and -(1/2)hw(corresponds to a certain negative energy level). In the case that it follows the laws of negative mass because it is in the domain of negative energy, it cannot reach -(1/2)hw, which is the first negative energy level, because it is stable at the state of high energy and it tries to have higher value of energy.
This is because the energy level 0^- is much higher than the energy level -(1/2)hw. Thus, this implies that the law of negative mass itself does not allow a situation where positive mass at the positive energy level transitions to the negative energy level.
Even if it reaches -(1/2)hw, it is most stable state for negative mass and "the problem of the transition of the energy level of minus infinity" does not occur.
As we have examined above, "the problem of the transition of the energy level of minus infinity" does not occur, and thus positive mass and negative mass can exist in the same universe. This is a very important result because it means that negative mass and negative energy can exist stably in our universe.
2)The runaway motion problem is wrong.
Runaway motion is an argument that the two masses continue to accelerate, in an ideal situation where the negative mass and the positive mass are exactly the same. Runaway motion is used as a rejection logic of negative mass because no large energy motion is observed.
a) The difference in mass when creating the pair of negative mass and positive mass
As a general conjecture, when positive and negative mass are born, the absolute value of mass will be exactly the same, but this conjecture is wrong. 
In the process of the pair creation of electron and positron, the effect of electromagnetic potential energy could be the same because the two particles had the same kind of energy(electron : positive energy, positron : positive energy). Therefore, the two particles could have the same mass. However, in the process of the pair creation of negative and positive mass, the effect of gravitational potential energy is different because the two particles have different types of energy(negative mass : negative value, positive mass : positive value).
This gravitational potential energy has a positive value and exists in a system containing two objects or two objects. If you add or subtract potential energy in two cases(Pair creation of electron and positron, Pair creation of negative mass and positive mass), you can see that they are different.
When creating two positive masses : In the process of the pair creation of electron and positron,
+10 : +10 ////// +10 : +10
-1 : -1   ////// +1 : +1
----------////// ---------
+9 = +9   ////// +11 = +11
But, in the process of the pair creation of negative and positive mass,
-10 : +10    ////// -10 : +10
-1 : -1      ////// +1 : +1
------------ ////// -------------
|-11| ≠| +9| //////| -9| ≠ |+11|
With the sign of negative mass and positive mass different, the difference occurs because the potential energy has a sign of either +  or - .
${m_ - } > 0,{m_ + } > 0$
\begin{equation}
{E_T} = 0 = ( - {m_ - }{c^2}) + ( + {m_ + }{c^2}) + \frac{{G{m_ + }{m_ - }}}{r} = 0
\end{equation}
\begin{equation}
{m_ - } = {m_ + } + \frac{{G{m_ + }{m_ - }}}{{r{c^2}}}
\end{equation}
In case the negative mass and the positive mass are pair created in the vacuum, according to the Energy Conservation Law, there must be a mass difference between the negative mass and the positive mass.
\begin{equation}
{|-m_ -| } > {m_ + }
\end{equation}
Acceleration is determined by the size of the opponent's mass. If the absolute value of the negative mass is greater than the absolute value of the positive mass, there is a repulsive gravitational effect between the two. In this case, the acceleration of positive mass is greater. As time passes, the two masses become more and more distant. In other words, the ideal situation of pairing is broken. Because the accelerations are not the same and the distance of the pairing increases, the interaction of the other particles becomes involved. Therefore, runaway motion does not occur.
This logic may be used as a theoretical basis(energy conservation law, mass difference, repulsive gravitational effect) for the presence of two masses after pair creation without pair annihilation. Please watch(${|-m_ -| } > {m_ + }$ case) the linked video.
https://youtu.be/MZtS7cBMIc4?t=118
b) There is a possibility that the gravitational potential energy will break the ideal situation.
Although the absolute values of the masses of two objects are exactly the same, there is a gravitational potential energy between them.
\begin{equation}
U =  - \frac{{G( + m)( - m)}}{r} =  + \frac{{Gmm}}{r} > 0
\end{equation}
This gravitational potential energy has a positive value and exists in a system containing two objects or two objects. And, since all energy is a source of gravity, the gravitational potential energy must also act gravity source.
That is, even if the masses of negative mass and positive mass are exactly the same, the gravitational potential energy between them breaks this ideal situation.
3) Wheel problem with negative and positive mass is wrong.
4) Spin-2 field problem is wrong.
5) Creation tensor problem
The creation tensor introduced by Farnes violates the law of conservation of energy. However, the notion of vacuum energy or cosmological constant introduced by the mainstream also violates the law of conservation of energy (The total energy of the universe is not conserved). However, the logic presented above is likely to fulfill the role of creation tensor while satisfying the law of energy conservation.
In case the negative mass and the positive mass are pair created in the vacuum, according to the Energy Conservation Law, there must be a mass difference between the negative mass and the positive mass.
Since the creation ratio of the negative mass and the positive mass is different, it is possible to explain the effect of dark energy while satisfying the energy conservation law.
2. Negative mass is the result of the Friedmann equation and a candidate for dark energy 
From the discovery of the accelerating expansion of the universe, people generally claim the existence of cosmological constants or vacuum energy. However, the truth is ~
Nobel Lecture by Adam G. Riess ; 2011 Nobel Prize in Physics, Refer to 11m : 00s ~
https://www.nobelprize.org/mediaplayer/?id=1729
Negative Mass? Actually the first indication of the discovery!
Days later… What does this mean? There cannot be negative mass, but would Einstein’s Cosmological Constant explain this acceleration?
In 1998 observations, the first result of the Friedmann equation was negative (gravitational) mass density. Researchers who had difficulty accepting negative mass have corrected the equation. And they argue that the accelerating expansion of the universe is evidence of the existence of a cosmological constant.
Anyway, negative mass is one of the solutions for dark energy. However, this also has the potential to explain the dark matter effect.
3. How negative mass acts as dark matter
If negative mass and positive mass were born together, positive mass has attractive effect each other, so it forms star and galaxy structure now. But negative mass has repulsive effect each other, so they cannot make massive mass structure like star or galaxy.
Negative masses(dark matter) will be uniformly distributed all over space. Uniformly distributed negative mass receives attractive effect from massive positive mass, so dark matter which has negative mass is clustered around galaxy.(in case of |-m_| << m+)
Negative masses can be stable structure around galaxy.
If there is an abundant negative mass outside the galaxy, negative masses are clustered to the galaxy. And, since the negative mass exerts a repulsive force (or pressure) on the positive mass, there is an additional centripetal force inside the galaxy. In other words, there is an additional centripetal force required for dark matter.
In this model, dark matter(negative mass) exists outside the galaxy, and there is only a gravitational effect inside the galaxy.
https://youtu.be/MZtS7cBMIc4?t=225
In the process of discarding the negative mass that is the result of the Friedmann equation, it is assumed that the false claims(1)Vacuum instability problem, 2)Runaway motion problem, 3)Wheel problem, 4)Spin-2 field problem ...) listed above played a key role. Since the rejection logics for the negative mass are wrong, the negative mass model needs to be reviewed again.
Please refer to my papers.
*1.Dark Matter is Negative Mass
https://www.researchgate.net/publication/324525352
*2.On Problems and Solutions of General Relativity
https://www.researchgate.net/publication/286935998
*3.Negative Mass and Negative Energy
https://www.youtube.com/watch?v=MZtS7cBMIc4
