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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?

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    $\begingroup$ Sabine Hossenfelder: No, negative masses have not revolutionized cosmology $\endgroup$ – Keith McClary Dec 17 '18 at 5:29
  • $\begingroup$ Hossenfelder seems unimpressed, says: (1) Farnes assumes repulsion between negative masses, which is inconsistent with GR; (2) the creation field has the same problems as in classic steady state theories; (3) Occam's razor favors dark matter and dark energy; (4) negative inertial mass implies an unstable vacuum, which we don't actually see. Farnes sent her a blustery reply to post as a comment on her blog. He says, "The creation term moderates the production rate of negative mass particles, and prevents this from being a catastrophic event." $\endgroup$ – Ben Crowell Dec 17 '18 at 14:09
  • $\begingroup$ Hossenfelder also complains that Farnes would "still have to bend over backward to demonstrate that the solution actually does fit the rotation curves which, frankly, I am rather skeptic about because I cannot see how you get the right scaling behavior (Tully-Fisher and all)." $\endgroup$ – Ben Crowell Dec 17 '18 at 14:19
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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.

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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.

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