Just skimming, I find two obvious issues with the proposed model:
First, saying that spacetime, considered as a 4-d hypersurface, has "two sides with two metrics" won't work. The metric of one side fully determines the metric of the other side since both sides belong to the same surface. That's why spacetime in standard Einstein GR only has one metric (which, btw, does not mean that spacetime in standard GR has only one "side", as the article claims). Two different metrics would have to describe two different, disjoint surfaces, which would have no connection to each other, which would mean the second one, being unobservable, would be scraped right off the model by Occam's razor.
Second, saying that negative mass would induce "opposite curvatures" as compared to positive mass, in the same spacetime, won't work. One spacetime can only have one curvature at any given ponit. Considering the simpler example of a 2-d surface should make this intuitively obvious--the same surface can't have two different curvatures at the same point.
Also just skimming, and furthermore not a physicist, but I'm not sure your critique works:
> Two different metrics would have to describe two different, disjoint surfaces, which would have no connection to each other, which would mean the second one, being unobservable, would be scraped right off the model by Occam's razor.
The theory states that the two surfaces are not disjoint:
> What is important to note however, is that the two field equations are coupled, i.e. a mass always creates a positive curvature in spacetime according to its own metric (where the mass appears visible), and it also always induces a negative curvature in the conjugate metric (where the mass appears invisible).
I do find it confusing why this would be called two metrics, however, since it seems to be describing a unified spacetime "surface".
As for your second critique:
> One spacetime can only have one curvature at any given ponit. Considering the simpler example of a 2-d surface should make this intuitively obvious--the same surface can't have two different curvatures at the same point.
But if the surface has two sides, can it not? Consider the classic "gravity well" demonstration of a heavy ball placed on an elastic membrane. It forms a concave surface. Now turn your head upside down and look at the membrane from underneath. You'll see a convex surface. Same membrane, different curvatures.
Anyhow, I'm certainly not equipped to analyse this theory, but I do like that it attempts to make falsifiable predictions. I guess it's an attempt to explain dark energy? It would appear to leave problems of dark matter unaddressed, however.
> But if the surface has two sides, can it not? Consider the classic "gravity well" demonstration of a heavy ball placed on an elastic membrane. It forms a concave surface. Now turn your head upside down and look at the membrane from underneath. You'll see a convex surface. Same membrane, different curvatures.
You're thinking of this as someone who can look at the surface from the outside, in which case it makes sense to consider convex and concave curvatures to be different. But if you're restricted to moving within the surface, there's no way to tell the difference.
Within the surface, you can only measure the distances traveled along certain paths. For these distances, it doesn't matter whether you're walking across a hill or a valley of the opposite shape. The metrics of these surfaces are exactly the same.
That doesn't mean that negative curvature is impossible, just that it isn't as simple as inverting convex and concave. A negatively curved two-dimensional surface curves simultaneously in opposite directions, like a saddle point. But there's no way to have two surfaces with inverted curvatures at corresponding points, since curvature is determined by the arrangement of points, which means that inverting curvature obliterates the whole concept of "corresponding points" by arranging them differently.
> The theory states that the two surfaces are not disjoint
Yes, but that just underscores my point that one surface can only have one metric.
> But if the surface has two sides, can it not?
No. You can describe the one curvature in two different ways, depending on which side you choose as your viewpoint. But it's still just one surface and one curvature, not two.
First, saying that spacetime, considered as a 4-d hypersurface, has "two sides with two metrics" won't work. The metric of one side fully determines the metric of the other side since both sides belong to the same surface. That's why spacetime in standard Einstein GR only has one metric (which, btw, does not mean that spacetime in standard GR has only one "side", as the article claims). Two different metrics would have to describe two different, disjoint surfaces, which would have no connection to each other, which would mean the second one, being unobservable, would be scraped right off the model by Occam's razor.
Second, saying that negative mass would induce "opposite curvatures" as compared to positive mass, in the same spacetime, won't work. One spacetime can only have one curvature at any given ponit. Considering the simpler example of a 2-d surface should make this intuitively obvious--the same surface can't have two different curvatures at the same point.