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Dark matter is believed to be a substance of unknown origin with mass that is distributed in space.

Can the same observed effects be explained by an intrinsic curvature of regions of space without presence of any mass energy in them? Say during big ban the space got randomly curved such that there are areas with curvature that is just the property of space, like valleys and hills in a landscape.

If so, it might be that there are no dark matter particles or any baryonic matter to explain visible effects.

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    $\begingroup$ Wikipedia: “Primordial black holes are non-baryonic, and as such are plausible dark matter candidates” $\endgroup$
    – Ghoster
    Commented May 25, 2023 at 4:24

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It has been considered that dark matter might not actually exist as a particle, but this simply doesn't fit the data. In particular, we can't explain the bullet cluster with such a presumption. Dark matter must be something physical in spacetime that influences the stress-energy tensor.

Relevant XKCD

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