Small nitpick on choice of words here - homogenous probably isn't the right word to use, instead the correct term is probably invariant.
The universe appears homogenous at various scales, meaning it's self-same within some amount of tolerance across itself. The distribution is homogenous. That's different from invariance, the assumption that a variable (in this case an intrinsic property such as mass) remains unchanged over time for a given subject of study, such as a particle.
Even if a given property can vary from subject to subject (even wildly), the sum of all subjects could still appear homogeneous in their distribution.
>why do we assume spacetime to be homogenous in its nature?
Because it's distribution appears to be consistent, at least as far as we can measure. That's not the same thing as objects at the quantum scale being invariant (or variable) in some way that we currently think is the opposite.
>Couldn't then dark matter be explained by some variations on a large scale? Like giant "wrinkles" in spacetime?
Considering the scales at which these fluctuations would have to occur for us to have not already measured them I'm doubtful they could build up to anything like that, even in aggregate and random patterns.
>They would then behave as pseudo black holes, or more like "black trenches", that lead to the structures we see today in the universe. The structures seem to have more mass than what we can actually see, but are in fact just placed in locations that behave differently gravity wise?
I don't think I'm really qualified to answer on how possible this interpretation is, but with the confirmation of gravitational waves a few years back we confirmed another piece of Einstein's theories and seem to have a good grasp on the observational effects of gravity at least. There was a recent announcement about mapping of the Gravitational Wave Background [0] using pulsars spread across the galaxy that was super cool too you might be interested in that I would say is related to this question.
The real answer is that theories like this require quite a bit of work to manipulate existing and complex math, and that you'd need someone who can translate an idea like yours into a mathematical model that fits with our observational data. That's an exceedingly difficult thing to do, as evidenced by the last 70ish years of physics.
The universe appears homogenous at various scales, meaning it's self-same within some amount of tolerance across itself. The distribution is homogenous. That's different from invariance, the assumption that a variable (in this case an intrinsic property such as mass) remains unchanged over time for a given subject of study, such as a particle.
Even if a given property can vary from subject to subject (even wildly), the sum of all subjects could still appear homogeneous in their distribution.
>why do we assume spacetime to be homogenous in its nature?
Because it's distribution appears to be consistent, at least as far as we can measure. That's not the same thing as objects at the quantum scale being invariant (or variable) in some way that we currently think is the opposite.
>Couldn't then dark matter be explained by some variations on a large scale? Like giant "wrinkles" in spacetime?
Considering the scales at which these fluctuations would have to occur for us to have not already measured them I'm doubtful they could build up to anything like that, even in aggregate and random patterns.
>They would then behave as pseudo black holes, or more like "black trenches", that lead to the structures we see today in the universe. The structures seem to have more mass than what we can actually see, but are in fact just placed in locations that behave differently gravity wise?
I don't think I'm really qualified to answer on how possible this interpretation is, but with the confirmation of gravitational waves a few years back we confirmed another piece of Einstein's theories and seem to have a good grasp on the observational effects of gravity at least. There was a recent announcement about mapping of the Gravitational Wave Background [0] using pulsars spread across the galaxy that was super cool too you might be interested in that I would say is related to this question.
The real answer is that theories like this require quite a bit of work to manipulate existing and complex math, and that you'd need someone who can translate an idea like yours into a mathematical model that fits with our observational data. That's an exceedingly difficult thing to do, as evidenced by the last 70ish years of physics.
[0]: https://www.space.com/gravitational-wave-background-universe...