That's literally what dark matter is. It's something else that bends space. It's called "dark" because no one knows what it is.
It's called "dark" because we can't see it, except for the gravitational effects it has on visible matter.
Neutrinos hardly interact at all with normal matter, as such it is a form of dark matter called hot dark matter[1].
However based on measurements we've ruled out[2] neutrinos as the main source of dark matter, hence we're looking for something else.
Since the only clue we have so far is the gravitational effect, it is possible that the solution is to modify the theory of gravity instead of finding new particles. People are looking into this as well. And heck, maybe it's both. Time will tell!
[1]: https://en.wikipedia.org/wiki/Hot_dark_matter
[2]: http://w.astro.berkeley.edu/~mwhite/darkmatter/hdm.html
It is rarely mentioned amongst all the Higgs back-slapping, that the Standard Model does not yet have a complete and verified theory of neutrino physics: masses? Majorana/Dirac? self-anti-particle? chiralities? ...
There may be right-handed neutrinos that do not interact via the weak force (which is maximally parity-violating). They would only interact gravitationally and play a role dark matter: