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No. (No, it predicts right things locally; no, dark energy is not in conflict with GR; and probably no on the scale of galaxies, with some assumptions).

We can (and do) test General Relativity to exquisite precision in the solar system.

Those tests constrain the local density of any sort of effectively undetectable matter which includes among other things the (thermal) cosmic neutrino background, lots and lots of relativistic neutrinos, and a fair amount of ultrarelativistic neutrinos (like those that ANITA studies).

Effective undetectability is a function of current technology versus the goodness of estimate of (high) flux of the particles; we can spot small numbers of GZK-interaction neutrinos (with various observatories, including ANITA), we can spot small numbers of Super-KK neutrinos (mostly because we know the path they follow), we can spot small numbers of solar neutrinos (there are A LOT of them and we also know what direction they're coming from), but we have no real hope right now of spotting relic neutrinos (since as we take the momentum to zero, we lose the ability to spot recoil interactions; the emitted photons get drowned out by the CMB; the cosmic neutrinos are also travelling in random directions, like the cosmic photons).

If we take the local density of any of these neutrinos way up, their gravitational effects in the solar system (and indeed in similar systems we can study with various different telescopes) will be pronounced, and straightforward to study with General Relativity.

We do see pronounced gravitational effects at the scale of galaxies; one way to explain them is to add a thin dust of slow-moving mass where the dust motes remain on extremely stable orbits (implying no heating from (photon) radiation, no cooling by emitting (dark? photon? whatever) radiation, and no collisions with ordinary matter dust).

Dark matter is extremely sparse at the scale of star systems -- but then star systems are extremely sparse at the scale of large galaxies! (Likewise, the interstellar medium is extremely sparse, but there's a lot of space among the stars!) Low-interaction is easy enough; Earth is highly opaque to ultrarelativistic neutrinos, but as you take the momentum of the neutrinos down, Earth becomes highly transparent to them (so do telescopes and other instruments, alas, which is why they are hard to observe). (Standard-model) neutrinos are too light to stay in the places where the gravitational effects are observed -- gravitational interactions with the ordinary mass of the galaxy would kick them away. So something else is needed. The question is what, microscopically, it is. However, wishing the gravitational effects away doesn't work, and neither does modifying General Relativity (at least not so far).

In the standard cosmology, Dark Energy is precisely a component of the Einstein Field Equations of General Relativity (it's literally \Lambda, the cosmological constant). So it is entirely the opposite of being in conflict with General Relativity. The research question is mainly why it takes on the value it does, and whether it does so in any sort of spacetime-position-dependent way.




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