How is are privacy/anonymity affected by the use of HTTP/2? Did anyone look into this yet?

I suppose that timing attacks might be simpler, because HTTP/2 has sever push and not-requested content might be sent, until the browser cancels them. On the other hand the use of a single (encrypted) stream might make that harder, when looked on from the outside.

Does the protocol introduce new possibilities for fingerprinting?

Is there any research on this yet? Does the TBB take HTTP/2 into consideration? If there was no research yet, would it make sense to disable HTTP/2 for now, until implications are better understood (and workarounds for any problems that might pop up are in place)?

And maybe as side question: How does HTTP/2 affect browsing speed? The protocol might be optimized, but high latency seems to be a bigger issue than with HTTP/1.1.