Modifications to Einstein-Hilbert action

[quasar_4]

I have been reading about some quantum gravity topics, and am wondering: how many different modifications to the Einstein-Hilbert action have been proposed? Is this a pretty big trend in research in quantum gravity right now?

 

[Haelfix]

Oye, that question involves counting an absolutely huge literature both for quantum gravity and even just for classical physics. There are uncountably many modifications possible (I haven't said anything about whether they are consistent or not) and in general you need to analyze each in turn to see if they can make sense, at least as effective field theories.

It starts with Brans Dicke models, Weyl gravity, and now days people chitchat about f(r) gravity and higher derivative models.. blah blah blah.

I'd say all the variants tend to be less elegant, more complex and harder to account for all the experimental successes, but indeed some can be shown to be plausible candidates.

 

[quasar_4]

Hm, so one might consider grouping the various sorts of propositions into different categories? It's hard trying to gauge the main points in the literature, because as you said, there's just so much... the math's not so bad coming from GR, but how all the modified theories relate, and what's getting tweaked with each separate one, is quite confusing to me!

 

[Haelfix]

I guess it all starts with what assumptions you want to drop and what symmetries you want to keep or to add and what regime you want your new theory to live in.

So for instance you could add a scalar term, and you'd like it to not affect the predictions of the low energy GR predictions (eg galaxies, structure formation, etc). So one way would be to make the scalar very heavy, and integrate it out to retrieve GR as the low energy physics.

But at high energy scales, it will generically give you new physics. This happens a lot in various quantum gravity theories. For instance string theory has something called a Dilaton, which is just an example of a scalar term added to the EH action. Alternatively something like a supergravity theory would generate a theory with a bunch of heavy scalars.

But maybe you don't want that, and want the scalar to be light so that its relatively trivial at high energies and affects the GR predictions. This would be something more like Brans-Dicke theory. Generically you will have more constraints from experiment for this sort of action.

So yea you could classify things based on the (scalar,vector, tensor) structure if you so chose.