# Why do we need to modify GR with theories like F(R) ?

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## Main Question or Discussion Point

Hi all,

I’d like to ask why do we need to modify the General Relativity with theories like F(R) modified gravity ?

Thanx

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phinds
Gold Member
2019 Award
Hi all,

I’d like to ask why do we need to modify the General Relativity with theories like F(R) modified gravity ?

Thanx
Who says we need to?

Let me ask the question in a different way.. why modified gravity theories have been made ?
And what are the consequences of a theory like F(R)?

Paul Colby
Gold Member
Let me ask the question in a different way.. why modified gravity theories have been made ?
And what are the consequences of a theory like F(R)?
The answer is clearly because one can. However, the hope is that one such theory might one day account for new phenomena like dark X where X is some value of observational data.

https://en.wikipedia.org/wiki/F(R)_gravity

Wiki is often a great source of very top level intro. There are also likely reviews.

Yeah, look since I started recently to study GR and its modified theories, I liked to discuss this here in the form ..

So dose not GR account for universe acceleration? I think it explains that depending on the cosmological constant ?
On the other side Dark energy assumed to cause the univrse expansion, so now GR dose not account this?
I’m little confused

Paul Colby
Gold Member
On the other side Dark energy assumed to cause the univrse expansion, so now GR dose not account this?
I’m little confused
Confusion is good. I'm not an expert by any means so if some of this is garbled you've been warned. Spiral galaxies don't work the way they are supposed to. The stars in them don't have the velocity profile one would expect based on Newton or standard GR. No, standard GR doesn't explain the accelerated expansion at early times as far as I know.

I see, thanks :)

Ibix
Dark energy doesn't cause the universe to expand. It just changes the expansion rate (or rate of change of expansion rate, in fact).

There are two things you should consider when data do not match theory. One is that theory is correct but you are missing something about the data. For example, Pluto was found because Neptune was not in quite the predicted place. And the Pioneer Anomaly turned out to be an unexpected thrust effect from the craft itself.

The other is to consider that the theory is wrong. For example, the anomalous precession of Mercury was, in fact, correctly predicted by GR where Newtonian gravity failed.

So GR can explain cosmology and galactic rotation curves, if you hypothesise some additional stuff that we can't see but have named dark matter and dark energy. But investigating alternative theories of gravity is also important - or at least has been. My understanding is that dark matter in particular is winning the argument even if we haven't directly detected it.

There are other reasons to develop alternative theories. One is why not? It can be interesting, and studying generalised models can yield insight even when they're not directly physically relevant. Another is so-called test theories, where you do something like assert that $F=GMm/(r+\alpha)^2$, then gather data to estimate the value of $\alpha$, which Newtonian gravity assumes to be zero. Here you aren't really proposing that $\alpha\neq 0$, but you are just checking anyway.

Finally, we look for theories of gravity to replace GR. It doesn't fit well with quantum theory, and it has singularities that we strongly suspect are only there in the maths. We expect there to be a better theory of gravity - we just haven't found it yet.

I don't honestly know where f(R) theories fit into that. Probably a mix of all of them, but I don't know.

Paul Colby
Gold Member
Looks to me like $f(R)$ theories are people writing down alternative Lagrangians and having at it. I found one "review" in the archive search.

https://arxiv.org/abs/1002.3868

Looks to be in the middle of the fray (not for beginners) type of paper but interesting read.

What I've read is that a special case of f(R) gravity, let´s say R2 gravity (starobinsky inflation model), gives a possible explanation of inflation in the first second of the universe. I'm almost sure that the most recent analysis of the B modes of the CMB are giving a dim signal (not 5 sigma of course) that one of the most probable (if not the most probable) hypothesis behind Inflation (if it happens to be true) is precisely Starobinsky Inflation (that is to say that, in this hypothesis, inflation was not caused by a new field - let's say, "inflaton"- but by a new metric term in the Lagrangian.

The stars in them don't have the velocity profile one would expect based on Newton or standard GR.
... and on our knowledge about the mass distribution which is known to be incomplete.

PeterDonis
Mentor
2019 Award
Spiral galaxies don't work the way they are supposed to. The stars in them don't have the velocity profile one would expect based on Newton or standard GR.
No, the stars don't have the velocity profile one would expect based on only taking into account the visible mass distribution and Newton or standard GR (the two are the same to within experimental error for this case). So one obvious way to proceed is to hypothesize additional mass that is not visible, i.e., dark matter.

If the dark matter hypothesis only helped to explain this one observation, that would only be weak evidence in its favor. But hypothesizing dark matter helps to explain a number of other observations as well, whereas no other hypothesis for explaining galaxy rotation curves does so. That is why dark matter is the current front runner.

standard GR doesn't explain the accelerated expansion at early times as far as I know.
Sure it does, with the appropriate stress-energy tensor for the inflaton field. Inflationary models use standard GR. They don't modify the laws of gravitation at all. They just introduce an inflaton field (a scalar field, at least in all of the models I am familiar with) and plug its stress-energy tensor into the Einstein Field Equation. The fact that a scalar field with a large vacuum expectation value yields a stress-energy tensor that causes rapid acceleration expansion (inflation) is easily shown and is a common homework problem in GR textbooks.

Paul Colby
Gold Member
No, the stars don't have the velocity profile one would expect based on only taking into account the visible mass distribution and Newton or standard GR (the two are the same to within experimental error for this case). So one obvious way to proceed is to hypothesize additional mass that is not visible, i.e., dark matter.
Sure, the question was why look at other theories. Has the mass distribution been measured, no. Is it the mass distribution the likely mechanism, yes. That's the prevailing view and, from what I hear, the best fit to the data.

haushofer
Hi all,

I’d like to ask why do we need to modify the General Relativity with theories like F(R) modified gravity ?

Thanx
We don't need to per se. But from an effective field theory point of view (EFT, a term which, I think, is highly relevant here and isn't mentioned before), one often takes the following philosophy:

* Consider the symmetries of your theory
* write down all the possible terms in your action
* put coefficients in front of them and let experiment decide what these coefficients are

Naively, the "f(R)-terms" contain higher order derivatives. And since the only length scale we know in GR is the Planck scale, the naive thing to do is to let units decide that these "f(R)-terms" are surpressed by powers of the Planck length. You've noticed the occurences of the word "naive" here, so this is all in the case of "gravity doesn't contain any other parameters beside the Planck length". Other theories, like string theory, also contain their own parameters (in this case the string length).

So, if you like the EFT-philosophy, the Einstein equations are just leading order terms in a theory which can be much more complicated (and whose complications probably only play a role at small lengtscales). Hence the "f(R)-terms".