Talk:F(R) gravity

Derivation of field equations

I'm thinking of adding some of the intermediate steps of the derivation for the field equations for metric theory. Does anyone disagree/has any suggestions? Let me now. —Preceding unsigned comment added by 130.225.212.4 (talk) 15:19, 3 March 2009 (UTC)

I think that sounds like a good idea. It's way too early to worry that the article size is too big, so more detail can only improve the article in my opinion. One of these days when I find time I'd like to expand the Palatini section. Cheers, General Epitaph (talk) 01:58, 13 March 2009 (UTC)

Besides the derivation of the field equations, I also added a few things about massive gravity waves and a new reference. I think the article would also benefit if we expanded the other sections as well. Finally, I plan to add a few things about how f(R) theories manage to create acceleration without weird ad-hoc potentials etc.--130.225.212.4 (talk) 12:41, 20 March 2009 (UTC)

Cosmological constant

I fail to see how f(R) theories solve the cosmological constant problem. We still need to explain why the cosmological constant is so small (or even tinier compared to ΛCDM models). And the cosmological constant receives radiative corrections of order $\Lambda ^{4}$ where Λ is either the Planck scale or the SUSY breaking scale.

Hep thinker (talk) 13:49, 12 May 2009 (UTC)

Taylor expand f(R): $f(R)=f(0)+f'(0)R+...\,$ the constant term corresponds to Lambda and the 1st order term to GR. You can find many more elaborate models that approach arbitrarily close to Lambda and if I find time I might expand the relevant section.130.225.212.4 (talk) 08:57, 14 May 2009 (UTC)

Summary of "known problems" and obervational tests.

The article says in the introduction "Although it is an active field of research, there are known problems with the theory." and there are some comments scattered through the text. A section listing the "known problems" with each variant would be a useful addition for those of us not familiar with this work.

Some information on how it could be distinguished observationally from GR would also help, for example this article rules out some alternatives to GR but not f(R):

"Gravitational redshift of galaxies in clusters as predicted by general relativity"

George Dishman (talk) 14:09, 30 September 2011 (UTC)

Since f(R) gravity includes the case that f(R)=R which is GR and variations which are arbitrarily close to that such as f(R)=R+aR² for a arbitrarily close to zero, it is impossible to exclude f(R) entirely. One must specify a particular function for f which is palpably different from the identity function before such an experimental test could even be designed. JRSpriggs (talk) 23:57, 2 October 2011 (UTC)

I have added a section starting to talk about observational constraints. This needs much more work, particularly on cosmological tests. Hopefully people will continue to add things. --- BobQQ 20:41, 25 June 2012.

Dispersive waves

I am a little uncertain about the equation for gravitational waves featuring $h_{f}$. Since the scalar mode is massive it should be dispersive, therefore I think the formula giving the argument as just a function of $(t-v_{G}z)$ would only be appropriate for a single frequency component, and it would be necessary to prescribe the dispersion relation for the entire wavepacket. --- BobQQ 20:46, 25 June 2012.

Scalar of curvature without a metric?

To BobQQ: You just added "For metric f(R) gravity," to a sentence in your new section f(R) gravity#Observational tests. This makes me wonder what f(R) gravity would mean without a metric tensor. Since the scalar of curvature, R, is defined by

$R=R_{\alpha \beta }g^{\alpha \beta }\,,$

I do not see how one can even talk about f(R) gravity without the metric being present. With what do you replace the $g^{\alpha \beta }\,$? JRSpriggs (talk) 17:11, 26 June 2012 (UTC)

That is metric f(R) gravity as opposed to Palatini or metric-affine f(R) gravity. All three are documented in the main article, and in each case there is still a metric, the difference is in the derivation of the field equations. --- BobQQ (talk) 22:05, 26 June 2012 (UTC)

Thank you for clarifying that. Perhaps it would be better to say "metric-only f(R) gravity" or "f(R) gravity with Levi-Civita connection". JRSpriggs (talk) 23:38, 26 June 2012 (UTC)

Kleinert and Schmidt

I have just been through filling in information for the references. In doing so, I noticed that the paper by Kleinert & Schmidt only has four citations according to the NASA ADS. Having a small number of citations doesn't mean that the paper has anything wrong with it. However, I don't think it can be justified that it popularised the field. Currently the page reads: "It has become an active field of research following work by Starobinsky[2], and later Kleinert and Schmidt[3]". For comparison, the Starobinsky paper has 1190 citations. I suggest that unless anyone can justify the inclusion of the work of Kleinert & Schmidt, this is removed as spurious. — BobQQ (talk) 21:46, 24 July 2012 (UTC)

Although the article by Starobinsky has a much larger number of citations than Kleinert and Schmidt's (KS), it is not for its proposal of f(R)-gravity theories. It is for its proposal of smoothing out the singularity in the standard cosmological model by a loop effect in Einstein gravity. Thus Starobinsky's citation does, strictly speaking, not even belong into a Wikipedia article on f(R)-gravity. The general physical idea that all bending stiffnesses become weaker if the bending is more dramatic was first introduced by KS. It is motivated by the fact that all curvature stiffness of spacetime has its origin in the vacuum fluctuations of all quantum fields in the universe (Andrei Sakharov) whose trace-log creates a general action f(R). The fact that many people who based their work on this idea have not cited KS cannot be an argument against inserting that seminal paper into a Wikipedia article on the subject. Here historical correctness must be the relevant criterion. Best regards, Thomas Schultz 91.66.244.220 (talk) 07:21, 12 August 2012 (UTC)

It may that Starobinsky's work is cited for other reasons, but I think it is unfair to say it is not for f(R)-gravity. A quick scroll through the citing papers on NASA ADS does show a large number of papers with f(R) in the title; I suspect more are related than just indicated by their titles. It certainly seems notable enough to merit inclusion. I believe that it's main relevance is that it introduces an R² term which leads to rapid expansion of the early Universe, it is thus a possible explanation for inflation, which makes it relevant for cosmologists.

I am afraid I do not follow your explanation of bending stiffness. I am willing to trust you that it is of significance, and was first suggested by that work. However, that is not my concern with including the paper. I think it is incorrect to say that it popularised the theory. With so few citations it is obviously not popular. Similarly, there are many papers on f(R) gravity that predate that work. It cannot have been fundamental in establishing the field: if it did, I would at least trust the reviewing process of peer review journals to ensure it gets the citation it deserved.

By the way, I notice that your other contributions are to include references from Kleinert to Phase transitions, Classical XY model, Ising model. Are you a fan? — BobQQ (talk) 14:24, 12 August 2012 (UTC)

The cosmological constant term in the Lagrangian is as if spacetime had surface tension. The R term is as if spacetime had a stiffness that resists bending. So when he says that "all bending stiffnesses become weaker if the bending is more dramatic", what he is saying is that the R² term has a negative coefficient. JRSpriggs (talk) 18:20, 12 August 2012 (UTC)

Thank you, I think that explains the first half. I'm assuming that the sign of the coefficient also depends upon the various sign conventions, but as long as it is the the right relative to the others it works out. — BobQQ (talk) 20:10, 12 August 2012 (UTC)

Signs in variation of the Ricci Scalar

Hi! Is there a sign-error in the variation of the Ricci scalar? I get: $\delta R=R_{\mu \nu }\delta g^{\mu \nu }+\nabla ^{\mu }\nabla ^{\nu }\delta g_{\mu \nu }-g^{\mu \nu }\Box \delta g_{\mu \nu }$, so just the two signs switched. Then if you do partial integration, the signs change again and one obtains the same field equations. -- 129.240.190.125 (talk) 16:58, 22 March 2013 (UTC)

Perhaps you are forgetting that

$\delta g_{\mu \nu }=-g_{\mu \alpha }g_{\beta \nu }\delta g^{\alpha \beta }\,,$

right? Notice the minus sign!

Also since you must integrate by parts twice (for the two derivatives in each of the last two terms), their minus signs cancel each other. JRSpriggs (talk) 06:39, 23 March 2013 (UTC)

Yep, that's it! Thank's for that! -- 129.240.190.125 (talk) 09:27, 23 March 2013 (UTC)

Modified Newton's constant

In the discussion of the modified Newton's constant, what is k? Clearly not the FLRW curvature (the potential is singular when k=0) Bobathon71 (talk) 13:21, 15 December 2015 (UTC)

Factors in "Equivalent formalism" section

In the section Equivalent Formalism the factors of $\kappa$ (and 2?) are a bit wrong at least if we want the action for the scalar $\tilde{\Phi}$ to be canonically normalized. Indeed, $(\tilde{\nabla}\tilde{\Phi})^2$ is multiplied by $1/4\kappa$, while a canonically normalized one would be multiplied by $1/2$ only, certainly no $\kappa$, see for instance Einstein–Hilbert_action#Derivation_of_Einstein's_field_equations. — Preceding unsigned comment added by 2A01:E34:EC45:750:CD53:F3FC:F954:66AC (talk) 22:03, 8 May 2020 (UTC)