Starobinsky Inflation and Supergravity

[Urs Schreiber]

The available experimental data prefers plateau models of cosmic inflation, and among them Starobinsky inflation (aka R^2 inflation) is preferred, even if maybe not significantly.

Since Starobinsky inflation is pure gravity (the inflaton field here is an effective incarnation of a higher gravitational curvature correction), it lends itself to embedding into supergravity models. There are some claims that the match of Starobsinsky inflation to data further improves after embedding into supergravity.

For instance Alexandre-Houston-Mavromatos claim that under mild (?) assumptions gravitino condensation produces just the right Starobinsky potential (here), while Dalianis-Farakos claim that a problem with the size of the initial homogeneous patch goes away after embedding into supergravity (here).

Clearly there are assumptions going into such statements. It would be good to have some feeling as to how robust these are. Does anyone here have further insight on this? I'd be grateful for comments and pointers.

 

[Mordred]

might help to have greater details than the links you posted.

https://arxiv.org/abs/1312.1155

At least now we have some of formulas involved.
I was hoping Encyclopedia inflationaris would have some further details but I don't see this particular model under this article which analyzes numerous inflationary models. However its still useful as it provides additional details on Higgs inflation which the first article does a comparison.

https://arxiv.org/abs/1303.3787

Hope this helps

 

[Urs Schreiber]

might help to have greater details than the links you posted.
https://arxiv.org/abs/1312.1155
At least now we have some of formulas involved.
Hope this helps

That one and further relevant articles are referenced from where my links point to. In fact the one you just cited is not really relevant to the question regarding the relation to supergravity.

But if you haven't seen the Starobinsky model before, then please don't bother. What I am after here is some expert who would have some inside knowledge beyond what one sees from the published literature. Any such expert here on this forum?

 

[Mordred]

That one and further relevant articles are referenced from where my links point to. In fact the one you just cited is not really relevant to the question regarding the relation to supergravity.

But if you haven't seen the Starobinsky model before, then please don't bother. What I am after here is some expert who would have some inside knowledge beyond what one sees from the published literature. Any such expert here on this forum?

Sorry for trying to help provide some additional resources. I seriously hope this type of response hasn't become typical on this forum. If that's the case I have better things to do

 

[Urs Schreiber]

I seriously hope this type of response hasn't become typical on this forum. If that's the case I have better things to do

Hey Mordred, sorry, and my apologies if I have upset you. But then you need to help me see what you mean.

I had gone through some effort of collecting and commenting on precise pointers to the background on the question I have (to recall, they are here). Now you give what seems to me to be a random pointer to a reference that speaks about the Starobinsky inflation, but does not touch on the question that I asked, which regards the embedding into supergravity (these same authors do discuss that question elsewhere, in other articles, as referenced behind my link above). If you do feel your reference is a reply to my question, please help me and give me more details, such as which statement or equation on which page you suggest me to look at again.

 

[Mordred]

No problem. Comparing robustness between inflationary models is to say the least tricky. Which was why I was hoping Encyclopedia inflationaris would have provided some insight as that is the purpose of the ASPIC library.

As far as supergravity embedding this sounds like a SUSY based model. In this regards its easily related to the SO(10) MSSM Higgs inflation. Which is most likely one of the reasons their is similarities. When I click your hyperlinks specific to your question I keep getting the same page. In other words I'm not getting the specific details directly concerning your question

Ah found the equations give me a bit

Edit its going to take a bit of study.

 

[Urs Schreiber]

When I click your hyperlinks specific to your question I keep getting the same page.

The links I gave point to specific anchor points in one big page on Starobinsky inflation. The anchors are supposed to take you directly to those paragraphs where the exact issue that I asked about is referenced.

If this works, you should be taken to the page, scrolled down to that specific paragraph, with that paragraph (or its headline) highlighted in gray.

If this does not work on your system, it would help me to hear which specific installation, browser type and browser version you are using. Then I can forward that information to our sysadmin for it to be fixed (if possible).

 

[Mordred]

I'm looking at the articles referenced by page for the specific formulas. Its going to take me a bit to go through. The one paper referenced (Farakos) is dealing with tighter constraints than the Starobinky.

It seems to be suggesting an earlier symmetry breaking scheme via the gravitino. This will cause additional thermodynamic degrees of freedom which should deviate from strictly scalar field modelling. This will also have implications on the number of e folds. In essence Farakov is arguing that if inflation started at the end of the Planck era inflation shouldn't have occurred instead a collapse should have resulted. I find that difficult to swallow so need time to better understand his argument. Particularly since one of his arguments involve curvature. Yet curvature a such a tightly condensed size scale shouldn't be an issue as were literally dealing with less than a Planck length. Why should curvature matter at such a finite scale? At the moment I'm finding Farakov's arguments difficult to buy into

Get back to you when I gather more details

 

[Mordred]

Ok Starobinky R^2 model vs Farokov's R+R^2 model. From what I can tell the R^2 is a better fit to the Planck constraints. Several of the referenced Planck papers agree that the Starobinsky model fits within the Planck constraints. From what I see the Farokov doesn't match as close.

Some further insights Both models are f (r ) gravity which is in essence a modified gravity theory. You can get a pedagogonal review here. There is a small section covering Sarobinsky.

http://xxx.lanl.gov/abs/1002.4928

I found the Sarobinsky inflation comparison in encuclopedia inflationaris. see section 4.13 it mentions some issue with fine tuning which Farakov has been alluding to.

I'm not really familiar enough on F (R) gravity to give an accurate assessment on it.

 

[Urs Schreiber]

Ok Starobinky R^2 model vs Farokov's R+R^2 model.

Mordred, wait a second. There is no such distinction, the original Starobinsky model also has an R-term. It's a correction of Einstein gravity by a higher curvature term. And the author you mean to quote is called Farakos, not Farokov. The modification of the Starobinsky model that he and coauthors (and several other groups) consider is extension to super-gravity, and that's what my question is about.

I do appreciate that you are energetic about trying to provide me with feedback, thanks. But while you are trying to learn about the basics underlying the question that I am asking, let's maybe leave it at that. If we produce too much noise here than the chances that some expert sees this and replies become smaller still.

 

[Mordred]

Sure at least you can see some further details from the extra links. As stated not too familiar with the F(R) models. Though I will be surprised if anyone is already familiar with these models specifically. More likely anyone replying will have to examine them as I have been doing lol.

The question I have is how familiar with the mathematical specifics with these models are you? Is there a specific problem you are having in understanding them?
A more targetted direction of interest might help.
Ie is your concern more on supergravity as opposed to the distinctions between the two?

You may find this handy as well but as this is a very complex topic it might help

https://arxiv.org/abs/1005.3630

However I'm simply not familiar enough with these specific models. So would need considerable time studying them