Is Phi Squared Inflation Compatible with Latest Planck Data?

[slatts]

Looking at blogs about the 2-5-15 Planck data release, I noticed a couple of them claiming that it rules out some of the simplest models of inflation, including one called "phi squared inflation". I can't read the specialized characters in physics notations, but I'm figuring this is the same as "curvature squared inflation". Could someone do me the favor of verifying this, and telling me whether either of them is a version of "new" (AKA "slow roll") inflation or a version of "chaotic" inflation? This would help me keep a layman's grip on the subject, in view of the fact that a February 9th paper endorsed by the Planck organization itself states that the latest data IS compatible with "simple inflationary models". Thanks.

 

[Chalnoth]

No, it's not the same. Curvature squared inflation models are quite different and well within the error bars, while $\phi^2$ looks disfavored.

 

[slatts]

Thanks. I've been especially interested in Aguirre & Gratton's attempt to bridge the gap between steady-state and inflationary cosmologies, which was critiqued by Vilenkin in 2013's "Arrows of Time and the Beginning of the Universe", on the web. Vilenkin sees the AG version as compatible with false-vacuum inflation, and also with the BGV Theorem, which requires a beginning for inflation itself, but not necessarily for the multiverse containing it. (He does see the AG multiverse as having a little problem of being "surrounded by singularities", but I'm guessing that would be unavoidable, as the Cauchy surface--which he equates to a three-sphere--would presumably be dual, and consist, at each instant of global time, of a sub-Planck-scale diminishing sphere within a larger expanding one, with a contingent impossibility of any determination as to which they occupy by those dwelling on either.) Is phi squared inflation one of the large-field versions or one of the false-vacuum varieties?

 

[slatts]

Thanks again, for the LaTex reply. I'm flattered that you thought I'd understand it. Eventually, I was able to figure out that the Greek letter phi--which Wikipedia says means "angle"--stands for the inflaton field. A 2014 piece on a failed attempt to renormalize chaotic inflation that was crawling with phi ^2 [of course, I think of it as fi^2] strongly suggests that chaotic inflation must've been the "simple model" that the blogger in Cambridge felt had gotten ruled out by Planck's data release. That would leave the false-vacuum-compatible AG scenario in the clear. (As you can imagine, I picture the singularities which Vilenkin says "besiege" it to be a handy privacy fence. What's wrong with that?)

 

[bapowell]

Is phi squared inflation one of the large-field versions or one of the false-vacuum varieties?

Large field. Plot it out -- it's the parabola $V \sim \phi^2$ and so it has no false vacuum ($V(0) = 0$). The field begins far from the minimum, at a distance of several Planck units at least, and rolls down.

 

[slatts]

Thanks mucho. I'm amazed to have been right about something.