November 5, 2002

Inflation and High Energy Physics

So, can one use measurements of the CMBR to detect the influence of high energy physics on the power-spectrum of primordial density fluctuations? Obviously, one crucial factor is the size of the corrections to the power spectrum induced by high energy physics at a scale Λ.

The usual calculation assumes as an initial condition that the inflaton field starts in the standard “Bunch-Davies” vacuum. But Danielsson and Easther et al have argued that a wider class of de Sitter-invariant vacua, the so-called α-vacua might plausibly be taken as initial conditions for the state of the inflaton field. If do, then the corrections to the power spectrum are of the order H/Λ, where H is the expansion rate at the time when a fluctuation of a given scale crosses out of the horizon.

The Stanford group have argued that it is problematic for the initial state of the inflaton field to be anything other than the Bunch-Davies vacuum. If they’re right, then the effect of high energy physics can only be encoded in higher dimension operators in the effective lagrangian for the inflaton, which lead to corrections of the order (H/Λ)2. While they try to put a bold face on it, it seems highly unlikely we could ever measure such a small effect.

Recently, it seems that the argument has been swinging in favour of the α-vacuum guys. If so, the effect might be eminently measurable in the near future.

The fly in the ointment (as Steve Weinberg keeps emphasizing to me) is that, while it is true that the power spectrum of fluctuations as they leave the horizon depends only on the slope of the inflaton potential at that time, what we see today depends on the whole shape of the inflaton potential. With a variable-slope potential, we can get pretty much anything we want.

If Steve’s right, there’s not much that we can conclude from these observations.

Posted by distler at November 5, 2002 6:06 PM

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