Second, you seem to be implying (eq.2) that the translation non-invariance is characterised by a fixed _comoving_ length scale. So the zone of influence of the ’speck of dust’ (or piece of string, etc) that sources the violation effectively grows along with the scale factor. While this may be convenient for considering things occurring at one given era, it seems physically counterintuitive. If the new physics that produces translation non-invariance has a certain length scale, which generally implies an energy scale, I would not expect this scale to change hugely with time. This is more or less what you are arguing anyway in comparing the inflationary energy density to the Planck energy: you are thinking that new physics kicks in with a certain fixed physical (not comoving) energy and length scale.
Of course the imprints which it leaves at any given time will grow with the Universe’s expansion, so the actual effect on the calculations might not be very large.

This could have some bearing on the question of whether you need to assume that ‘the violation vanishes after the inflationary era’. If the _physical_ length scale of the violation is fixed, say somewhere round the GUT scale, then it doesn’t have to be turned off by hand – it just gets diluted to insignificance once the Hubble length gets much bigger.

But I’m really not too impressed that one can make “impressively precise predictions” with the current hypothesis. The current set of hypothesis gives one so many degrees of freedom that practically anything can be “predicted”. E.g., you want to explain the distribution and velocities of matter in a galaxy. How do you do that in the current regime? Well, you design a distribution of “dark matter” specifically to explain the observations, overlay it on the galaxy, and — surprise! — it predicts your observations with impressive precision. Doesn’t seem very satisfying to me.

Sean, thank you for your willingness to post this kind of stuff! I like your political ideas too!

You can keep the puppies. They leave too much biological dirt!

&lt \delta_0 \delta_0 \delta_1 &gt ~ (x-z)^2/d^2 P_k^2

(P_k is the power spectrum)

Have you taken a look at the non-gaussianities for such a model? I.e. the leading non-Gaussian term would be

~ (x-z)/d^2 P_k^2

if we assume \delta_1 is some form of expansion in \delta, i.e. \delta_1 ~ \delta_0^2.

This looks suspiciously like the f_NL bound that you might just grab off from WMAP5 results (roughly).