Constraining Inflationary Models I: The Spectral Index.

Inflation is characterized by an exponential expansion.  (Literally.)  One interesting property of an exponential expansion is that it is, what is known as, scale invariant.  This means if a 1 meter chunk of space doubled in size, then so did a 10 meter, and a 17 meter, and a 1898876 meter, etc...

If inflation was a purely classical process, then the spectrum of perturbations (fluctuations of spacetime) produced by inflation should be completely scale invariant.  (Since the expansion was an exponential.)  Without going into the technical details, cosmologists quantify just how scale invariant these perturbations are with a parameter call the spectral index n_s.  If n_s = 1, the perturbations are completely scale invariant.

However, if inflation is quantum in nature, the exponential expansion should end with measurable quantum fluctuations in it.  If this is the case, the spectral index should not quite be one.  Various inflationary models predict different values for n_s with a single scalar field inflation predicting n_s  = 0.96.

The latest WMAP 7 papers show that the best value, to one sigma, is n_s = 0.963±0.012.  See the plot above to see the best fit values for the spectral index n_s and the tensor to scalar ratio r. (Which will be talked about in the next post.)  Also in this plot are various predictions for many popular models of inflation.  As you can see, many are still withing the 95% confidence window. (Not all models are shown.)

This shows a couple things: One inflation really is a quantum process.  The value you get from a purely classical exponential expansion is ruled out by 3 sigma.  Second, as stated before, the simplest model of a single scalar field driving inflation is the one that works best.

Unfortunately,  enough other inflationary models are within a sigma or two of this value that we need more parameters to distinguish between the models.