7.3. Beyond the energy scale
To go beyond the energy scale entails bringing together as wide a range of observations as possible to try and constrain the wide parameter family. When restricted parameter sets are considered quite interesting constraints can be quoted, but these weaken once the parameter space is widened. Until recently no-one attempted a plausibly large parameter space, but recently Tegmark [28] considered a nine-parameter family of models, including the three inflationary parameters, which is the first attempt to get to grips with the large families of models that need to be considered for us to become convinced we are on the right track.
At present, observations are only quite weakly constraining concerning quantities beyond the inflationary energy scale. The spectral index is known to lie near one, with the plausible range, depending on what parameters one allows to vary, stretching from perhaps 0.8 to 1.2. As it happens, that is more or less the range which current inflation models tend to cover, and so most models survive. The holy grail for inflation model building is an accurate measurement of n, say with an error bar of around 0.01 or better. Such a measurement would exclude the vast majority of the models currently under discussion. MAP, and certainly PLANCK, ought to be able to deliver a measurement at around this accuracy level, and perhaps may even be able to see deviations from perfect power-law behaviour. [29, 30]
At the moment there is no evidence favouring a gravitational wave contribution to COBE, but equally the upper limit on such a contribution, perhaps around r < 1 depending on other parameters (see Ref. [31] for a recent analysis), is unable to rule out much in the way of interesting models (though it is a combination of the constraints on n and r that kills extended inflation). If such a contribution can be identified, it will be very strong support for inflation, but since many models, especially of the currently-popular hybrid type, predict insignificant gravitational wave production, even the strongest achievable upper limits may tell us nothing.
A particularly powerful test of inflation will be whether or not the microwave anisotropy spectrum (the Cl) proves to contain an oscillatory peak structure. [32] Such a structure is evidence of phase coherence in the evolution of perturbations (meaning that the perturbations of a given wavenumber are at a calculable phase of oscillation). Such phase coherence would indicate that perturbations are entirely in the growing mode, which in turn implies that they have been evolving sufficiently long for the decaying mode to become negligible. For modes around the horizon scale at decoupling, this implies that they were already in place while well outside the horizon, which is a characteristic of inflationary perturbations (a characteristic not shared by topological defect models, for instance). This fairly qualitative test, if satisfied, will provide strong support for the inflationary paradigm, while if a multiple peak structure is not observed that will imply that the inflationary mechanism is not the sole source of perturbations in the Universe.