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C. Tests of Inflation

We first briefly discuss the classic tests of inflation and then continue with some more subtle issues. More extended discussion of many aspects of these tests can be found in the report of the P4.3 group on CMB and Inflation.

1. Density

Essentially all models of inflation involve a large amount of slow-roll inflationary expansion, much more than the minimum 60 e-foldings required. The curvature of the Universe today is completely negligible in these models, and thus we have the prediction Omegatot = rhobartot / rhoc ident 1. However, we only measure rhobartot and rhoc in the part of the Universe we can observe. Fluctuations in the matter density on the scale of the present Hubble radius (part of the same spectrum of fluctuations that produced galaxies and other structure) give the distribution in the predicted Omegatot a small width at the level of one part in 100,000 (much smaller than the current observational uncertainty).

The current observations on this front are consistent with the predictions from inflation. Data from the three most recent CMB experiments give Omegatot = 1.01 ± .08, 0.97 ± .10, 1.0 ± .14 (from DASI [Halverson et al.(2001), Pryke et al.(2001)], BOOMERANG [Netterfield et al.(2001)], and MAXIMA [Lee et al.(2001)] respectively). Combining all these experiments and others [Wang et al.(2001)] results in Omegatot = 1.0+ .06- .05. This result is particularly impressive since the largest contribution to Omegatot comes from the mysterious dark energy. Little is known about the nature of the dark matter and energy of the Universe (see sections II and III of this report). The one sure thing is that it all adds up to match the inflationary prediction. Future observations will determine Omegatot to higher precision and offer an opportunity to either confirm or falsify the standard inflationary picture.

2. Coherence from inflation

As discussed at length by the P4.3 group, inflation gives the density fluctuations a special property called "coherence" [Albrecht(1997)]. This property is related to the dominance of very specific perturbation modes. One manifestation of coherence from inflation is a specific type of oscillation in the spectrum of CMB anisotropies. Each new round of CMB data has increased the observational evidence that these oscillations are really there. Already a class of competing models for the origin of cosmic structure, the cosmic defect models, have failed largely because they lacked sufficient coherence to match the data. Figure 1 illustrates this important result. Future observations will produce much more stringent tests of coherence and provide an opportunity to support or falsify the inflationary origin of cosmic structure.

Figure 1

Figure 1. Coherence in the CMB: Three models of the Cosmic Microwave Background anisotropies are shown with a compilation of the data. The two dashed curves represent defect models. The short-dashed curve is an exotic departure from the standard picture with the sole motivation of providing a better fit to the data, but even this curve fails to fit the oscillatory behavior. The inflation model (solid curve) with its coherence-related oscillations fits well. Details of this plot can be found in [Albrecht(2000)].

3. Gravity waves from inflation

Perhaps the boldest prediction of the inflationary picture is the existence of a cosmic gravity wave background (CGB). There is no known alternative physical process that would predict anything comparable, so the detection of this background would be powerful evidence in favor of inflationary cosmology. As with the density perturbations, the gravity wave background is the result of stretching the zero-point quantum fluctuations in quantum gravitational wave fields (tensor metric perturbations) to cosmic scales. Observation of the gravity wave background would provide strong evidence that the tensor modes of Einstein gravity are quantum mechanical, a very significant result given the problematic nature of quantum gravity. At the levels predicted by inflation, however, the CGB will be very hard to detect. Perhaps the best hope is through signatures in the polarization of the Cosmic Microwave Background, as discussed in the P4.3 report. It seems that a direct detection of the CGB will remain a challenge for future generations of cosmologists, but one with very exciting implications. (Extensive discussion of these and related issues can be found in the reports of the P4.6 group. A nice summary can be found in ref. [Hughes et al.(2001)]).

4. The scalar spectral index

As examined at length in the P4.3 report, inflation predicts a "nearly scale invariant" spectrum of density perturbations (scalar metric perturbations). This corresponds to a "scalar spectral index" ns for density perturbations of nearly unity. So far, the CMB observations are remarkably consistent with this value, and increasingly tight constraints on the spectral index can be expected in the near future. The precise nature of the deviations from scale-invariance depend on the model, but deviations of much more than 20% are outside the scope of the standard paradigm.

5. Further tests of inflation

As more data comes in, one can begin to take seriously the idea of making even more detailed tests of the inflationary machinery. After all, a model of inflation proposes a very specific origin for the perturbations that formed every observed object in the Universe. Interesting work has been done on the prospects of actually reconstructing the inflaton potential from cosmological data, and the possibility of other tests is currently an active subject of investigation. (Further discussion on reconstruction of the inflaton potential can be found in [Hughes et al.(2001), Turner and White(1996)]).

6. Can one really test inflation?

A wide variety of models of the Universe have some kind of inflationary period. A standard paradigm has emerged, which encompasses the vast majority of existing models. That is the picture described so far in this section. There are a few intriguing alternative scenarios which incorporate a period of cosmic inflation but which look very different. For example, there are models in which our Universe exists inside a single bubble produced in a cosmic phase transition. A small amount of inflation is arranged to happen inside the bubble, and in such models Omegatot neq 1 is possible.

So what does it mean to test inflation? The tests described above are tests of the standard paradigm of inflation. If all the tests come out positive, the standard picture will have passed some impressive milestones. If one or more tests are negative, the standard picture will have been falsified, and attention will shift to alternative ideas. Thus the field is poised to make dramatic progress. There is a standard paradigm which is clearly falsifiable by experiments that are well within reach.

Occasionally there are debates about whether testing the standard picture described above is truly testing inflation, because exotic alternatives exist. As always, what is tested by observations is determined by the nature of the observations, not by abstract philosophical debates. We urge the community to not let these debates of principle detract from the fact that there is very exciting progress to be made.

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