6. THE STATUS OF INFLATION

Down to Earth astronomers are not convinced that inflation is a useful model. For them, inflation is a cute idea that takes a geometric flatness problem and replaces it with an inflaton potential flatness problem. It moves the problem to earlier times, it does not solve it. Inflation doesn't solve the fine-tuning problem. It moves the problem from "Why is the Universe so flat?" to "Why is the inflaton potential so flat?". When asked, "Why is the Universe so flat?", Mr Inflation responds, "Because my inflaton potential is so flat." "But why is your inflaton potential so flat?" "I don't know. It's just an initial condition." This may or may not be progress. If we are content to believe that spatial flatness is less fundamental than inflaton potential flatness then we have made progress.

Models of inflation usually consist of choosing a form for the potential V(). A simple model of the potential is V() = m2 2 / 2 where the derivative with respect to is V' = m2 and V" = m2. This leads to a prediction for the observable spectral index of the CMB power spectrum: ns = 1 - 8mp / 2 (e.g. Liddle & Lyth 2000). Estimates of the slope of the CMB power spectrum ns and its derivative dns / dk have begun to constrain models of the inflaton potential (Table 1 and Spergel 2003).

The observational scorecard of inflation is mixed. Based on inflation, many theorists became convinced that the Universe was spatially flat despite many measurements to the contrary. The Universe has now been measured to be flat to high precision - score one for inflation. Based on vanilla inflation, most theorists thought that the flatness would be without - score one for the observers. Guth wanted to use the Georgi-Glashow GUT model as the potential to form structure. It didn't work - score one against inflation. But other plausible inflaton potentials can work. Inflation seems to be the only show in town as far as producing the seeds of structure - score one for inflation. Inflation predicts the spectral index of CMB fluctuations to be ns 1 - score one for inflation. But we knew that ns 1 before inflation (minus 1/2 point for cheating). So far most of inflation's predictions have been retrodictions - explaining things that it was designed to explain.

Inflationary models and the new ekpyrotic models make different predictions about the slope nT of the tensor mode contribution to the CMB power spectrum. Inflation has higher amplitudes at large angular scales while ekpyrotic models have the opposite. However, since the amplitude T is unknown, finding the ratio of the amplitude of tensor to scalar modes, r = T / S ~ 0, does not really distinguish the two models. Finding a value r > 0 would however be interpreted as favoring inflation over ekpyrosis. Recent WMAP measurements of the CMB power spectrum yield r < 0.71 at the 95% confidence level.

Measurements of CMB polarization over the next five years will add more diagnostic power to CMB parameter estimation and may be able to usefully constrain the slope and amplitude of tensor modes if they exist at a detectable level.

One can be skeptical about the status of the problems that inflation claims to have solved. After all, the electron mass is the same everywhere. The constants of nature are the same everywhere. The laws of physics seem to be the same everywhere. If these uniformities need no explanation then why should the uniform temperatures, flat geometry and seeds of structure need an explanation. Is this first group more fundamental than the second?

The general principle seems to be that if we can't imagine plausible alternatives then no explanation seems necessary. Thus, dreaming up imaginary alternatives creates imaginary problems, to which imaginary solutions can be devised, whose explanatory power depends on whether the Universe could have been other than what it is. However, it is not easy to judge the reality of counterfactuals. Yes, inflation can cure the initial condition ills of the standard big bang model, but is inflation a panacea or a placebo?

Inflation is not a theory of everything. It is not based on M-theory or any candidate for a theory of everything. It is based on a scalar field. The inflation may not be due to a scalar field and its potential V(). Maybe it has more to do with extra-dimensions?