Planck and the inflationary universe

Last week saw the first release of new measurements of the cosmic microwave background by the Planck satellite . There have been many articles and blogposts on the results (see last post), all noting that the data fit well to the standard ‘ΛCDM’ model of a universe containing dark energy (69.2 +- .019 %), dark matter (25.8 ± 0.4%) and ordinary matter (4.82 ± 0.05%). Other results are a slightly revised value of the Hubble constant (67.3 +- 1.2 km/s/MPC) and a revised estimate of the period of expansion (13.8 billion years), aka ‘a new age for the universe’. However, there has been relatively little discussion of the implications of the Planck data for the theory of inflation.

As we saw in previous posts, the theory of cosmic inflation suggests that the universe underwent an extremely rapid, gigantic expansion in the first fractions of an instant, expanding in volume by a factor of about 10⁷⁸  in the time interval 10⁻³⁶ to 10⁻³² of the first second. Such numbers seem crazy in comparison with the relatively sedate expansion of space observed today (Hubble constant above), but inflation gives a very neat solution to several different problems associated with the big bang model; a lack of magnetic monopoles in the universe, the smoothness of the cosmic microwave background, and the fact that the geometry of space appears to be flat. Best of all, it can be shown that inflation provides a natural explanation for the tiny perturbations in the microwave background that gave rise to today’s galaxies (it is thought that quantum fluctuations in the infant universe were amplified by inflation to become the seeds of today’s galactic structures).

Inflation posits an extremely rapid expansion of space in the first fractions of a second

Inflation has become an extremely successful paradigm in big bang cosmology, and today there are few non-inflationary explanations for the geometry of the universe or the formation of structure. But what exactly was the mechanism of inflation? There are over a hundred distinct models; although the WMAP satellite gave results that are consistent with the general idea, the data did not allow one to discriminate between the different models of inflation. So how about Planck?

The first result is that Planck gives a measurement of Ω_k = -0.0005 +- .07 for the curvature of space. This indicates a universe that is very close indeed to flatness. This result confirms and extends  many complementary measurements of the geometry of the universe and strengthens the case for inflation (essentially, inflation predicts that the universe expanded so quickly that any large-scale curvature was quickly smoothed out, just as a balloon blown up to gigantic proportions will appear flat to an observer). Explaining a spatial curvature that is exactly flat without inflation is extremely difficult as it requires a very special balance between the competing forces of expansion and gravity, so this is an important triumph for inflation.

A second profound result from Planck is that the ‘power’ spectrum of the perturbations in the microwave background has a ‘spectral index’ of 0.96 +-.009. This value, close to 1 but slightly less, is exactly consistent with almost all models of inflation. Best of all, the Planck data allow allow us to separate out two spectral parameters that could not be disentangled before (n_s and r, see here). The upshot is that the new data render some inflationary models very improbable, while others remain possible but with new constraints.

Inflationary models (lines and circles) vs the Planck data; points within dark blue and grey shading represent confidence intervals of 95% and 68% respectively

In particular, many complicated inflationary models such as power-law, double-field, and hybrid-model inflation are now effectively ruled out. (These results are backed by a lack of detection of non-Gaussianity in the CMB spectrum). Instead, the simplest ‘slow-roll single field’ type models are firmly in the frame of possibility (yellow and orange lines for example) . Intriguingly, it seems a Higgs-type field is also a possibility if it is strongly coupled to gravity.

Slow-roll inflation; a slowly decaying potential is required for inflation to end in a manner consistent with the observable universe

All in all, a spectacular vindication for inflation, a theory that was once considered far too contrived to be true. You can find more on this in the official summary of the Planck results here  (p36) or the specific Planck paper ‘Constraints on Inflation’ here.  This is how science progresses; painstaking analysis of models gives predictions that can be compared to emerging data. Many possible scenarios are ruled out, while others remain possible. Overall, it is important not to lose sight of the main result i.e. that the extraordinary phenomenon of cosmic inflation is almost certainly right and the simplest models are looking most likely! (Note that there is a misprint in the summary paper: the text on page 36 should refer to fig 26, not 23 – you saw it here first).

The next step is that more detailed observations by Planck may be able to detect a phenomenon known as B-mode polarization in the microwave background; if so, this could allow us to narrow the inflationary candidates down further, not to mention provide us with the first observation of gravitational waves.

Planck and the cyclic universe

One intriguing alternative to inflation is the ekpyrotic cyclic universe. In this model, the big bang is the result of a collision of two branes in a cyclic universe. Such models can reproduce all the characteristics of a standard big bang universe in a natural way, without the extra premise of inflation and its special initial conditions. As a bonus, the postulate of a big bang in the context of a cyclic universe is very attractive because it sidesteps difficult philosophical questions such as ‘when did the laws of physics become the laws of physics?’ or ‘when did spacetime become spacetime?’

During his presentation at Cambridge last week (see last post), Professor Paul Shellard mentioned that the new Planck data render many cyclic models, including the ekpyrotic universe, a lot less likely. At question time, I asked him what aspect of the new data disfavours the cyclic theories; it seems the lack of non-Gaussianities in the CMB spectrum rules out the conversion mechanism required by most cyclic models. However, Paul also suggested that the cyclic theorists would no doubt overcome this temporary setback by tweaking their models! I haven’t found much on this in the Planck papers so more on this later…