Liam Mc Allister: Inflation in String Theory

Here we go with another report from PPC 2008. This one is on the talk by Liam Mc Allister from yesterday afternoon session. In this case, I feel obliged to warn that my utter ignorance of the subject discussed makes it quite probable that my notes contain nonsensical statements. I apologize in advance, and hope that what I manage to put together is still of any use to you, dear reader.

The main idea discussed in Liam’s talk is the following: if we detect primordial tensor perturbations in the cosmic microwave background (CMB) we will know that the inflaton -the scalar particle responsible for the inflation epoch- moved more than a Planck distance in field space. Understanding such a system requires confronting true quantum gravity questions. String theory provides a tool to study this.

Inflation predicts scalar fluctuations in the CMB temperature. These evolve to create approximately scale-invariant fluctuations, which are also approximately gaussian. The goal we set to ourselves is to use cosmological observations to probe physics at the highest energy scales.

The scalar field has a potential which drives acceleration. Acceleration is prolonged if is rather flat. How reasonable is that picture ? This is not a macroscopic model. What is ? The simplest inflation models often invoke smooth potentials over field ranges larger than the Planck mass. In an effective field theory with a cutoff one writes the potential with powers of the ratio . Flatness is then imposed over distances . But must be smaller than the Planck mass, except in a theory of quantum gravity.

So one needs to assume something about quantum gravity to write a potential. It is too easy to write an inflation model, so it is not constrained enough to be predictive. We need to move to some more constrained scenario.

Allowing an arbitrary metric on the kinetic term, and an arbitrary number of fields in the lagrangian, the potential is very model-dependent. The kinetic term has higher derivative terms. One can write the kinetic term of the scalar fields with a metric tensor G. G is the metric on some manifold, and can well depend on the field themselves. An important notion is that of the field range.

Liam noted that the prospects for excitement in theory and experiments are coupled. If the parameter is smaller than 1, there are no tensors and no non-gaussianity, and in that case we may never get more clues about the inflaton sector than we have right now. We will have to be lucky, but the good thing is that if we are, we are both ways. Observationally non-minimal scenarios are often theoretically non-minimal: detectable tensors require a large field range, and this requires a high-energy input. If anything goes well it will do so both experimentally and theoretically.

String theory lives in 10 dimensions. To connect to 4D reality string theory, we compactify the 6 additional dimensions. Additional dimensions are small otherwise we would not see a newtonian law of gravity, since gravity would propagate too much away from our brane.

Moduli correspond to massless scalar fields in 4-dimensions. Size and shape moduli for the Calabi-Yau manifold. Light scalars with gravitational strength couplings absorb energy during inflation. They can spoil
the pattern of big bang nucleosynthesis (BBN) and overclose the universe. The solution is therefore that sufficiently massive fields decay before BBN, so they are harmless for it (however, if they decay to gravitinos they may still be harmful).

The main technical extension: D-branes, by Polchinski in 1995. If you take a D-brane and you wrap it in the compact space, it takes energy that creates a potential for the moduli. It makes the space rigid.
The tension of D-branes makes distorting the space cost energy. This creates a potential for the moduli.

Any light scalars that do not couple to the SM are called moduli. Warped D-brane inflation: it implies warped throats. A CAlabi-Yau space is distorted to make a throat. This is a Randall-Sundrum region. It is the way by which string theory realizes it. A D-3 brane and an anti-D3 brane attract each other.

The tensor-to-scalar ratio is large only if the field is moving over planckian distances, . That is the diameter of the field space. It is ultraviolet-sensitive but not too much so.
In our framework, observable tensors in CMB mean that there has been trans-planckian field variation.

Can we compute the in a model of string inflation ? Liam says we can.
Planckian distances can be computed in string theory using the geometry. The field is the position in the throat, so is the length of the throat. It is reduced to a problem in geometry. The field range is computed to , where N is the number of colors in Yang-mills theory associated to the throat region. N is at least a few hundred!
So the parameter is small with respect to the threshold for detection in the next decade, since .

N has to be large for us to be using supergravity. You can conceive a configuration with N not large,
but then we cannot compute it. It is not in the regime of honest physics, in that case. There are boundaries
in the space of string parameters. So we are constraining ourselves in a region where we can make computations. It would be very interesting to find a string theory that gives a large value of .

Liam’s conclusions were that inflation in string theory is developing rapidly and believable predictions are starting to become available. In D-brane inflation, the computation of field range in Planck units shows that detectable tensors are virtually impossible.