maxitg / susy-dbi Goto Github PK

Slow roll approximation is not valid due to instanton corrections being the same order of magnitude as \mu.

There are two possible fixes:

1. Set \beta << 1. In this limit, inflation can still be produced, however, the behavior changes considerably, fine-tuning is required, and the results are essentially similar to
   https://arxiv.org/abs/1712.01357
2. Set T << 1. In this limit, instanton corrections are much smaller than \mu, however, since T only appears as an overall factor in the slow-roll Lagrangian, results do not change at all.

The paper motivates the model from the trans-Planckian problem of axion inflation (the fact that we must take the axion scale f > Mp in the original potential of natural inflation). It would be very interesting to provide also a scan of the values of f obtained for the various realizations presented in figures 1 and 2. Does this scan extend in the sub-Planckian region ? (the scan should be easily done, once the above questions 2.4 and 5 are answered).

Nearly all relations in the paper are given in an implicit way, (for example keeping derivatives of the superpotential unspecified). In my opinion, the paper would improve if it showed the following explicit results

A check that the real directions ρ1 and ρ2 are indeed stable, also in presence of Wsb and of subleading terms in 1/T. To ensure that these direction are stable during inflation, and to avoid potential problems with isocurvature modes from inflation, one should verify that the real directions are sufficiently heavy, namely parametrically heavier than the Hubble rate. One should provide the explicit expressions for the masses (from the curvature of the scalar potential in the minimum) in terms of the parameters of the model, and verify that they are greater than H (also given explicitly in terms of the parameters of the model).

The scan shown in Figure 1 contains no real information, unless one specifies what is varied
among the different points. The only information I could find on this regard is we allow α1 to vary
at the end of page 12. How is it varied ? (in which range ? Is it a uniform sampling in linear units
? In log units ?) What is chosen for the other parameters of the model ? (?,?,A,T). How is the cor-
rect normalization of the scalar perturbations enforced? (this is typically done by fixing the overall
scale of the scalar potential). Are subleading terms in 1 important ? The scan strategy should T
T be completely described, so that any reader, if interested, could precisely reproduce those figures.

It would be useful to see the explicit form of V(a−), when the other fields are set to the minimum. In this way the reader can see the explicit form of the inflaton potential used in the numerical evolutions. If many terms are present, it would be useful to single out the dominant ones (I would expect the usual cosine potential, plus corrections; please provide the expression for the dominant term and the leading correction). 2.4) The parametrization (3.19) suggests that ρk = ak = 0 in the minimum of the potential. Therefore, as it is standard, the axion scale fk is obtained from the minimization of the scalar potential. Please provide the explicit relation that gives fk in terms of the parameters of the model.

I don't understand eq.(6.1). The conventional way to find the end
of inflation is to find the moment at which $\ddot a = 0$ (second derivative of the
scale factor with respect to time). The number of e-folds during inflation is
typically defined from $a(N ) \equiv a_{end} e^{-N}$ , which gives $\frac{dN}{dt} = -H$ (where $a_{end}$ is the value of the scale factor at the end of inflation, and H is the Hubble
rate). In this way, $N = 0$ at the end of inflation, while N is positive at
early times during inflation. How is eq. (6.1) used to determine the end of
inflation ? What is the purpose of setting $\theta_n = \frac{1}{16}$? Why don't the authors
find from their numerical evolutions the point at which $\ddot a = 0$

There are different shapes of non-gaussianity (the equilateral and the local shapes being the most studied ones), and the limits on non-gaussianity strongly depend on the shape. By shape, we mean the dependence of the bispectrum on the ratios k2/k1 and k3/k1. The paper cites [64,65,66]. Eq. 11 of [64], which is also eq. 1 of [65], and eq. 17 of [66] defines the so called local shape. This is different from the shape of non-Gaussianity obtained in DBI models, which is very close to the equilateral shape (see for instance Section 2.1 of the Planck paper 1502.01592). Moreover the works [64,65,66], although very important, are rather outdated by now. So, this part of the paper should be updated, and the value of fNL should be compared to the current limits (see 1502.01592) or future forecasts on equilateral non-Gaussianity, not the local one.

A similar analysis should be done for the combination a+. After eq. (3.26), the paper states 1
a+ undergoes fast roll.... thus we suppress a+. This point should be clarified. My understanding is that this sentence means that a+ has a much larger mass than a?, so we can consistently set a+ = 0. This should be shown explicitly, by computing explicitly the mass of this field (in terms of the parameters in the model) and showing that it is indeed greater than H.

What value of m in (3.11) is taken in the concrete numerical evaluations?