Multi-brid Inflation Research Articles

Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling

Using the δN formalism we consider the non-linear curvatureperturbation in multi-field models of inflation with non-minimalcoupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einsteinframes. Exploiting results already known in the Einstein frame, wegive expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation.In the case that an adiabatic limit has not been reached, we find thatin general these quantities differ from those associated with theEinstein frame curvature perturbation, and also confirm theirequivalence in the absence of isocurvature modes. We then proceed toconsider two analytically soluble examples, the first involving anon-minimally coupled `spectator' field and the second being anon-minimally coupled extension of the multi-brid inflation model. Inthe first model we find that predictions can easily be brought intoagreement with the recent Planck results, as the tensor-to-scalarratio is generally small, the spectral tilt tuneable and the non-gaussianitysuppressed. In the second model we find that predictions for all threeparameters can differ substantially from those predicted in theminimally coupled case, and that the recent Planck results forthe spectral tilt can be used to constrain the non-minimal couplingparameters.

LARGE NON-GAUSSIANITY FROM MULTI-BRID INFLATION

A model of multi-component hybrid inflation, dubbed multi-brid inflation, which may yield a large non-Gaussian paramter fNL, was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories. In this talk, in order to see if this result is a general feature of multi-brid inflation, we consider a model with a potential with an exponent quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation. Focusing on the case of two-brid inflation, we find that large non-Gaussianity is also possible in the present model. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.

Quadra-spectrum and quint-spectrum from inflation and curvaton models

We calculate the quadra-spectrum and quint-spectrum, corresponding to five and six point correlation functions of the curvature perturbation. For single field inflation with standard kinetic term, the quadra-spectrum and quint-spectrum are small, which are suppressed by slow roll parameters. The calculation can be generalized to multiple fields. When there is no entropy perturbation, the quadra-spectrum and quint-spectrum are suppressed as well. With the presence of entropy perturbation, the quadra-spectrum and quint-spectrum can get boosted. We illustrate this boost in the multi-brid inflation model. For the curvaton scenario, the quadra-spectrum and quint-spectrum are also large in the small r limit. We also calculate representative terms of quadra-spectrum and quint-spectrum for inflation with generalized kinetic terms, and estimate their order of magnitude for quasi-single field inflation.

A geometric description of the non-Gaussianity generated at the end of multi-field inflation

In this paper we mainly focus on the curvature perturbation generated at the end of multi-field inflation, such as the multi-brid inflation. Since the curvature perturbation is produced on the super-horizon scale, the bispectrum and trispectrum have a local shape. The size of bispectrum is measured by fNL and the trispectrum is characterized by two parameters τNL and gNL. For simplicity, the trajectory of inflaton is assumed to be a straight line in the field space and then the entropic perturbations do not contribute to the curvature perturbation during inflation. As long as the background inflaton path is not orthogonal to the hyper-surface for inflation to end, the entropic perturbation can make a contribution to the curvature perturbation at the end of inflation and a large local-type non-Gaussiantiy is expected. An interesting thing is that the non-Gaussianity parameters are completely determined by the geometric properties of the hyper-surface of the end of inflation. For example, fNL is proportional to the curvature of the curve on this hyper-surface along the adiabatic direction and gNL is related to the change of the curvature radius per unit arc-length of this curve. Both fNL and gNL can be positive or negative respectively, but τNL must be positive and not less than ((6/5)fNL)2.

The trispectrum in the multi-brid inflation

The trispectrum is at least as important as the bispectrum and its size can be characterized by two parameters τNL and gNL. In this short paper, we focus on the Multi-brid inflation, in particular the two-brid inflation model in arXiv.0805.0974, and find that τNL is always positive and roughly equals to [(6/5)fNL]2 for the low scale inflation, but gNL can be negative or positive and its order of magnitude can be the same as that of τNL or even larger.

Large Non-Gaussianity from Multi-Brid Inflation

A model of multi-component hybrid inflation, dubbed multi-brid inflation, in which various observable quantities including the non-Gaussianity parameter f_{NL} can be analytically calculated was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories, provided that the ratio of the two masses is large. One might question whether the resulting large non-Gaussianity is specific to this particular form of the potential and the condition for the end of inflation. In this paper, we consider a model of multi-brid inflation with a potential given by an exponential function of terms quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation than those studied previously. Then, focusing on the case of two-brid inflation, we find that large non-Gaussianity is possible in the present model even for the equal-mass case. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.

Multi-Brid Inflation and Non-Gaussianity

We consider a class of multi-component hybrid inflation models whose evolution may be analytically solved under the slow-roll approximation. We call it multi-brid inflation (or $n$-brid inflation where $n$ stands for the number of inflaton fields). As an explicit example, we consider a two-brid inflation model, in which the inflaton potentials are of exponential type and a waterfall field that terminates inflation has the standard quartic potential with two minima. Using the $\delta N$ formalism, we derive an expression for the curvature perturbation valid to full nonlinear order. Then we give an explicit expression for the curvature perturbation to second order in the inflaton perturbation. We find that the final form of the curvature perturbation depends crucially on how the inflation ends. Using this expression, we present closed analytical expressions for the spectrum of the curvature perturbation ${\cal P}_{S}(k)$, the spectral index $n_S$, the tensor to scalar ratio $r$, and the non-Gaussian parameter $f_{NL}^{\rm local}$, in terms of the model parameters. We find that a wide range of the parameter space $(n_S, r, f_{NL}^{\rm local})$ can be covered by varying the model parameters within a physically reasonable range. In particular, for plausible values of the model parameters, we may have large non-Gaussianity $f_{NL}^{\rm local}\sim 10$--100. This is in sharp contrast to the case of single-field hybrid inflation in which these parameters are tightly constrained.