Inflation driven by a single, minimally coupled, slowly rolling field generically yields a negligible primordial non-Gaussianity. We discuss two distinct mechanisms by which a non-trivial potential can generate large non-Gaussianities. Firstly, if the inflaton traverses a feature in the potential, or if the inflationary phase is short enough so that initial transient contributions to the background dynamics have not been erased, modes near horizon-crossing can acquire significant non-Gaussianities. Secondly, potentials with small-scale structure may induce significant non-Gaussianities while the relevant modes are deep inside the horizon. The first case includes the "step" potential we previously analyzed while the second "resonance" case is novel. We derive analytic approximations for the 3-point terms generated by both mechanisms written as products of functions of the three individual momenta, permitting the use of efficient analysis algorithms. Finally, we present a significantly improved approach to regularizing and numerically evaluating the integrals that contribute to the 3-point function.
We perform a general study of the primordial scalar non-Gaussianities in multi-field inflationary models in Einstein gravity. We consider models governed by a Lagrangian which is a general function of the scalar fields and their first spacetime derivatives. We use $δN$ formalism to relate scalar fields and curvature perturbations. We calculate the explicit cubic order perturbation action and the three-point function of curvature perturbation evaluated at horizon-crossing. Under reasonable assumptions, in the limit of small slow-varying parameters and a sound speed $c_s$ close to one, we find t…
We compute the amplitude of the non-Gaussianities in inflationary models with multiple, uncoupled scalar fields. This calculation thus applies to all models of assisted inflation, including N-flation, where inflation is driven by multiple axion fields arising from shift symmetries in a flux stabilized string vacuum. The non-Gaussianities are associated with nonlinear evolution of the field (and density) perturbations, characterized by the parameter $f_{NL}$. We derive a general expression for the nonlinear parameter, incorporating the evolution of perturbations after horizon-crossing. This is …
We study the non-Gaussianity in the simplest infrared (IR) model of the DBI inflation. We show that the non-Gaussianity in such a model is compatible with the current observational bound, and is within the sensitivity of future experiments. We also discuss the scale dependence of the non-Gaussianity. In the DBI inflation, such a feature can be used as a probe to the properties of the background geometry of the extra dimensions or internal space.
An inflationary single field model with a non-trivial kinetic term for the inflaton is discussed. It is shown that it is possible to have large primordial non-gaussianities and large tensor-to-scalar ratio in a simple concrete model with just a scalar field and a generalized kinetic term for the inflaton field. This is potentially interesting in the prospect of new forthcoming observations.
We compute the leading order contribution to the four-point function of the primordial curvature perturbation in a class of single field models where the inflationary Lagrangian is a general function of the inflaton and its first derivative. This class of models includes string motivated inflationary models such as DBI inflation. We find that the trispectrum for some range of parameters could potentially be observed in future experiments. Moreover, the trispectrum can distinguish DBI inflation from other inflation models with large non-Gaussianities which typically have a similar bispectrum. W…
We investigate the noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of string length and slow-roll parameter, we find that in the models with small speed of sound the noncommutative modifications could be observable if assuming a relatively low string scale. In particular, the dominant modification of non-Gaussianity estimator f_{NL} could reach O(1) in DBI inflation and K-inflation. The corrections are sensitive to the speed of sound and the choice of string length scale. Moreover the shapes of the corrected non-Gaussianities are dist…
We analyze the trajectories for multifield DBI inflation, which can arise in brane inflation models, and show that the trajectories are the same as in typical slow roll inflation. We calculate the power spectrum and find that the higher derivative terms of the DBI action lead to a suppression of the contribution from the isocurvature perturbations. We also calculate the bispectrum generated by the isocurvature perturbation, and find that it leads to distinctive features.
We perform a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Dif…
We calculate the three-point correlation function evaluated at horizon crossing for a set of interacting scalar fields coupled to gravity during inflation. This provides the initial condition for the three-point function of the curvature perturbation in the Sasaki--Stewart δN formulation. We find that the effect is small, of the order of a slow-roll parameter, and that the non-gaussianity can be determined on large scales once the unperturbed background evolution is known. As an example of the use of our formalism, we calculate the primordial non-gaussianity arising in a model of assisted infl…
We calculate the three-point function for primordial scalar fluctuations in a single field inflationary scenario where the scalar field Lagrangian is a completely general function of the field and its first derivative. We obtain an explicit expression for the three-point correlation function in a self-consistent approximation scheme where the expansion rate varies slowly, analogous to the slow-roll limit in standard, single-field inflation. The three-point function can be written in terms of the familiar slow-roll parameters and three new parameters which measure the non-trivial kinetic struct…
We study the impact of higher dimension operators in the inflaton Lagrangian on the non-gaussianity of the scalar spectrum. These terms can strongly enhance the effect without spoiling slow-roll, though it is difficult to exceed f_NL ~ 1, because the scale which suppresses the operators cannot be too low, if we want the effective field theory description to make sense. In particular we explicitly calculate the 3-point function given by an higher derivative interaction of the form (\nablaϕ)^4, which is expected to give the most important contribution. The angular dependence of the result turns …
We compute non-Gaussianities in N-flation, a string motivated model of assisted inflation with quadratic, separable potentials and masses given by the Marcenko-Pastur distribution. After estimating parameters characterizing the bi- and trispectrum in the horizon crossing approximation, we focus on the non-linearity parameter $f_{NL}$, a measure of the bispectrum; we compute its magnitude for narrow and broad spreads of masses, including the evolution of modes after horizon crossing. We identify additional contributions due to said evolution and show that they are suppressed as long as the fiel…
We present a class of models in which the primordial metric fluctuations do not necessarily obey Gaussian statistics. These models are realizations of mechanisms in which non-Gaussianity is first generated by a light scalar field and then transferred into curvature fluctuations during or at the end of inflation. For this class of models we present generic results for the probability distribution functions of the metric perturbation at the end of inflation. It is stressed that finite volume effects can induce non trivial effects that we sketch.
We present projections for reconstruction of the inflationary potential expected from ESA's upcoming Planck Surveyor CMB mission. We focus on the effects that tensor perturbations and the presence of non-Gaussianities have on reconstruction efforts in the context of non-canonical inflation models. We consider potential constraints for different combinations of detection/null-detection of tensors and non-Gaussianities. We perform Markov Chain Monte Carlo and flow analyses on a simulated Planck-precision data set to obtain constraints. We find that a failure to detect non-Gaussianities precludes…
We explore extensions of hybrid inflationary models in the context of supersymmetric D-term inflation. We point out that a large variety of inflationary scenarios can be encountered when the field content is extended. It is not only possible to get curvaton type models but also scenarios in which different fields, with nontrivial statistical properties, contribute to the primordial curvature fluctuations. We explore more particularly the parameter space of these multiple field inflationary models. It is shown that there exists a large domain in which significant primordial non-Gaussianities ca…
Effective Field Theory (EFT) is an efficient method for parametrizing unknown high energy physics effects on low energy data. When applied to time-dependent backgrounds, EFT must be supplemented with initial conditions. In these proceedings, I briefly describe such approach, especially in the case of inflationary, almost-de Sitter backgrounds. I present certain self-consistency constraints that bound the size of possible deviations of the initial state from the standard thermal vacuum. I also estimate the maximum size of non-Gaussianities due to a non-thermal initial state which is compatible …
We compute the 3-point correlation function for a general model of inflation driven by a single, minimally coupled scalar field. Our approach is based on the numerical evaluation of both the perturbation equations and the integrals which contribute to the 3-point function. Consequently, we can analyze models where the potential has a "feature", in the vicinity of which the slow roll parameters may take on large, transient values. This introduces both scale and shape dependent non-Gaussianities into the primordial perturbations. As an example of our methodology, we examine the ``step'' potentia…
We study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended delta N-formalism, we analyse in detail two illustrative examples. The first is a mixed curvaton-inflaton scenario in which fluctuations of both the inflaton and a curvaton (a light isocurvature field during inflation) contribute to the primordial density perturbation. The second example is that of double inflation involving two decoupled massive scalar fields during inflation. In the mixed curvaton-inflaton scenario we find that th…
We study the bispectrum of the curvature perturbation on uniform energy density hypersurfaces in models of inflation with two scalar fields evolving simultaneously. In the case of a separable potential, it is possible to compute the curvature perturbation up to second order in the perturbations, generated on large scales due to the presence of non-adiabatic perturbations, by employing the $δN$-formalism, in the slow-roll approximation. In this case, we provide an analytic formula for the nonlinear parameter $f_{NL}$. We apply this formula to double inflation with two massive fields, showing th…
We study the dependence on configuration in momentum space of the primordial 3-point function of density perturbations in several different scenarios: standard slow-roll inflation, curvaton and variable decay models, ghost inflation, models with higher derivative operators and the DBI model of inflation. We define a cosine between the distributions using a measure based on the ability of experiments to distinguish between them. We find that models fall into two broad categories with fairly orthogonal distributions. Models where non-Gaussianity is created at horizon-crossing during inflation an…
In writing a covariant effective action for single field inflation, one is allowed to add a Gauss-Bonnet and axion-type curvature couplings. These couplings represent modifications of gravity, and are the unique higher-curvature terms that lead to second order equations of motion in four dimensions. In this paper we study the observational consequences of such couplings for models with large non-gaussianities. Our focus is on the Gauss-Bonnet term. In particular, we study an effective action where the scalar Lagrangian is a general function of the inflaton and its first derivative. We show tha…
We consider second order inflationary perturbations in the case of two scalar fields, $σ$ and the inflaton $ϕ$. We derive an expression for the non-Gaussianity of perturbations and apply the results to hybrid inflation. We isolate the contributions due to $σ$ and evaluate the resulting terms to show that $σ$-induced non-Gaussianities dominate over inflaton-induced non-Gaussianities when $m^2_σ \gtrsim ηH^2$, where $η$ is the slow-roll parameter. This may provide a useful test of hybrid inflation in forthcoming CMB experiments.
We consider the expected level of primordial non-Gaussianities in models in which density perturbations are produced by spatial fluctuations in the decay rate of the inflaton. We consider both the non-Gaussianities resulting from the self-couplings of the field that controls the decay rate as well as from the non-linear relation between field and curvature perturbations. We show that in these scenario non-Gaussianities are of the "local" form, that is well described be the ansatz R =Rg + f_{NL} (Rg^2 - <Rg^2>). This is a consequence of the fact that they were created when modes were already ou…
In the literature there have been incompatible estimates for the amount of non-Gaussianity in hybrid inflation. In this note we point out the sources for the discrepancies and show that the results for the amount of non-Gaussianity in hybrid inflation obtained by two different methods, namely, perturbing Einstein equation to second order and the separate universe approach, indeed are compatible. This provides confidence in the methods themselves and in the actual computation of non-Gaussianities.
In this paper, we use the result in [7] to calculate the non-Gaussianity of the racetrack models in [3, 5]. The two models give different non- Gaussianities. Both of them are reasonable.
In certain implementations of the brane inflationary paradigm, the exit from inflation occurs when the branes annihilate through tachyon condensation. We investigate various cosmological effects produced by this tachyonic era. We find that only a very small region of the parameter space (corresponding to slow-roll with tiny inflaton mass) allows for the tachyon to contribute some e-folds to inflation. In addition, non-adiabatic density perturbations are generated at the end of inflation. When the brane is moving relativistically this contribution can be of the same order as fluctuations produc…
Recently a mechanism was proposed whereby the primordial density perturbations are generated at the end of inflation. We continue the analysis of the proposed model of this mechanism and calculate the maximum extent to which the density perturbations produced via this model can dominate over those of the standard inflationary paradigm. In addition, we provide a straightforward variation of this model which allows for greater amplification of the density perturbations. Finally, we show that a variation in the implementation of the original model results in significant non-gaussianities in the r…
We propose a novel inflationary scenario in string theory in which the inflaton field is a 'Wilson line' degree of freedom in the worldvolume of a probe Dp-brane, in a warped flux compactification. Kinetic terms for Wilson line fields on the world volume of a D-brane take a nonstandard Dirac-Born-Infeld (DBI) form. Thus, we work in the framework of DBI inflation. This extends the original slow roll Wilson line inflationary scenario, where only the quadratic piece was considered. Warped DBI Wilson line inflation offers an attractive alternative to ordinary (position field) DBI inflation, inasmu…
We calculate the bispectrum of single-field braneworld inflation, triggered by either an ordinary scalar field or a cosmological tachyon, by means of a gradient expansion of large-scale non-linear perturbations coupled to stochastic dynamics. The resulting effect is identical to that for single-field 4D standard inflation, the non-linearity parameter being proportional to the scalar spectral index in the limit of collapsing momentum. If the slow-roll approximation is assumed, braneworld and tachyon non-Gaussianities are subdominant with respect to the post-inflationary contribution. However, b…
Developing on the ideas of (section 4 of) [1] and [2] and using the formalisms of [3] and [4], after inclusion of perturbative and non-perturbative alpha' corrections to the Kaehler potential and (D1- and D3-) instanton generated superpotential, we show the possibility of getting finite values for the non-linear parameter f_{NL} while looking for non-Gaussianities in type IIB compactifications on orientifolds of the Swiss Cheese Calabi-Yau WCP^4[1,1,1,6,9] in the L(arge) V(olume) S(cenarios) limit. First we show that in the context of multi-field slow-roll inflation, for the Calabi-Yau volume …
