We study the slow-roll inflation models, where the inflaton slow-rolls along a trajectory whose orthogonal directions are lifted by potentials with masses of order the Hubble parameter. In these models large non-Gaussianities can be generated through the transformation from the isocurvature modes to the curvature mode, once the inflaton trajectory turns. We find large bispectra with one-parameter family of novel shapes, interpolating between the equilateral and local shape. According to the in-in formalism, the shapes of these non-Gaussianities are different from a simple projection from the isocurvature non-Gaussian correlation functions.
We reconsider magnetogenesis in the context of three-form inflation, and its backreaction. In particular, we focus on first order perturbation theory during inflation and subsequent radiation era: we discuss the consistency of the perturbative approach, and elaborate on the possible non-Gaussian signatures of the model.
This is a pedagogical review on primordial non-Gaussianities from inflation models. We introduce formalisms and techniques that are used to compute such quantities. We review different mechanisms which can generate observable large non-Gaussianities during inflation, and distinctive signatures they leave on the non-Gaussian profiles. They are potentially powerful probes to the dynamics of inflation. We also provide a non-technical and qualitative summary of the main results and underlying physics.
In quasi-single field inflation models, massive isocurvature modes, that are coupled to the inflaton and have mass of order the Hubble parameter, can have nontrivial impacts on density perturbations, especially non-Gaussianities. We study a simple example of quasi-single field inflation in terms of turning inflaton trajectory. Large bispectra with a one-parameter family of novel shapes arise, lying between the well-known local and equilateral shape. The trispectra can also be very large and its magnitude tNL can be much larger than fNL squared.
We describe a two-field model that generalizes Natural Inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. We analyze how the dynamics fundamentally depends on the mass of the radial mode and calculate/estimate the non-Gaussianities arising from such a scenario.
We review the theory of inflationary perturbations. Perturbations at both linear and nonlinear orders are reviewed. We also review a variety of inflation models, emphasizing their signatures on cosmic perturbations.
These notes present a detailed introduction to Maldacena's calculation of the three-point function generated by the simplest class of inflationary models: those with a single inflaton field whose potential satisfies the slow-roll conditions and whose quantum fluctuations start in the asymptotic Bunch-Davies vacuum state. The three-point function should be the most readily observed evidence for non-Gaussianities amongst the primordial fluctuations produced by inflation. In these inflationary theories the non-Gaussianities are predicted to be extremely small, being naturally suppressed by the sm…
The methods of effective field theory are used to study generic theories of inflation with a single inflaton field and to perform a general analysis of the associated non-Gaussianities. We investigate the amplitudes and shapes of the various generic three-point correlators, the bispectra, which may be generated by different classes of single-field inflationary models. Besides the well-known results for the DBI-like models and the ghost inflationary theories, we point out that curvature-related interactions may give rise to large non-Gaussianities in the form of bispectra characterized by a fla…
We compute analytic expressions for the non-linearity parameters characterizing the bi- and tri-spectrum of primordial curvature perturbations generated during an inflationary epoch of the early universe driven by an arbitrary number of fields. We assume neither slow roll nor a separable potential; instead, to compute Non-Gaussianities, we assume a separable Hubble parameter. We apply the formalism to an exact solvable toy-model and show under which conditions observably large non-Gaussianities are produced.
We investigate the non-Gaussianities of inflation driven by a single scalar field coupling non-minimally to the Einstein Gravity. We assume that the form of the scalar field is very general with an arbitrary sound speed. For convenience to study, we take the subclass that the non-minimal coupling term is linear to the Ricci scalar $R$. We define a parameter $μ\equivε_h/ε_θ$ where $ε_h$ and $ε_θ$ are two kinds of slow-roll parameters, and obtain the dependence of the shape of the 3-point correlation function on $μ$. We also show the estimator $F_{NL}$ in the equilateral limit. Finally, based on…
Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally-induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator $ρ$…
We consider a variant of hybrid inflation where the waterfall phase transition happens during inflation. By adjusting the parameters associated with the mass of the waterfall field we arrange that the phase transition is not sharp so inflation can proceed for about 50-60 e-folds after the waterfall phase transition. We show that one can work in the limit where the quantum back-reactions are subdominant compared to the classical back-reactions. It is shown that significant amount of large scale curvature perturbations are induced from the entropy perturbations. The curvature perturbations spect…
We investigate thermal inflation in double-screen entropic cosmology. We find that its realization is general, resulting from the system evolution from non-equilibrium to equilibrium. Furthermore, going beyond the background evolution, we study the primordial curvature perturbations arising from the universe interior, as well as from the thermal fluctuations generated on the holographic screens. We show that the power spectrum is nearly scale-invariant with a red tilt, while the tensor-to-scalar ratio is in agreement with observations. Finally, we examine the non-Gaussianities of primordial cu…
We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in generalized G-inflation, i.e., the most general single-field inflation model with second order field equations. It is shown that the most general cubic action for the tensor perturbation (gravitational wave) $h_{ij}$ is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each $h_{ij}$. The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the prese…
In arXiv:0908.4089, we have proposed a model where natural inflation is realized on a steep potential as a consequence of the interaction of the inflaton with gauge fields through an axion-like coupling. In the present work we study the nongaussianities and the spectrum of tensor modes generated in this scenario. The nongaussianities turn out to be compatible with current observations and can be large enough to be detectable by Planck. The non-observation of tensor modes imposes new constraints on the parameter space of the system that are about one order of magnitude stronger than those found…
In this paper we investigate the inflationary phenomenology of an Einstein-Gauss-Bonnet theory compatible with the GW170817 event, by imposing the constant-roll evolution on the scalar field. We develop the constant-roll GW170817-compatible Einstein-Gauss-Bonnet formalism, and we calculate the slow-roll indices and the observational indices of inflation, for several models of interest. As we demonstrate, the phenomenological viability of the models we study is achieved for a wide range of the free parameters. In addition, for the same values of the free parameters that guarantee the inflationa…
We characterize graviton non-Gaussianities in models of inflation where de Sitter boosts are spontaneously broken. We discuss which of the symmetry breaking patterns studied in Nicolis et al., 2015 can sustain a period of quasi de Sitter expansion, and show that the symmetry breaking pattern of Solid Inflation allows the most freedom for graviton interactions. We comment on the phenomenological consequences of some of these interactions. As a byproduct of this analysis we construct the "EFT of Solid Inflation", which has all the useful features of the EFT of Inflation but for the case of broke…
Using the recently developed effective field theory of inflation, we argue that the size and the shape of the non-Gaussianities generated by single-field inflation are generically well described by two parameters: f_NL^equil, which characterizes the size of the signal that is peaked on equilateral configurations, and f_NL^orthog, which instead characterizes the size of the signal which is peaked both on equilateral configurations and flat-triangle configurations (with opposite signs). The shape of non-Gaussianities associated with f_NL^orthog is orthogonal to the one associated to f_NL^equil, …
We compute the non-Gaussianities that arise in single field, slow roll inflationary models arising from arbitrary homogeneous initial states, as well as subleading contributions to the power spectrum. Non Bunch-Davies vacuum initial states can arise if the transition to the single field, slow roll inflation phase occurs only shortly before observable modes left the horizon. They can also arise from new physics at high energies that has been integrated out. Our general result for the bispectrum exhibits several features that were previously seen in special cases.
We perform the analysis of the trispectrum of curvature perturbations generated by the interactions characterizing a general theory of single-field inflation obtained by effective field theory methods. We find that curvature-generated interaction terms, which can in general give an important contribution to the amplitude of the four-point function, show some new distinctive features in the form of their trispectrum shape-function. These interesting interactions are invariant under some recently proposed symmetries of the general theory and, as shown explicitly, do allow for a large value of th…
We explore the superhorizon generation of large fnl of the local form in two field inflation. We calculate the two- and three-point observables in a general class of potentials which allow for an analytic treatment using the delta N formalism. Motivated by the conservation of the curvature perturbation outside the horizon in the adiabatic mode and also by the observed adiabaticity of the power spectrum, we follow the evolution of fnl^{local} until it is driven into the adibatic solution by passing through a phase of effectively single field inflation. We find that although large fnl^{local} ma…
We set up cosmological perturbation theory and study the cosmological implications of the so-called ``generalized Galileon'' developed in \cite{Deffayet:2011gz,horndeski}. This is the most general scalar field theory whose Lagrangian contains derivatives up to second order while keeping second order equations of motion, and contains as sub-cases $k$-inflation, $G$-inflation and many other models. We calculate the power spectrum of the primordial curvature perturbation, finding a modification of the usual consistency relation of the tensor-to-scalar ratio in $k$-inflation or perfect fluid model…
For very general scalar-field theories in which the equations of motion are at second-order, we evaluate the three-point correlation function of primordial scalar perturbations generated during inflation. We show that the shape of non-Gaussianities is well approximated by the equilateral type. The equilateral non-linear parameter f_NL^equil is derived on the quasi de Sitter background where the slow-variation parameters are much smaller than unity. We apply our formula for f_NL^equil to a number of single-field models of inflation--such as k-inflation, k-inflation with Galileon terms, potentia…
We use holographic techniques to compute inflationary non-Gaussianities for general single-field inflation, including models with a non-trivial sound speed. In this holographic approach, the inflationary dynamics is captured by a relevant deformation of the dual conformal field theory (CFT) in the UV, while the inflationary correlators are computed by conformal perturbation theory. In this paper, we discuss the effects of higher derivative operators, such as $(\partial_μϕ\partial^μϕ)^{m}$, which are known to induce a non-trivial sound speed and source potentially large non-Gaussianities. We co…
Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly non-geodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble scales, and to their exponential amplification. Supported by first-principle numerical computations, and by the analytical insight provided by the effective field theory of inflation, we show that the bispectrum is enhanced in flattened configurations, and we argue that an analogous result holds for all higher-order correlation functions.…
Two-field slow-roll inflation is the most conservative modification of a single-field model. The main motivations to study it are its entropic mode and non-Gaussianity. Several years ago, for a two-field model with additive separable potentials, Vernizzi and Wands invented an analytic method to estimate its non-Gaussianities. Later on, Choi et al. applied this method to the model with multiplicative separable potentials. In this note, we design a larger class of models whose non-Gaussianity can be estimated by the same method. Under some simplistic assumptions, roughly these models are unlikel…
We provide a dynamical mechanism to generate localized features during inflation. The local feature is due to a sharp waterfall phase transition which is coupled to the inflaton field. The key effect is the contributions of waterfall quantum fluctuations which induce a sharp peak on the curvature perturbation which can be as large as the background curvature perturbation from inflaton field. Due to non-Gaussian nature of waterfall quantum fluctuations a large spike non-Gaussianity is produced which is narrowly peaked at modes which leave the Hubble radius at the time of phase transition. The l…
This article examines how breaking a Lorentz-invariant description of nature at tiny space-time intervals would affect the non-Gaussian character of the pattern of primordial perturbations left by inflation. We specifically study a set of irrelevant operators that preserve the spatial symmetries of the usual inflationary background. The non-Gaussian component in the primordial fluctuations can be much larger than the usual, small, inflationary prediction and can thus lead to much stronger constraints on the role of "trans-Planckian" physics in inflation than those from the measurements of the …
We study multi-field DBI inflation models with a waterfall phase transition. This transition happens for a D3 brane moving in the warped conifold if there is an instability along angular directions. The transition converts the angular perturbations into the curvature perturbation. Thanks to this conversion, multi-field models can evade the stringent constraints that strongly disfavour single field ultra-violet DBI inflation models in string theory. We explicitly demonstrate that our model satisfies current observational constraints on the spectral index and equilateral non-Gaussianity as well …
In the context of Type IIB LARGE volume orientifold setup equipped with poly-instanton corrections, the standard single-field poly-instanton inflation driven by a 'Wilson' divisor volume modulus is generalized by the inclusion of respective axion modulus. This two-field dynamics results in a "Roulette" type inflation with the presence of several inflationary trajectories which could produce 50 (or more) e-foldings. The evolution of various trajectories along with physical observables are studied. The possibility of generating primordial non-Gaussianities in the slow-roll as well as in the beyo…
We generalize the Effective Field Theory of Inflation to include additional light scalar degrees of freedom that are in their vacuum at the time the modes of interest are crossing the horizon. In order to make the scalars light in a natural way we consider the case where they are the Goldstone bosons of a global symmetry group or are partially protected by an approximate supersymmetry. We write the most general Lagrangian that couples the scalar mode associated to the breaking of time translation during inflation to the additional light scalar fields. This Lagrangian is constrained by diffeomo…
We study multifield aspects of Dirac-Born-Infeld (DBI) inflation. More specifically, we consider an inflationary phase driven by the radial motion of a D-brane in a conical throat and determine how the D-brane fluctuations in the angular directions can be converted into curvature perturbations when the tachyonic instability arises at the end of inflation. The simultaneous presence of multiple fields and non-standard kinetic terms gives both local and equilateral shapes for non-Gaussianities in the bispectrum. We also study the trispectrum, pointing out that it acquires a particular momentum de…
We study the planar regime of curvature perturbations for single field inflationary models in an axially symmetric Bianchi I background. In a theory with standard scalar field action, the power spectrum for such modes has a pole as the planarity parameter goes to zero. We show that constraints from back reaction lead to a strong lower bound on the planarity parameter for high-momentum planar modes and use this bound to calculate the signal-to-noise ratio of the anisotropic power spectrum in the CMB, which in turn places an upper bound on the Hubble scale during inflation allowed in our model. …
We study graviton non-Gaussianities in the EFT of Inflation. At leading (second) order in derivatives, the graviton bispectrum is fixed by Einstein gravity. There are only two contributions at third order. One of them breaks parity. They come from operators that directly involve the foliation: we then expect sizable non-Gaussianities in three-point functions involving both gravitons and scalars. However, we show that at leading order in slow roll the parity-odd operator does not modify these mixed correlators. We then identify the operators that can affect the graviton bispectrum at fourth ord…
In previous work, two of us have proposed a model of inflationary magnetogenesis based on a rolling auxiliary field able both to account for the magnetic fields inferred by the (non) observation of gamma-rays from blazars, and to start the galactic dynamo, without incurring in any strong coupling or strong backreaction regime. Here we evaluate the correction to the scalar spectrum and bispectrum with respect to single-field slow-roll inflation generated in that scenario. The strongest constraints on the model originate from the non-observation of a scalar bispectrum. Nevertheless, even when th…
We study the cosmology of the multifield relativistic Galileon model in which an induced gravity term is added to the Dirac-Born-Infeld action. We highlight the physical insight that is gained by employing a bimetric perspective in which the induced gravity and Einstein-Hilbert action are treated on equal footing. We derive the conditions under which a phase of quasi exponential inflation can be sustained and demonstrate the existence of a critical background energy density above which cosmological fluctuations become ghosts. At the non-linear level, this scenario provides the first concrete e…
We investigate the primordial non-Gaussianities from the trispectra in multi-field inflation models, which can be seen as generalization of multi-field $k$-inflation and multi-DBI inflation. We derive the full fourth-order perturbation action for the inflaton fields and evaluate the four-point correlation functions for the perturbations in the limit $\ca \ll 1$ and $\ce \ll1$. There are three types of momentum-dependent shape functions which arise from three types of four-point interaction vertices. The final trispectrum of the curvature perturbation can be expressed in terms of the deformatio…
We analyze primordial non-gaussianities in presence of an ultra-slow phase during the inflationary dynamics, focusing on scenarios relevant for the production of primordial black holes. We compute the three-point correlation function of comoving curvature perturbations finding that non-gaussianities are sizable, and predominantly local. In the context of threshold statistics, we analyze their impact for the abundance of primordial black holes, and their interplay with the non-gaussianities arising from the non-linear relation between density and curvature perturbations. We find that non-gaussi…
In this letter we study adiabatic and isocurvature perturbations in the frame of inflation with multiple sound speeds involved. We suggest this scenario can be realized by a number of generalized scalar fields with arbitrary kinetic forms. These scalars have their own sound speeds respectively, so the propagations of field fluctuations are individual. Specifically, we study a model constructed by two DBI type actions. We find that the critical length scale for the freezing of perturbations corresponds to the maximum sound horizon. Moreover, if the mass term of one field is much lighter than th…
Inflationary cosmological perturbations of quantum-mechanical origin generically interact with all degrees of freedom present in the early Universe. Therefore, they must be viewed as an open quantum system in interaction with an environment. This implies that, under some conditions, decoherence can take place. The presence of the environment can also induce modifications in the power spectrum, thus offering an observational probe of cosmic decoherence. Here, we demonstrate that this also leads to non Gaussianities that we calculate using the Lindblad equation formalism. We show that, while the…
Inflation can be supported in very steep potentials if it is generated by rapidly turning fields, which can be natural in negatively curved field spaces. The curvature perturbation, $ζ$, of these models undergoes an exponential, transient amplification around the time of horizon crossing, but can still be compatible with observations at the level of the power spectrum. However, a recent analysis (based on a proposed single-field effective theory with an imaginary speed of sound) found that the trispectrum and other higher-order, non-Gaussian correlators also undergo similar exponential enhance…
We propose a new mechanism to generate primordial curvature perturbations, based on the resonant production of particles during inflation. It is known that this phenomenon can trap the inflaton for a fraction of e-fold. This effect is governed by the mass of the produced particles and by their coupling to the inflaton, parameters which can depend on the expectation value of other fields. If one of such additional fields - a 'modulaton' - is light, then its fluctuations, acquired during the earlier stages of inflation, will induce a spatial modulation of the trapping, and thus of the end of inf…
Heavy scalar fields can undergo an instability during inflation as a result of their kinetic couplings with the inflaton. This is known as the geometrical destabilization of inflation, as it relies on the effect of the negative curvature of the field-space manifold overcoming the stabilizing force of the potential. This instability can drive the system away from its original path in field space into a new inflationary attractor, a scenario that we dub sidetracked inflation. We study this second phase and its observable consequences in several classes of two-field models. We show that cosmologi…
Very few explicit inflationary scenarios are known to generate a large bispectrum of orthogonal shape. Dirac-Born-Infeld Galileon inflation, in which an induced gravity term is added to the DBI action, is one such model. We formulate it in the language of the effective field theory of inflation by identifying the unitary gauge operators that govern the behavior of its cosmological fluctuations. We show how to recover rather easily from this its power spectrum and bispectrum, which we calculated previously using standard cosmological perturbation theory. We push our calculations up to the deter…
For the original hybrid inflation as well as the supersymmetric F-term and D-term hybrid models, we calculate the level of non-gaussianities and the power spectrum of curvature perturbations generated during the waterfall, taking into account the contribution of entropic modes. We focus on the regime of mild waterfall, in which inflation continues for more than about 60 e-folds N during the waterfall. We find that the associated f_nl parameter goes typically from f_nl \simeq -1 / N_exit in the regime with N >> 60, where N_exit is the number of e-folds between the time of Hubble exit of a pivot…
We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson πis softly broken to a discrete subgroup. This case includes and generalizes recently proposed String Theory inspired models of Inflation based on Axion Monodromy. The models we study have the property that the 2-point function oscillates as a function of the wavenumber, leading to oscillations in the CMB power spectrum. The non-linear realization of time diffeomorphisms induces some self-interactions for the Goldstone boson that lead to a peculiar non-Gaussianity whose…
We consider a model of inflation consisting a triplet of $U(1)$ vector fields with the parity violating interaction which is non-minimally coupled to inflaton. The vector field sector enjoys global $O(3)$ symmetry which admits isotropic configuration and provides not only vector modes but also scalar and tensor modes. We decompose the scalar perturbations into the adiabatic, entropy and isocurvature perturbations and compute all power spectra and cross correlations of the scalar and the tensor sectors. The tensor modes associated with the vector fields contribute to the power spectrum of gravi…
Tensor non-Gaussianity represents an important future probe of the physics of inflation. Inspired by recent works, we elaborate further on the possibility of significant primordial tensor non-Gaussianities sourced by extra fields during inflation. Unitarity constraints limit the impact of extra (spinning) particle content by means of a lower bound on the corresponding mass spectrum. For spin-2 particles, this takes the form of the well-known Higuchi bound. Massive ($m\gtrsim H$) particles will typically decay during inflation unless they are non-minimally coupled to the inflaton sector: the in…
We compute the three-point correlation function of primordial scalar density perturbations in a general single-field inflationary scenario, where a scalar field phi has a direct coupling with the Ricci scalar R and the Gauss-Bonnet term GB. Our analysis also covers the models in which the Lagrangian includes a function non-linear in the field kinetic energy X=-(nabla phi)^2/2, and a Galileon-type field self-interaction G(phi, X)*(Box phi), where G is a function of phi and X. We provide a general analytic formula for the equilateral non-Gaussianity parameter f_{NL}^{equil} associated with the b…
It has been found that the primordial non-Gaussianity of the curvature perturbation in the case of non-Bunch-Davies initial states can be enhanced compared with those in the case of the Bunch-Davies one due to the interactions among the perturbations on subhorizon scales. The purpose of the present paper is to investigate whether tensor non-Gaussianities can also be enhanced or not by the same mechanism. We consider general gravity theory in the presence of an inflaton, and evaluate the tensor auto-bispectrum and the cross-bispectrum involving one tensor and two scalar modes with the non-Bunch…
In the Horndeski's most general scalar-tensor theories, we derive the three-point correlation function of scalar non-Gaussianities generated during single-field inflation in the presence of slow-variation corrections to the leading-order term. Unlike previous works, the resulting bispectrum is valid for any shape of non-Gaussianities. In the squeezed limit, for example, this gives rise to the same consistency relation as that derived by Maldacena in standard single-field slow-roll inflation. We estimate the shape close to the squeezed one at which the effect of the term inversely proportional …
Inflationary perturbations in multi-field theories can exhibit a transient tachyonic instability as a consequence of their non-trivial motion in the internal field space. When an effective single-field description is applicable, the resulting theory is characterized by fluctuations that propagate with an $imaginary$ speed of sound. We use the effective field theory of fluctuations to study such a set-up in a model-independent manner, highlighting the peculiarities and subtleties that make it different from the standard case. In particular, perturbations feature exponentially growing and decayi…
The discovery of gravitational waves from merging binary black holes has generated considerable interest in examining whether these black holes could have a primordial origin. If a significant number of black holes have to be produced in the early universe, the primordial scalar power spectrum should have an enhanced amplitude on small scales, when compared to the COBE normalized values on the larger scales that is strongly constrained by the anisotropies in the cosmic microwave background. In the inflationary scenario driven by a single, canonical scalar field, such power spectra can be achie…
We re-analyse current single-field inflationary models related to primordial black holes formation. We do so by taking into account recent developments on the estimations of their abundances and the influence of non-gaussianities. We show that, for all of them, the gaussian approximation, which is typically used to estimate the primordial black holes abundances, fails. However, in the case in which the inflaton potential has an inflection point, the contribution of non-gaussianities is only perturbative. Finally, we infer that only models featuring an inflection point in the inflationary poten…
We use Minkowski Functionals to explore the presence of non-Gaussian signatures in simulated cosmic microwave background (CMB) maps. Precisely, we analyse the non-Gaussianities produced from the angular power spectra emerging from a class of inflationary models with a primordial step-like potential. This class of models are able to perform the best-fit of the low-$\ell$ `features', revealed first in the CMB angular power spectrum by the WMAP experiment and then confirmed by the Planck collaboration maps. Indeed, such models generate oscillatory features in the primordial power spectrum of scal…
We investigate primordial perturbations and non-gaussianities in the Hořava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Hořava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are ``slow-roll suppressed'' in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral…
We consider the most general three point function for gravitational waves produced during a period of exactly de Sitter expansion. The de Sitter isometries constrain the possible shapes to only three: two preserving parity and one violating parity. These isometries imply that these correlation functions should be conformal invariant. One of the shapes is produced by the ordinary gravity action. The other shape is produced by a higher derivative correction and could be as large as the gravity contribution. The parity violating shape does not contribute to the bispectrum [1106.3228, 1108.0175], …
