Chapter 7 (Non-Gaussianities and Primordial Black Holes) in the book "Primordial Black Holes'', Springer 2024, Ed. Christian Byrnes, Gabriele Franciolini, Tomohiro Harada, Paolo Pani, and Misao Sasaki. ISBN: 978-981-97-8887-3. 46 pages, 13 figures, 1 table. Minor revisions. Published version
The most promising mechanism of generating PBHs is by the enhancement of power spectrum of the primordial curvature perturbation, which is usually accompanied by the the enhancement of non-Gaussianity that crucially changes the abundance of PBHs. In this review I will discuss how non-Gaussianity is generated in single field inflation as well as in the curvaton scenario, and then discuss how to calculate PBH mass function and induced gravitational waves (GWs) with such non-Gaussianities. When the PBH abundance is fixed, non-Gaussianity only has mild impact on the spectral shape of the induced GWs, which gives relatively robust predictions in the mHz and nHz GW experiments.
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…
This contribution gives an overview on primordial non-Gaussianities from a theoretical perspective. After presenting a general formalism to describe nonlinear cosmological perturbations, several classes of models, illustrated with examples, are discussed: multi-field inflation with non-standard Lagrangians, modulaton fields, curvaton fields. In the latter case, a special emphasis is put on the isocurvature perturbations, which could leave a specific signature in non-Gaussianities.
We investigate the relation between the non-Gaussianities of the primordial perturbations and the sound speed of the tensor perturbations, that is, the propagation speed of the gravitational waves. We find that the sound speed of the tensor perturbations is directly related not to the auto-bispectrum of the tensor perturbations but to the cross-bispectrum of the primordial perturbations, especially, the scalar-tensor-tensor bispectrum. This result is in sharp contrast with the case of the scalar (curvature) perturbations, where their reduced sound speed enhances their auto-bispectrum. Our find…
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…
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.
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 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…
The origin of the seeds which develop into the observed super-massive black holes at high redshifts may be hard to interpret in the context of the standard $ΛCDM$ of early universe cosmology based on Gaussian primordial perturbations. Here we consider the modification of the halo mass function obtained by introducing skewness and kurtosis of the primordial fluctuations. We show that such primordial non-Gaussianities constrained by the current observational bounds on the nonlinearity parameters of $f_{NL}$ and $g_{NL}$ are not effective at greatly increasing the number density of seeds which co…
We utilize the Canny edge detection algorithm as an estimator for primordial non-Gaussianities. In preliminary tests on simulated sky patches with a window size of 57 degrees and multipole moments $l$ up to 1024, we find a $3σ$ distinction between maps with local non-Gaussianity $f_{NL}=350$ (or $f_{NL}=-700$) and Gaussian maps. We present evidence that high resolution CMB studies will strongly enhance the sensitivity of the Canny algorithm to non-Gaussianity, making it a promising technique to estimate primordial non-Gaussianity.
Within the so-called cosmological collider program, imprints of new particles on primordial non-Gaussianities have been studied intensively. In particular, their non-analytic features in the soft limit provide a smoking gun for new particles at the inflation scale. While this approach is very powerful to probe particles of the mass near the Hubble scale, the signal is exponentially suppressed for heavy particles. In this paper, to enlarge the scope of the cosmological collider, we explore a new approach to probing spins of heavy particles from signs of Wilson coefficients of the inflaton effec…
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…
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 revisit a possible scale-dependence of local-type primordial non-Gaussianities induced by super-horizon evolution of scalar field perturbations. We develop the formulation based on $δN$ formalism and derive the generalized form of the local-type bispectrum and also trispectrum which allows us to implement the scale-dependence and suitably compare model prediction with observational data. We propose simple but phenomenologically meaningful expressions, which encompass the information of a wide range of physically motivated models. We also formulate large-scale power spectrum and bispectrum o…
It was pointed out recently that in some inflationary models quantum loops containing a scalar of mass $m$ that couples to the inflaton can be the dominant source of primordial non-Gaussianities. We explore this phenomenon in the simplest such model focusing on the behavior of the primordial curvature fluctuations for small $m/H$. Explicit calculations are done for the three and four point curvature fluctuation correlations. Constraints on the parameters of the model from the CMB limits on primordial non-Gaussianity are discussed. The bi-spectrum in the squeezed limit and the tri-spectrum in t…
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 …
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…
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…
We study how primordial non-Gaussianities affect the clustering of voids at large scales. We derive a formula of the bias of voids induced from the non-Gaussianities by making use of the functional integral method. In a similar way as of haloes, we find that primordial non-Gaussianities can generate scale-dependence in the bias of voids at large scales. In addition, we show that by observing the cross power spectrum of voids and haloes we could check the consistency relation between the non-linearity parameters f_NL and tau_NL. Large voids (high peak objects) would be good targets since the ef…
Deviations from Gaussian statistics of the cosmological density fluctuations, so-called primordial non-Gaussianities (NG), are one of the most informative fingerprints of the origin of structures in the universe. Indeed, they can probe physics at energy scales inaccessible to laboratory experiments, and are sensitive to the interactions of the field(s) that generated the primordial fluctuations, contrary to the Gaussian linear theory. As a result, they can discriminate between inflationary models that are otherwise almost indistinguishable. In this short review, we explain how to compute the n…
We study the cosmological collider phenomenology of neutrinos in an effective field theory. The mass spectrum of neutrinos and their characteristic oscillatory signatures in the squeezed limit bispectrum are computed. Both dS-covariant and slow-roll corrections are considered, so is the scenario of electroweak symmetry breaking during inflation. Interestingly, we show that the slow-roll background of the inflaton provides a chemical potential for the neutrino production. The chemical potential greatly amplifies the oscillatory signal and makes the signal observably large for heavy neutrinos wi…
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 …
It has been pointed out that matter bounce cosmology driven by a k-essence field cannot satisfy simultaneously the observational bounds on the tensor-to-scalar ratio and non-Gaussianity of the curvature perturbation. In this paper, we show that this is not the case in more general scalar-tensor theories. To do so, we evaluate the power spectra and the bispectra of scalar and tensor perturbations on a general contracting background in the Horndeski theory. We then discuss how one can discriminate contracting models from inflation based on non-Gaussian signatures of tensor perturbations.
We propose a new method to numerically calculate higher-order correlation functions of primordial fluctuations generated from any early-universe scenario. Our key-starting point is the realization that the tree-level In-In formalism is intrinsically separable. This enables us to use modal techniques to efficiently calculate and represent non-Gaussian shapes in a separable form well suited to data analysis. We prove the feasibility and the accuracy of our method by applying it to simple single-field inflationary models in which analytical results are available, and we perform non-trivial consis…
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…
We explore the use of galaxy bispectra with multitracer technique as a possible probe of primordial non-Gaussianities. We forecast future constraints on non-linearity parameters, $f_{\rm NL}^{\rm eq}$ and $f_{\rm NL}^{\rm orth}$, which respectively characterize the equilateral- and orthogonal-types primordial bispectra, and show that the multitracer analysis would be effective with reducing the cosmic-variance noise if the number density of galaxies is high enough. We find that the measurement of galaxy bispectrum by future galaxy surveys can reach the constraints on the non-local type primord…
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 clarify the features of primordial non-Gaussianities of tensor perturbations in Gao's unifying framework of scalar-tensor theories. The general Lagrangian is given in terms of the ADM variables so that the framework maintains spatial covariance and includes the Horndeski theory and Gleyzes-Langlois-Piazza-Vernizzi (GLPV) generalization as specific cases. It is shown that the GLPV generalization does not give rise to any new terms in the cubic action compared to the case of the Horndeski theory, but four new terms appear in more general theories beyond GLPV. We compute the tensor 3-point cor…
We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order…
We develop a new method to constraint primordial non-Gaussianities of the local kind using unclustered tracers of the Large Scale Structure. We show that in the limit of low noise, zero bias tracers yield large improvement over standard methods, mostly due to vanishing sampling variance. We propose a simple technique to construct such a tracer, using environmental information obtained from the original sample, and validate our method with N-body simulations. Our results indicate that $σ_{f_{\mathrm{NL}}^{\mathrm{loc}}}\simeq1$ can be reached using only information on a single tracer of suffici…
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…
We apply the time-renormalization group approach to study the effect of primordial non-Gaussianities in the non-linear evolution of cosmological dark matter density perturbations. This method improves the standard perturbation approach by solving renormalization group-like equations governing the dynamics of gravitational instability. The primordial bispectra constructed from the dark matter density contrast and the velocity fields represent initial conditions for the renormalization group flow. We consider local, equilateral and folded shapes for the initial non-Gaussianity and analyze as wel…
In single-field inflationary models with a low sound speed, the orthogonal shape of the primordial bispectrum arises due to partial cancellations between equilateral-type shapes. This fact allows for a speed of sound c_s as low as about 0.01, which is actually weakly preferred by WMAP data. For such values, the trispectrum, scaling like 1/c_s^4, is of order 10^8 and is therefore comparable to, and greater than, the 1 sigma observational bound t_NL^eq=(-3.11 +- 7.5)*10^6. Hence, the trispectrum is already constraining inflationary mechanisms candidates for generating an orthogonal bispectrum at…
The evolution with time of the abundance of galaxy clusters is very sensitive to the statistical properties of the primordial density perturbations. It can thus be used to probe small deviations from Gaussianity in the initial conditions. The characterization of such deviations would help distinguish between different inflationary scenarios, and provide us with information on physical processes which took place in the early Universe. We have found that when the information contained in the galaxy cluster counts is used to reconstruct the dark energy equation of state as a function of redshift,…
We investigate the signature of primordial non-Gaussianities in the weak lensing bispectrum, in particular the signals generated by local, orthogonal and equilateral non-Gaussianities. The questions we address include the signal-to-noise ratio generated in the Euclid weak lensing survey (we find the 1sigma-errors for fNL are 200, 575 and 1628 for local, orthogonal and equilateral non-Gaussianities, respectively), misestimations of fNL if one chooses the wrong non-Gaussianity model (misestimations by up to a factor of +/-3 in fNL are possible, depending on the choice of the model), the probabil…
We investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three-point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon after isotropization. In this momentum regime, the early time dynamics admits a WKB description and the late time dynamics can be described in terms of a non-Bunch Davies vacuum state which encodes the information of initial anisotropy in the background spacetime. We compute the bi-spectrum for curvature perturbation in a canonical single-field action with and without higher derivative operator…
We present an all-sky formalism for the Cosmic Microwave Background (CMB) bispectrum induced by the primordial non-Gaussianities not only in scalar but also in vector and tensor fluctuations. We find that the bispectrum can be formed in an explicitly rationally invariant way by taking into account the angular and polarization dependences of the vector and tensor modes. To demonstrate this and present how to use our formalism, we consider a specific example of the correlation between two scalars and a graviton as the source of non-Gaussianity. As a result, we show that the CMB reduced bispectru…
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…
We study via numerical N-body/SPH chemistry simulations the effects of primordial non-Gaussianities on the formation of the first stars and galaxies, and investigate the impact of supernova feedback in cosmologies with different fnl. Density distributions are biased to higher values, so star formation and the consequent feedback processes take place earlier in high-fnl models and later in low-fnl ones. Mechanical feedback is responsible for shocking and evacuating the gas from star forming sites earlier in the highly non-Gaussian cases, because of the larger bias at high densities. Chemical fe…
We investigate new shapes of local primordial non-Gaussianities in the CMB. Allowing for a primordial isocurvature mode along with the main adiabatic one, the angular bispectrum is in general a superposition of six distinct shapes: the usual adiabatic term, a purely isocurvature component and four additional components that arise from correlations between the adiabatic and isocurvature modes. We present a class of early Universe models in which various hierarchies between these six components can be obtained, while satisfying the present upper bound on the isocurvature fraction in the power sp…
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…
We investigate the effects of primordial non-Gaussianities in the primordial Universe on the baryonic structure formation process. By relating the cosmic star formation rate in Gaussian and non-Gaussian scenarios to the detectability of high-redshift sources of reionization, we derive the expected Gamma-Ray Burst rate in the different models. We find that counts of high-redshift Gamma-Ray Bursts can be used as cosmological probes of non-Gaussianities and that they are suitable candidates to distinguish non-Gaussian effects at early epochs.
In this paper, we study the effects of parity violation on non-gaussianities of primordial gravitational waves in the framework of Hořava-Lifshitz theory of gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear. By calculating the three point function, we find that the leading-order contributions to the non-gaussianities come from the usual second-order derivative terms, which produce the same bispectrum as that found in general relativity. The contributions from high-order spatial n-th derivative terms are always suppressed by a fac…
The redshift dependence of the abundance of galaxy clusters is very sensitive to the statistical properties of primordial density perturbations. It can thus be used to probe small deviations from Gaussian initial conditions. Such deviations constitute a very important signature of many inflationary scenarios, and are thus expected to provide crucial information on physical processes which took place in the very early Universe. We have determined the biases which may be introduced in the estimation of cosmological parameters by wrongly assuming the absence of primordial non-Gaussianities. Altho…
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 continue to investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon well after isotropization. The late time dynamics of these modes is characterized by a non-Bunch Davies vacuum state which encodes all the information about initial anisotropy in the background space-time. We observe that, unlike the non-planar momenta, there exist regimes of planar momenta for which scale invariance of the power spectrum is strongly broken. This regime of planar mo…
We investigate how the consistency relations of large-scale structures are modified when the initial density field is not Gaussian. We consider both scenarios where the primordial density field can be written as a nonlinear functional of a Gaussian field and more general scenarios where the probability distribution of the primordial density field can be expanded around the Gaussian distribution, up to all orders over $δ_{L0}$. Working at linear order over the non-Gaussianity parameters $f_{\rm NL}^{(n)}$ or $S_n$, we find that the consistency relations for the matter density fields are modifie…
We investigate expected constraints on equilateral-type primordial non-Gaussianities from future/ongoing imaging surveys, making use of the fact that they enhance the halo/galaxy bispectrum on large scales. As model parameters to be constrained, in addition to $f_{\rm NL}^{\rm equil}$, which is related to the primordial bispectrum, we consider $g_{\rm NL}^{(\partial σ)^4}$, which is related to the primordial trispectrum that appeared in the effective field theory of inflation. After calculating the angular bispectra of the halo/galaxy clustering and weak gravitational lensing based on the inte…
We study the effects of a general type of features of the inflaton potential on the spectrum and bispectrum of primordial curvature perturbations. These features correspond to a discontinuity in the $n$-th order derivative of the potential which are dumped exponentially away from the value of the field where the feature happens. Interestingly we find that different values of the amplitude and of the order of the feature can lead to the same effects on the power spectrum on both large and short scales, and on the bispectrum at small scales. Only taking into account the bispectrum at large scale…
Fluctuations with wavelengths larger than the volume of a galaxy survey affect the measurement of the galaxy power spectrum within the survey itself. In the presence of local Primordial Non- Gaussianities (PNG), in addition to the super-sample matter density and tidal fluctuations, the large-scale gravitational potential also induces a modulation of the observed power spectrum. In this work we investigate this modulation by computing for the first time the response of the redshift-space galaxy power spectrum to the presence of a long wavelength gravitational potential, fully accounting for the…
This talk briefly explains how the breaking of a Lorentz-invariant description of nature at tiny space-time intervals might affect the non-Gaussian character of the primordial fluctuations left by inflation. For example, a model that contains irrelevant operators that only preserve the spatial symmetries along constant-time surfaces can generate a larger non-Gaussian component in the pattern of primordial fluctuations than is ordinarily predicted by inflation. This property can be useful for constraining models that allow some Lorentz violation at short distances, beyond the constraints possib…
The primordial bispectrum has been considered in the past decade as a powerful probe of the physical processes taking place in the early Universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that serves to discriminate among competing scenarios concerning the details of the origin of cosmological perturbations. However, all of the scenarios, based on the conventional approach to the so-called "quantum-to-classical transition" during inflation, lack the ability to point out the precise physical mechanism responsible for generating the inhomogeneity and…
Primordial non-Gaussianities provide an important test of inflationary models. Although the Planck CMB experiment has produced strong limits on non-Gaussianity on scales of clusters, there is still room for considerable non-Gaussianity on galactic scales. We have tested the effect of local non-Gaussianity on the high redshift galaxy population by running five cosmological N-body simulations down to z=6.5. For these simulations, we adopt the same initial phases, and either Gaussian or scale-dependent non-Gaussian primordial fluctuations, all consistent with the constraints set by Planck on clus…
