Calculating the primordial bispectrum predicted by a model of inflation and comparing it to what we see in the sky is very computationally intensive, necessitating layers of approximations and limiting the models which can be constrained. Exploiting the inherent separability of the tree level in-in formalism using expansions in separable basis functions provides a means by which to obviate some of these difficulties. Here, we develop this approach further into a practical and efficient numerical methodology which can be applied to a much wider and more complicated range of bispectrum phenomenology, making an important step forward towards observational pipelines which can directly confront specific models of inflation. We describe a simple augmented Legendre polynomial basis and its advantages, then test the method on single-field inflation models with non-trivial phenomenology, showing that our calculation of these coefficients is fast and accurate to high orders.
We present a new flexible estimator for comparing theoretical templates for the predicted bispectrum of the CMB anisotropy to observations. This estimator, based on binning in harmonic space, generalizes the optimal estimator of Komatsu, Spergel, and Wandelt by allowing an adjustable weighting scheme for masking possible foreground and other contaminants and detecting particular noteworthy features in the bispectrum. The utility of this estimator is illustrated by demonstrating how acoustic oscillations in the bispectrum and other details of the bispectral shape could be detected in the future…
We compute the full bispectra, namely both auto- and cross- bispectra, of primordial curvature and tensor perturbations in the most general single-field inflation model whose scalar and gravitational equations of motion are of second order. The formulae in the limits of k-inflation and potential-driven inflation are also given. These expressions are useful for estimating the full bispectra of temperature and polarization anisotropies of the cosmic microwave background radiation.
We use the long-wavelength formalism to compute the bispectral non-Gaussianity produced in two-field inflation. We find an exact result that is used as the basis of numerical studies, and an explicit analytical slow-roll expression for several classes of potentials that gives insight into the origin and importance of the various contributions to fNL. We also discuss the momentum dependence of fNL. Based on these results we find a simple model that produces a relatively large non-Gaussianity. We show that the long-wavelength formalism is a viable alternative to the standard delta-N formalism, a…
In single-field inflationary models the bispectra are usually given in the $ζ$-gauge, because its temporal part leads to the super-horizon conservation of fluctuations. However, this property is independent of the choice of {\it spatial} gauge, so in this letter we explore this freedom. We compute the variation of the bispectra under the most general spatial gauge transformation that is globally defined and privileges no point, direction or scale. In the squeezed configuration we then obtain a generalization of the classic $ζ$-gauge consistency relations, which we also derive through the `larg…
We discuss bispectra of single-field inflationary models described by general Lorentz invariant Lagrangians that are at most first order in field derivatives, including the fast-roll models investigated by Noller and Magueijo. Based on a factor analysis, we identify the least correlated basic contributions to the general shape and show quantitatively which templates provide a good approximation. We compute how relative contributions of basic shapes to the total bispectrum scale as slow roll is relaxed. To enable future comparison with CMB observations, we provide a modal expansion of these non…
Non-Gaussianity in the distribution of inflationary perturbations, measurable in statistics of the cosmic microwave background (CMB) and large scale structure fluctuations, can be used to probe non-trivial initial quantum states for these perturbations. The bispectrum shapes predicted for generic non-Bunch-Davies initial states are non-factorizable ("non-separable") and are highly oscillatory functions of the three constituent wavenumbers. This can make the computation of CMB bispectra, in particular, computationally intractable. To efficiently compare with CMB data one needs to construct a se…
We present examples of non-Gaussian statistics that can induce bispectra matching local and non-local (including equilateral) templates in biased sub-volumes. We find cases where the biasing from coupling to long wavelength modes affects only the power spectrum, only the bispectrum or both. Our results suggest that ruling out multi-field scenarios is quite difficult: some measurements of the scalar correlations, including the shape of the bispectrum, can be consistent with single-clock predictions even when cosmic variance from super-horizon modes is at work. Furthermore, if observations of th…
We develop a mathematical construction of non-Gaussian fields whose bispectra satisfy the single-clock inflation consistency relation. At the same order that our basis for bispectra recovers the two simplest single clock templates, we also find a third orthogonal template which has the single clock squeezed limit, peaks in folded configurations, and has very small coupling in the equilateral limit. We explore the map between templates and operators in a very general Lagrangian for single-clock fluctuations and find no significant overlap between the new template and models in the literature. W…
It is well known that non-trivial squeezed tensor bispectra can lead to anisotropies in the inflationary stochastic gravitational wave (GW) background, providing us with an alternative and complementary window to primordial non-Gaussianities (NGs) with respect to the CMB. Previous works have highlighted the detection prospects of parity-even tensor NGs via the GW $I$-mode anisotropies. In this work we extend this by analysing for the first time the additional information carried by GW $V$-mode anisotropies due to squeezed NGs. We show that GW $V$ modes allow us to probe parity-odd squeezed $\l…
Cross-correlations between Cosmic Microwave Background (CMB) temperature and polarization anisotropies and $μ$-spectral distortions have been considered to measure (squeezed) primordial scalar bispectra in a range of scales inaccessible to primary CMB bispectra. In this work we address whether it is possible to constrain tensor non-Gaussianities with these cross-correlations. We find that only primordial tensor bispectra with statistical anisotropies leave distinct signatures, while isotropic tensor bispectra leave either vanishing or highly suppressed signatures. We discuss how the angular de…
We propose an (optimal) estimator for a CMB bispectrum containing logarithmically spaced oscillations. There is tremendous theoretical interest in such bispectra, and they are predicted by a plethora of models, including axion monodromy models of inflation and initial state modifications. The number of resolved logarithmical oscillations in the bispectrum is limited due to the discrete resolution of the multipole bispectrum. We derive a simple relation between the maximum number of resolved oscillations and the frequency. We investigate several ways to factorize the primordial bispectrum, and …
There exist several models of inflation that produce primordial bispectra that contain a large number of oscillations. In this paper we discuss these models, and aim at finding a method of detecting such bispectra in the data. We explain how the recently proposed method of mode expansion of bispectra might be able to reconstruct these spectra from separable basis functions. Extracting these basis functions from the data might then lead to observational constraints on these models.
Long-short mode coupling during inflation, encoded in the squeezed bispectrum of curvature perturbations, induces a dependence of the local, small-scale power spectrum on long-wavelength perturbations, leading to a scale-dependent halo bias. While this scale dependence is absent in the large-scale limit for single-field inflation models that satisfy the consistency relation, certain models such as resonant non-Gaussianity show a peculiar behavior on intermediate scales. We reconsider the predictions for the halo bias in this model by working in Conformal Fermi Coordinates, which isolate the ph…
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…
[Abridged] A sharp cut-off in the primordial scalar power spectrum on large scales has been known to improve the fit to the cosmic microwave background (CMB) data when compared to the more standard, nearly scale invariant power spectrum that arises in slow roll inflation. In an earlier work, we had numerically investigated the characteristics of the scalar bispectrum generated in models with kinetically dominated initial conditions. In this work, we compare the scenario with two other competing scenarios (viz. punctuated inflation and a model due to Starobinsky) which also suppress the scalar …
Gravitational interferometers and cosmological observations of the cosmic microwave background offer us the prospect to probe the laws of gravity in the primordial universe. To study and interpret these datasets we need to know the possible graviton non-Gaussianities. To this end, we derive the most general tree-level three-point functions (bispectra) for a massless graviton to all orders in derivatives, assuming scale invariance. Instead of working with explicit Lagrangians, we take a bootstrap approach and obtain our results using the recently derived constraints from unitarity, locality and…
We investigate constraints on power spectra of the primordial curvature and tensor perturbations with priors based on single-field slow-roll inflation models. We stochastically draw the Hubble slow-roll parameters and generate the primordial power spectra using the inflationary flow equations. Using data from recent observations of CMB and several measurements of geometrical distances in the late Universe, Bayesian parameter estimation and model selection are performed for models that have separate priors on the slow-roll parameters. The same analysis is also performed adopting the standard pa…
We study temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation sourced from primordial cross-bispectra between metric perturbations and vector fields, which are generated from the inflation model where an inflaton and a vector field are coupled. In case the vector field survives after the reheating, both the primordial scalar and tensor fluctuations can be enhanced by the anisotropic stress composed of the vector fields during radiation dominated era. We show that through this enhancement the primordial cross-bispectra generate not only CMB bispectra but …
We investigate the degree to which the Cosmic Microwave Background (CMB) can be used to constrain primordial non-Gaussianity coming from the presence of spinning particles coupled to the inflaton. We compute the $\langle TTT \rangle$ and $\langle TTTT \rangle$ correlation functions arising from the exchange of a particle with spin $s$ and generic mass, and the corresponding signal-to-noise ratios for a cosmic-variance-limited CMB experiment. We show that already with \emph{Planck} data one could improve the theoretical bounds on the amplitude of these primordial templates by an order of magnit…
Upcoming full-sky large-scale structure surveys such as Euclid can probe the primordial Universe. Using the specifications for the Euclid survey, we estimate the constraints on the inflation potential beyond slow-roll. We use mock Euclid and Planck data from fiducial cosmological models using the Wiggly Whipped Inflation (WWI) framework, which generates features in the primordial power spectrum. We include Euclid cosmic shear and galaxy clustering, with two setups (Conservative and Realistic) for the non-linear cut-off. We find that the addition of Euclid data gives an improvement in constrain…
Violation of parity symmetry in the gravitational sector, which manifests into unequal left and right circular polarization states of primordial gravitational waves, represents a way to test high-energy modifications to general relativity. In this paper we study inflation within recently proposed chiral scalar-tensor theories of gravity, that extend Chern-Simons gravity by including parity-violating operators containing first and second derivatives of the non-minimally coupled scalar (inflaton) field. Given the degeneracy between different parity-violating theories at the level of the power sp…
The detection of Primordial Gravitational Waves (PGWs) is one of the most important goals of modern cosmology since PGWs can both provide substantial evidence for primordial inflation and shed light on its physical nature. Small scale experiments on gravitational waves such as LIGO/VIRGO and, in future, LISA and Einstein Telescope (ET), being sensitive to the stochastic background of gravitational waves, can be used together with the CMB data to constrain the inflationary parameters. In performing these analyses the primordial tensor spectrum is usually parametrized with a power law that inclu…
We derive a direct correlation between the power spectrum and bispectrum of the primordial curvature perturbation in terms of the Goldstone mode based on the effective field theory approach to inflation. We show examples of correlated bispectra for the parametrized feature models presented by the Planck collaboration. We also discuss the consistency relation and the validity of our explicit correlation between the power spectrum and bispectrum.
We study how to probe bispectra of stochastic gravitational waves with pulsar timing arrays. The bispectrum is a key to probe the origin of stochastic gravitational waves. In particular, the shape of the bispectrum carries valuable information of inflation models. We show that an appropriate filter function for three point correlations enables us to extract a specific configuration of momentum triangles in bispectra. We also calculate the overlap reduction functions and discuss strategy for detecting the bispectrum with multiple pulsars.
We consider the prospects of probing features in the primordial power spectrum with future Cosmic Microwave Background (CMB) polarization measurements. In the scope of the inflationary scenario, such features in the spectrum can be produced by local non-smooth pieces in an inflaton potential (smooth and quasi-flat in general) which in turn may originate from fast phase transitions during inflation in other quantum fields interacting with the inflaton. They can fit some outliers in the CMB temperature power spectrum which are unaddressed within the standard inflationary ${\mathrmΛ}$CDM model. W…
We develop a possibility of generating tensor non-Gaussianity in a kind of anisotropic inflation, where a $U(1)$ gauge field is kinetically coupled to a spectator scalar field. Owing to this coupling, the coherent mode of the electric field appears and softly breaks the isotropy of the Universe. We compute the bispectrum of linearly-polarized tensor perturbations sourced by the gauge field and find that it is strongly red-tilted and has distinctive statistical anisotropies including higher-order multipole moments. Interestingly, the tensor bispectra with the specific combinations of linear pol…
Enormous information about interactions is contained in the non-Gaussianities of the primordial curvature perturbations, which are essential to break the degeneracy of inflationary models. We study the primordial bispectra for G-inflation models predicting both sharp and broad peaks in the primordial scalar power spectrum. We calculate the non-Gaussianity parameter $f_{\mathrm{NL}}$ in the equilateral limit and squeezed limit numerically, and confirm that the consistency relation holds in these models. Even though $f_{\mathrm{NL}}$ becomes large at the scales before the power spectrum reaches …
We investigate parity-violating signatures of temperature and polarization bispectra of the cosmic microwave background (CMB) in an inflationary model where a rolling pseudoscalar produces large equilateral tensor non-Gaussianity. By a concrete computation based on full-sky formalism, it is shown that resultant CMB bispectra have nonzero signals in both parity-even $(\ell_1 + \ell_2 + \ell_3 = {\rm even})$ and parity-odd $(\ell_1 + \ell_2 + \ell_3 = {\rm odd})$ spaces, and are almost uncorrelated with usual scalar-mode equilateral bispectra. These characteristic signatures and polarization inf…
Supersolid inflation is a class of inflationary theories that simultaneously breaks time and space reparameterization invariance during inflation, with distinctive features for the dynamics of cosmological fluctuations. We investigate concrete realizations of such a scenario, including non-minimal couplings between gravity and the fields driving inflation. We focus in particular on the dynamics of primordial gravitational waves and discuss how their properties depend on the pattern of symmetry breaking that we consider. Tensor modes can have a blue spectrum, and for the first time we build mod…
A direct detection of primordial gravitational waves is the ultimate probe for any inflation model. While current CMB bounds predict the generic scale-invariant gravitational wave spectrum from slow-roll inflation to be below the reach of upcoming gravitational wave interferometers, this prospect may dramatically change if the inflaton is a pseudoscalar. In this case, a coupling to any abelian gauge field leads to a tachyonic instability for the latter and hence to a new source of gravitational waves, directly related to the dynamics of inflation. In this contribution we discuss how this setup…
We perform a detailed analysis on a primordial gravitational-wave background amplified during a Kasner-like pre-inflationary phase allowing for general triaxial anisotropies. It is found that the predicted angular distribution map of gravitational-wave intensity on large scales exhibits topologically distinctive patterns according to the degree of the pre-inflationary anisotropy, thereby serving as a potential probe for the pre-inflationary early universe with future all-sky observations of gravitational waves. We also derive an observational limit on the amplitude of such anisotropic gravitat…
We use the long-wavelength formalism to investigate the level of bispectral non-Gaussianity produced in two-field inflation models with standard kinetic terms. Even though the Planck satellite has so far not detected any primordial non-Gaussianity, it has tightened the constraints significantly, and it is important to better understand what regions of inflation model space have been ruled out, as well as prepare for the next generation of experiments that might reach the important milestone of Delta f_NL(local) = 1. We derive an alternative formulation of the previously derived integral expres…
We study signatures in the Cosmic Microwave Background (CMB) induced by the presence of strong spatial curvature prior to the epoch of inflation which generated our present universe. If inflation does not last sufficiently long to drive the large-scale spatial curvature to zero, then presently observable scales may have left the horizon while spatial slices could not be approximated by a flat, Euclidean geometry. We compute corrections to the power spectrum and non-gaussianity of the CMB temperature anisotropy in this scenario. The power spectrum does not receive significant corrections and is…
We investigate the potential for the LISA space-based interferometer to detect the stochastic gravitational wave background produced from different mechanisms during inflation. Focusing on well-motivated scenarios, we study the resulting contributions from particle production during inflation, inflationary spectator fields with varying speed of sound, effective field theories of inflation with specific patterns of symmetry breaking and models leading to the formation of primordial black holes. The projected sensitivities of LISA are used in a model-independent way for various detector designs …
We derive oscillatory signals in correlation functions in two-field open inflation by means of the in-in formalism; such signatures are caused by resonances between oscillations in the tunnelling field and fluctuations in the inflaton during the curvature dominated, intermediate and subsequent inflationary regime. While amplitudes are model-dependent, we find distinct oscillations in the power and bi-spectrum that can act as a direct probe of the curvature dominated phase and thus, indirectly, strengthen the claim of the string landscape if they were observed. We comment on the prospects of de…
Probing small-scale anisotropic inflation with stochastic gravitational-wave background
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院量子联合研究中心及物理系）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础科学与数学学院）
The aim of this paper is to probe the features of the bouncing cosmology with the current observational data. Basing on bounce inflation model, with high derivative term, we propose a general parametrization of primordial power spectrum which includes the typical bouncing parameters, such as bouncing time-scale, and energy scale. By applying Markov Chain Monto Carlo analysis with current data combination of Planck 2015, BAO and JLA, we report the posterior probability distributions of the parameters. We find that, bouncing models can well explain CMB observations, especially the deficit and os…
We explore possibility of using the three dimensional bispectra of the Ly-alpha forest and the redshifted 21-cm signal from the post-reionization epoch to constrain primordial non-Gaussianity. Both these fields map out the large scale distribution of neutral hydrogen and maybe treated as tracers of the underlying dark matter field. We first present the general formalism for the auto and cross bispectrum of two arbitrary three dimensional biased tracers and then apply it to the specific case. We have modeled the 3D Ly-alpha transmitted flux field as a continuous tracer sampled along 1D skewers …
Although cosmological observations suggest that the fluctuations of seed fields are almost Gaussian, the possibility of a small deviation of their fields from Gaussianity is widely discussed. Theoretically, there exist numerous inflationary scenarios which predict large and characteristic non-Gaussianities in the primordial perturbations. These model-dependent non-Gaussianities act as sources of the Cosmic Microwave Background (CMB) bispectrum; therefore, the analysis of the CMB bispectrum is very important and attractive in order to clarify the nature of the early Universe. Currently, the imp…
Galileon fields arise naturally from the decoupling limit of massive gravities, and possess special self-interactions which are protected by a spacetime generalization of Galilean symmetry. We briefly revisit the inflationary phenomenology of Galileon theories. Working from recent computations of the fluctuation Lagrangian to cubic order in the most general model with second-order equations of motion, we show that a distinct shape is present but with suppressed amplitude. A similar shape has been found in other higher-derivative models. It may be visible in a theory tuned to suppress the leadi…
Galaxy bispectrum is a promising probe of inflationary physics in the early universe as a measure of primordial non-Gaussianity (PNG), whereas its signal-to-noise ratio is significantly affected by the mode coupling due to non-linear gravitational growth. In this paper, we examine the standard reconstruction method of linear cosmic mass density fields from non-linear galaxy density fields to de-correlate the covariance in redshift-space galaxy bispectra. In particular, we evaluate the covariance of the bispectrum for massive-galaxy-sized dark matter halos with reconstruction by using 4000 inde…
A Bell experiment during inflation: probing quantum entanglement in tensor fluctuations through correlations of primordial scalar curvature perturbations
University of Barcelona（巴塞罗那大学）；Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INAF- Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；ICREA（加泰罗尼亚高级研究院）
Probing the Perturbative Reheating History of Decaying Oscillatory Inflation with ACT Constraints
College of Physics and Electronic Engineering, Chengdu Normal University（成都师范学院物理与电子信息学院）；Department of Physics, Xinzhou Normal University（忻州师范学院物理系）；School of Mathematics and Physics, University of South China（南华大学数学与物理学院）
The weak gravity conjecture imposes severe constraints on natural inflation. A trans-Planckian axion decay constant can only be realized if the potential exhibits an additional (subdominant) modulation with sub-Planckian periodicity. The resulting wiggles in the axion potential generate a characteristic modulation in the scalar power spectrum of inflation which is logarithmic in the angular scale. The compatibility of this modulation is tested against the most recent Cosmic Microwave Background (CMB) data by Planck and BICEP/Keck. Intriguingly, we find that the modulation completely resolves t…
