{"arxiv_id":"2012.05821","incoming":{"papers":69,"sentences":112,"groups":[{"kind":"extends","label":"Builds on it","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2112.05092","title":"Revisiting small-scale fluctuations in $\\alpha$-attractor models of inflation","url":"/paper/2112.05092","section":"Robustness of single-field predictions","sentence":"In [ref] it has been shown that multi-field models with strong turns in field space evade the single-field bound on the growth of $P_ζ$, and we demonstrate here that the same holds when the growth of the curvature perturbation is also due to the strong curvature of the hyperbolic field space.","intent_p":0.89,"contests_p":null},{"arxiv_id":"2409.09023","title":"Primordial Stochastic Gravitational Wave Backgrounds from a Sharp Feature in Three-field Inflation II: The Inflationary Era","url":"/paper/2409.09023","section":"Phenomenology","sentence":"Although we consider a full investigation outside the scope of this work, we have generalized some of the models in [ref] to three fields and have found that the features' behavior persists, and we see decaying oscillations in both turn rate and torsion during the trajectory's realignment.","intent_p":0.99,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2103.03025","title":"Comparing multi-field primordial feature models with the Planck data","url":"/paper/2103.03025","section":"Numerical solution","sentence":"We use the 2 field version of BINGO [ref] [This version, which was also used to produce the results of Refs. [ref] , is not yet publicly available.] to solve the model.","intent_p":1.0,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2409.09023","title":"Primordial Stochastic Gravitational Wave Backgrounds from a Sharp Feature in Three-field Inflation II: The Inflationary Era","url":"/paper/2409.09023","section":"Phenomenology","sentence":"References [ref] studied several such two-field models that produce observable signals in LISA – these features typically are not one top hat as we've studied here, but a series of sharp turns with decaying amplitude, although the observed power spectra and radiation-era SGWBs (inflationary-era SGWBs are not studied in their work) are qualitatively very similar to the two-field limit of ours.","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":27,"sentences":29,"quotes":[{"arxiv_id":"2103.01056","title":"Probing non-Gaussianities with the high frequency tail of induced gravitational waves","url":"/paper/2103.01056","section":"Introduction","sentence":"The so-called induced GWs have received a lot of attention recently [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"2101.11244","title":"Gravitational waves from type II axion-like curvaton model and its implication for NANOGrav result","url":"/paper/2101.11244","section":"Introduction","sentence":"This signal can be explained by the stochastic GW with $Ω_GW∼10^-9$ at $f∼10^-8$, which can be sourced by cosmic string [ref] , phase transitions [ref] , large density fluctuations in primordial black hole (PBH) formation models [ref] and other origin [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"2306.02758","title":"Exploring Critical Overdensity Thresholds in Inflationary Models of Primordial Black Holes Formation","url":"/paper/2306.02758","section":"Introduction","sentence":"In particular, there are numerous theoretical studies on the formation of PBHs from inflationary models, such as Refs. [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"2107.07620","title":"Mechanism of primordial black holes production and secondary gravitational waves in $\\alpha$-attractor Galileon inflationary scenario","url":"/paper/2107.07620","section":"Introduction","sentence":"Another assumption is that the scalar perturbations obey the non-Gaussian statistics [ref] .","intent_p":0.82,"contests_p":null},{"arxiv_id":"2205.05595","title":"Gravitational Waves From No-Scale Supergravity","url":"/paper/2205.05595","section":"Introduction","sentence":"There are numerous studies based on this scenario [ref] and we briefly discuss some of them.","intent_p":0.93,"contests_p":null}]}],"unlabelled_sentences":79},"outgoing":{"papers":142,"sentences":211,"groups":[{"kind":"contests","label":"Contests","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2005.12306","title":"Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak","url":"/paper/2005.12306","section":"The approach of template estimators","sentence":"However, as already mentioned before, the peak in the power spectrum produced in our models is different from a log-normal one, and the formulae derived in Ref. [ref] do not reproduce our results.], and to understand how they arise in our models, as well as to make contact with the types of feature produced in inflationary models reviewed in the Introduction and in Section [ref], we now divide our results in four classes and discuss them in turn. * Bump feature.","intent_p":0.51,"contests_p":0.76}]},{"kind":"extends","label":"Builds on","papers":1,"sentences":2,"quotes":[{"arxiv_id":"1411.2349","title":"Models of the Primordial Standard Clock","url":"/paper/1411.2349","section":"Model III","sentence":"As a third example, we consider the following modification by changing the shape of potential in the $Θ$ direction, again introduced in Refs. [ref] : [equation] The potential in the $Θ$ direction now acquires the form of chaotic inflation, therefore inflation ends smoothly without the need for an extra hybrid field to assist it.","intent_p":0.9,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":11,"sentences":15,"quotes":[{"arxiv_id":"2005.02895","title":"Generating PBHs and small-scale GWs in two-field models of inflation","url":"/paper/2005.02895","section":"A two-field model and useful formulae","sentence":"In this paper, we make use of the full numerical pipeline, developed in Ref. [ref] , to compute the PPS, the SGWB density and the abundance of PBHs.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1804.08577","title":"Semianalytic Calculation of Gravitational Wave Spectrum Nonlinearly Induced from Primordial Curvature Perturbations","url":"/paper/1804.08577","section":"Generated SGWB and detectability with future space-based interferometers","sentence":"The expression for the energy density of the gravitational waves is [ref] : [equation] In the equation above, $Ω_r,0≃8.6×10^-5$ is the density of radiation today and the functions in the integral are explicitly given by [equation] where $T(k η)$ is the standard transfer function in the radiation dominated era [equation] A complete analytical expression of the functions $ℐ_c,s$ is given in Eqs. (D.1) and (D.2) of Ref. [ref] (see also Ref. [ref] ).","intent_p":0.89,"contests_p":null},{"arxiv_id":"1804.07732","title":"A Cosmological Signature of the SM Higgs Instability: Gravitational Waves","url":"/paper/1804.07732","section":"Generated SGWB and detectability with future space-based interferometers","sentence":"The expression for the energy density of the gravitational waves is [ref] : [equation] In the equation above, $Ω_r,0≃8.6×10^-5$ is the density of radiation today and the functions in the integral are explicitly given by [equation] where $T(k η)$ is the standard transfer function in the radiation dominated era [equation] A complete analytical expression of the functions $ℐ_c,s$ is given in Eqs. (D.1) and (D.2) of Ref. [ref] (see also Ref. [ref] ).","intent_p":0.89,"contests_p":null},{"arxiv_id":"hep-th/0703290","title":"Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations","url":"/paper/hep-th/0703290","section":"Generated SGWB and detectability with future space-based interferometers","sentence":"The expression for the energy density of the gravitational waves is [ref] : [equation] In the equation above, $Ω_r,0≃8.6×10^-5$ is the density of radiation today and the functions in the integral are explicitly given by [equation] where $T(k η)$ is the standard transfer function in the radiation dominated era [equation] A complete analytical expression of the functions $ℐ_c,s$ is given in Eqs. (D.1) and (D.2) of Ref. [ref] (see also Ref. [ref] ).","intent_p":0.89,"contests_p":null},{"arxiv_id":"1906.09244","title":"Reconstructing the spectral shape of a stochastic gravitational wave background with LISA","url":"/paper/1906.09244","section":"The approach of signal reconstruction","sentence":"In the following, we adopt the formalism of the binned Power-Law integrated Sensitivity (PLS) curve introduced in Refs. [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"data_used","label":"Uses data or values from","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2009.04496","title":"The NANOGrav 12.5-year Data Set: Search For An Isotropic Stochastic Gravitational-Wave Background","url":"/paper/2009.04496","section":"The approach of template estimators","sentence":"The NANOGrav result can be interpreted as a SGWB signal fitted by a power-law with amplitude at $Ω_GW(5.5 nHz) ∈[3 ×10^-10, 2 ×10^-9]$ and a spectral index $α∈[-1.5, 0.5]$ at 2$σ$ [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":5,"sentences":7,"quotes":[{"arxiv_id":"2009.11845","title":"Improved reconstruction of a stochastic gravitational wave background with LISA","url":"/paper/2009.11845","section":"The approach of signal reconstruction","sentence":"With more advanced techniques such as those presented in Refs. [ref] , some of the bins in Fig. [ref] could indeed be merged without affecting the reconstruction at all.","intent_p":0.84,"contests_p":null},{"arxiv_id":"1906.09244","title":"Reconstructing the spectral shape of a stochastic gravitational wave background with LISA","url":"/paper/1906.09244","section":"The approach of signal reconstruction","sentence":"With more advanced techniques such as those presented in Refs. [ref] , some of the bins in Fig. [ref] could indeed be merged without affecting the reconstruction at all.","intent_p":0.84,"contests_p":null},{"arxiv_id":"2005.02895","title":"Generating PBHs and small-scale GWs in two-field models of inflation","url":"/paper/2005.02895","section":"Model III","sentence":"A potential very similar Eq. [ref] was also studied in Ref. [ref] where two of us presented results similar to the ones shown in this Subsection.","intent_p":0.96,"contests_p":null},{"arxiv_id":"1404.1536","title":"Standard Clock in Primordial Density Perturbations and Cosmic Microwave Background","url":"/paper/1404.1536","section":"The approach of template estimators","sentence":"This is different from the previous example, and closer to what happens in [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1411.2349","title":"Models of the Primordial Standard Clock","url":"/paper/1411.2349","section":"The approach of template estimators","sentence":"This is different from the previous example, and closer to what happens in [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":6,"sentences":6,"quotes":[{"arxiv_id":"2008.12202","title":"PBHs and secondary GWs from ultra slow roll and punctuated inflation","url":"/paper/2008.12202","section":"Conclusions","sentence":"Even more importantly, non-Gaussianities can significantly change the spectral shape of the SGWB [ref] possibly enhancing or washing out the oscillatory signal, which motivates further investigations in this direction.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1810.11000","title":"Gravitational Waves Induced by non-Gaussian Scalar Perturbations","url":"/paper/1810.11000","section":"Conclusions","sentence":"Even more importantly, non-Gaussianities can significantly change the spectral shape of the SGWB [ref] possibly enhancing or washing out the oscillatory signal, which motivates further investigations in this direction.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1811.09151","title":"Imprints of Primordial Non-Gaussianity on Gravitational Wave Spectrum","url":"/paper/1811.09151","section":"Conclusions","sentence":"Even more importantly, non-Gaussianities can significantly change the spectral shape of the SGWB [ref] possibly enhancing or washing out the oscillatory signal, which motivates further investigations in this direction.","intent_p":0.98,"contests_p":null},{"arxiv_id":"2004.08369","title":"Turning in the landscape: a new mechanism for generating Primordial Black Holes","url":"/paper/2004.08369","section":"Model III","sentence":"The fact that the growth of the PPS in multifield model can easily overcome the single-field limit on $n_s$ was also demonstrated in Refs. [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2004.06106","title":"Seeding primordial black holes in multifield inflation","url":"/paper/2004.06106","section":"Model III","sentence":"The fact that the growth of the PPS in multifield model can easily overcome the single-field limit on $n_s$ was also demonstrated in Refs. [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":51,"sentences":51,"quotes":[{"arxiv_id":"1509.07521","title":"Scale-dependent gravitational waves from a rolling axion","url":"/paper/1509.07521","section":"Comparison with other sources of SGWB","sentence":"Some physical mechanisms that are known to generate single or multi peaked structure of the SGWB are single-field inflationary models with a nearly inflection point [ref] or a non-canonical kinetic term [ref] , certain variants of axion inflation with explosive production of gauge fields [ref] , cosmic strings [ref] and strong first order phase transitions during the thermal era of the Universe [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"0806.1828","title":"Gravitational Wave Production by Collisions: More Bubbles","url":"/paper/0806.1828","section":"Comparison with other sources of SGWB","sentence":"Some physical mechanisms that are known to generate single or multi peaked structure of the SGWB are single-field inflationary models with a nearly inflection point [ref] or a non-canonical kinetic term [ref] , certain variants of axion inflation with explosive production of gauge fields [ref] , cosmic strings [ref] and strong first order phase transitions during the thermal era of the Universe [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"1109.0022","title":"Particle production during inflation and gravitational waves detectable by ground-based interferometers","url":"/paper/1109.0022","section":"Comparison with other sources of SGWB","sentence":"Some physical mechanisms that are known to generate single or multi peaked structure of the SGWB are single-field inflationary models with a nearly inflection point [ref] or a non-canonical kinetic term [ref] , certain variants of axion inflation with explosive production of gauge fields [ref] , cosmic strings [ref] and strong first order phase transitions during the thermal era of the Universe [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"1110.3327","title":"Gauge Field Production in Axion Inflation: Consequences for Monodromy, non-Gaussianity in the CMB, and Gravitational Waves at Interferometers","url":"/paper/1110.3327","section":"Comparison with other sources of SGWB","sentence":"Some physical mechanisms that are known to generate single or multi peaked structure of the SGWB are single-field inflationary models with a nearly inflection point [ref] or a non-canonical kinetic term [ref] , certain variants of axion inflation with explosive production of gauge fields [ref] , cosmic strings [ref] and strong first order phase transitions during the thermal era of the Universe [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"1610.03763","title":"Gravitational waves at interferometer scales and primordial black holes in axion inflation","url":"/paper/1610.03763","section":"Comparison with other sources of SGWB","sentence":"Some physical mechanisms that are known to generate single or multi peaked structure of the SGWB are single-field inflationary models with a nearly inflection point [ref] or a non-canonical kinetic term [ref] , certain variants of axion inflation with explosive production of gauge fields [ref] , cosmic strings [ref] and strong first order phase transitions during the thermal era of the Universe [ref] .","intent_p":0.87,"contests_p":null}]}],"unlabelled_sentences":128},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. 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