{"arxiv_id":"0908.4035","incoming":{"papers":16,"sentences":23,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":3,"sentences":4,"quotes":[{"arxiv_id":"1205.0161","title":"Curvature Perturbation Spectrum in Two-field Inflation with a Turning Trajectory","url":"/paper/1205.0161","section":"Introduction","sentence":"Assuming for simplicity that the field is approximately in a circular motion with a small and constant angular velocity, one can use the in-in formulism [ref] to calculate the 2-point function of the curvature perturbation by quantizing the curvature and isocurvature perturbations as free fields, with the coupling terms as interaction vertices [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2208.03629","title":"Cosmological perturbations in the spatially covariant gravity with a dynamical lapse function","url":"/paper/2208.03629","section":"Using in-in formalism for the correction to spectra","sentence":"We use the field-theoretical perturbative method [ref] to calculate the influence of the new field.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1504.01528","title":"Correlation of isocurvature perturbation and non-Gaussianity","url":"/paper/1504.01528","section":"B. Computation of the correction to the leading order $_$","sentence":"To see, we compute the correction to $_$ due to $^I_(2)$ using the commutator form of the in-in formalism [ref] in a similar fashion as in [ref] .","intent_p":0.97,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1205.5275","title":"Influence of heavy modes on perturbations in multiple field inflation","url":"/paper/1205.5275","section":"Introduction","sentence":"We also assume that the trajectory is straight before and after the turn[This differs from a few works [ref] , where the trajectory follows a circle with constant angular velocity (which we refer to as “constant turn\").].","intent_p":0.92,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1009.1311","title":"On primordial trispectrum from exchanging scalar modes in general multiple field inflationary models","url":"/paper/1009.1311","section":"Linear Perturbations","sentence":"As was shown in [ref] , the cross-correlations between adiabatic/entropic modes would be enhanced by a small $/$ ratio.].","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":5,"sentences":7,"quotes":[{"arxiv_id":"1307.2564","title":"Coupling structure of multi-field primordial perturbations","url":"/paper/1307.2564","section":"Introduction and motivation","sentence":"When the turning rate is relatively small, the correlations between adiabatic and isocurbature modes have been studied perturbatively [ref] .","intent_p":0.83,"contests_p":null},{"arxiv_id":"1008.3198","title":"Note on Non-Gaussianities in Two-field Inflation","url":"/paper/1008.3198","section":"Introduction","sentence":"Some others put their stake on signatures that cannot appear in the simplest single-field model, such as a large deviation from the Gaussian distribution in the CMB temperature fluctuations.[As a partial list, see [ref] and references therein for various models and recent development along this direction.]","intent_p":0.82,"contests_p":null},{"arxiv_id":"1607.08609","title":"Cumulative effects in inflation with ultra-light entropy modes","url":"/paper/1607.08609","section":"Introduction","sentence":"Light scalar fields, with masses much smaller than the Hubble expansion rate $H$, are known to produce potentially large levels of entropy perturbations during inflation [ref] that could lead to (1) non-adiabatic features in the Cosmic Microwave Background (CMB) [ref] , and (2) the super-horizon evolution of curvature perturbations [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"1009.1311","title":"On primordial trispectrum from exchanging scalar modes in general multiple field inflationary models","url":"/paper/1009.1311","section":"Introduction","sentence":"A short list of these models and mechanisms includes $k$-inflation or models with general non-canonical kinetic terms [ref] , multi-field inflation [ref] , the curvaton scenario [ref] , inhomogeneous “end-of-inflation\" models such as hybrid/multibrid models [ref] , cosmic string [ref] , loops [ref] , modified initial vacuum [ref] , ghost inflation [ref] , quasi-single field model [ref] , vector fields [ref] and so on.","intent_p":0.96,"contests_p":null},{"arxiv_id":"1106.0446","title":"Applications of Cosmological Perturbation Theory","url":"/paper/1106.0446","section":"Entropy or Non-Adiabatic Perturbations from Inflation","sentence":"See, e.g. Refs. [ref] and references therein.","intent_p":0.97,"contests_p":null}]}],"unlabelled_sentences":10},"outgoing":{"papers":54,"sentences":167,"groups":[{"kind":"contests","label":"Contests","papers":3,"sentences":3,"quotes":[{"arxiv_id":"0704.0212","title":"Curvature and isocurvature perturbations in two-field inflation","url":"/paper/0704.0212","section":"Conclusion and Discussion","sentence":"However, one can verify that, for models with different adiabatic/entropy speeds of sound, the “diagonalization\" cannot be done easily and thus the treatments in [ref] cannot be viewed as good approximation in this case.","intent_p":1.0,"contests_p":0.87},{"arxiv_id":"astro-ph/0106022","title":"Oscillations During Inflation and the Cosmological Density Perturbations","url":"/paper/astro-ph/0106022","section":"Conclusion and Discussion","sentence":"However, one can verify that, for models with different adiabatic/entropy speeds of sound, the “diagonalization\" cannot be done easily and thus the treatments in [ref] cannot be viewed as good approximation in this case.","intent_p":1.0,"contests_p":0.87},{"arxiv_id":"astro-ph/0605679","title":"Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion","url":"/paper/astro-ph/0605679","section":"Conclusion and Discussion","sentence":"However, one can verify that, for models with different adiabatic/entropy speeds of sound, the “diagonalization\" cannot be done easily and thus the treatments in [ref] cannot be viewed as good approximation in this case.","intent_p":1.0,"contests_p":0.87}]},{"kind":"extends","label":"Builds on","papers":3,"sentences":6,"quotes":[{"arxiv_id":"astro-ph/0605679","title":"Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion","url":"/paper/astro-ph/0605679","section":"Around Horizon-crossings","sentence":"Thus our calculations can be viewed as generalization of previous results in [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"0704.0212","title":"Curvature and isocurvature perturbations in two-field inflation","url":"/paper/0704.0212","section":"Around Horizon-crossings","sentence":"Thus our calculations can be viewed as generalization of previous results in [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"astro-ph/0106022","title":"Oscillations During Inflation and the Cosmological Density Perturbations","url":"/paper/astro-ph/0106022","section":"Introduction","sentence":"Our work can be viewed as generalization of the analysis in [ref] to a general class of two-field models with non-canonical kinetic terms and arbitrary speeds of sound for adiabatic and entropy modes, $c_a ≠c_e$.","intent_p":1.0,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":5,"sentences":5,"quotes":[{"arxiv_id":"0804.3139","title":"Primordial fluctuations and non-Gaussianities in multi-field DBI inflation","url":"/paper/0804.3139","section":"Linear Perturbations","sentence":"After instantaneous adiabatic/entropy modes decomposition, up to total derivative terms, the second-order action for the scalar perturbations takes the form [ref] S_2≡∫dtd^3xa^3[1/2K_mnQ̇^mQ̇^n-δ_mn1/2a^2∂_iQ^m∂_iQ^n+Ξ_mnQ̇^mQ^n-1/2M_mnQ^mQ^n] , with K_mn ≡δ_mn + σ̇^2 P_,IK JL e^I_σ e^K_n e^J_σ e^L_m , = δ_mn + 1/c_a^2-1 δ_σm δ_σn + 1/c_e^2 - 1 δ_mn- δ_σm δ_σn , Ξ_mn ≡𝒩_IJe_m^Ie_n^J+(P_⟨IJ⟩+2P_⟨IK⟩⟨JL⟩X^KL)e_m^Iė_n^J , -M_mn = -ℳ_IJe_m^Ie_n^J+2𝒩_IJė_m^Ie_n^J+(P_⟨IJ⟩+2P_⟨IK⟩⟨JL⟩X^KL)ė_m^Iė_n^J , (m,n=σ,s) where 𝒩_IJ ≡ϕ̇^KP_⟨KI⟩,J-2/HX^KLX^NMP_⟨NI⟩⟨KL⟩P_⟨MJ⟩ , -ℳ_IJ ≡P_,IJ+(X^MNP_⟨MN⟩+2X^MNX^PQP_⟨MN⟩⟨PQ⟩-3H^2)X^KL/H^2P_⟨KI⟩P_⟨LJ⟩ +1/H(P_,I-2X^MNP_⟨MN⟩,I)P_⟨KJ⟩ϕ̇^K+1/a^3d/dt(a^3/HX^KLP_⟨KI⟩P_⟨LJ⟩) .","intent_p":0.84,"contests_p":null},{"arxiv_id":"0806.0336","title":"Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation","url":"/paper/0806.0336","section":"Linear Perturbations","sentence":"After instantaneous adiabatic/entropy modes decomposition, up to total derivative terms, the second-order action for the scalar perturbations takes the form [ref] S_2≡∫dtd^3xa^3[1/2K_mnQ̇^mQ̇^n-δ_mn1/2a^2∂_iQ^m∂_iQ^n+Ξ_mnQ̇^mQ^n-1/2M_mnQ^mQ^n] , with K_mn ≡δ_mn + σ̇^2 P_,IK JL e^I_σ e^K_n e^J_σ e^L_m , = δ_mn + 1/c_a^2-1 δ_σm δ_σn + 1/c_e^2 - 1 δ_mn- δ_σm δ_σn , Ξ_mn ≡𝒩_IJe_m^Ie_n^J+(P_⟨IJ⟩+2P_⟨IK⟩⟨JL⟩X^KL)e_m^Iė_n^J , -M_mn = -ℳ_IJe_m^Ie_n^J+2𝒩_IJė_m^Ie_n^J+(P_⟨IJ⟩+2P_⟨IK⟩⟨JL⟩X^KL)ė_m^Iė_n^J , (m,n=σ,s) where 𝒩_IJ ≡ϕ̇^KP_⟨KI⟩,J-2/HX^KLX^NMP_⟨NI⟩⟨KL⟩P_⟨MJ⟩ , -ℳ_IJ ≡P_,IJ+(X^MNP_⟨MN⟩+2X^MNX^PQP_⟨MN⟩⟨PQ⟩-3H^2)X^KL/H^2P_⟨KI⟩P_⟨LJ⟩ +1/H(P_,I-2X^MNP_⟨MN⟩,I)P_⟨KJ⟩ϕ̇^K+1/a^3d/dt(a^3/HX^KLP_⟨KI⟩P_⟨LJ⟩) .","intent_p":0.84,"contests_p":null},{"arxiv_id":"0806.0619","title":"Non-gaussianity from the bispectrum in general multiple field inflation","url":"/paper/0806.0619","section":"Linear Perturbations","sentence":"After instantaneous adiabatic/entropy modes decomposition, up to total derivative terms, the second-order action for the scalar perturbations takes the form [ref] S_2≡∫dtd^3xa^3[1/2K_mnQ̇^mQ̇^n-δ_mn1/2a^2∂_iQ^m∂_iQ^n+Ξ_mnQ̇^mQ^n-1/2M_mnQ^mQ^n] , with K_mn ≡δ_mn + σ̇^2 P_,IK JL e^I_σ e^K_n e^J_σ e^L_m , = δ_mn + 1/c_a^2-1 δ_σm δ_σn + 1/c_e^2 - 1 δ_mn- δ_σm δ_σn , Ξ_mn ≡𝒩_IJe_m^Ie_n^J+(P_⟨IJ⟩+2P_⟨IK⟩⟨JL⟩X^KL)e_m^Iė_n^J , -M_mn = -ℳ_IJe_m^Ie_n^J+2𝒩_IJė_m^Ie_n^J+(P_⟨IJ⟩+2P_⟨IK⟩⟨JL⟩X^KL)ė_m^Iė_n^J , (m,n=σ,s) where 𝒩_IJ ≡ϕ̇^KP_⟨KI⟩,J-2/HX^KLX^NMP_⟨NI⟩⟨KL⟩P_⟨MJ⟩ , -ℳ_IJ ≡P_,IJ+(X^MNP_⟨MN⟩+2X^MNX^PQP_⟨MN⟩⟨PQ⟩-3H^2)X^KL/H^2P_⟨KI⟩P_⟨LJ⟩ +1/H(P_,I-2X^MNP_⟨MN⟩,I)P_⟨KJ⟩ϕ̇^K+1/a^3d/dt(a^3/HX^KLP_⟨KI⟩P_⟨LJ⟩) .","intent_p":0.84,"contests_p":null},{"arxiv_id":"0906.1345","title":"Primordial Non-Gaussianities from the Trispectra in Multiple Field Inflationary Models","url":"/paper/0906.1345","section":"Linear Perturbations","sentence":"After instantaneous adiabatic/entropy modes decomposition, up to total derivative terms, the second-order action for the scalar perturbations takes the form [ref] S_2≡∫dtd^3xa^3[1/2K_mnQ̇^mQ̇^n-δ_mn1/2a^2∂_iQ^m∂_iQ^n+Ξ_mnQ̇^mQ^n-1/2M_mnQ^mQ^n] , with K_mn ≡δ_mn + σ̇^2 P_,IK JL e^I_σ e^K_n e^J_σ e^L_m , = δ_mn + 1/c_a^2-1 δ_σm δ_σn + 1/c_e^2 - 1 δ_mn- δ_σm δ_σn , Ξ_mn ≡𝒩_IJe_m^Ie_n^J+(P_⟨IJ⟩+2P_⟨IK⟩⟨JL⟩X^KL)e_m^Iė_n^J , -M_mn = -ℳ_IJe_m^Ie_n^J+2𝒩_IJė_m^Ie_n^J+(P_⟨IJ⟩+2P_⟨IK⟩⟨JL⟩X^KL)ė_m^Iė_n^J , (m,n=σ,s) where 𝒩_IJ ≡ϕ̇^KP_⟨KI⟩,J-2/HX^KLX^NMP_⟨NI⟩⟨KL⟩P_⟨MJ⟩ , -ℳ_IJ ≡P_,IJ+(X^MNP_⟨MN⟩+2X^MNX^PQP_⟨MN⟩⟨PQ⟩-3H^2)X^KL/H^2P_⟨KI⟩P_⟨LJ⟩ +1/H(P_,I-2X^MNP_⟨MN⟩,I)P_⟨KJ⟩ϕ̇^K+1/a^3d/dt(a^3/HX^KLP_⟨KI⟩P_⟨LJ⟩) .","intent_p":0.84,"contests_p":null},{"arxiv_id":"hep-th/0605045","title":"Observational Signatures and Non-Gaussianities of General Single Field Inflation","url":"/paper/hep-th/0605045","section":"Mode Solutions","sentence":"It is convenient to introduce new variable $x≡-c_akη$ to characterize the time-evolution[A similar treatment can be found in Appendix A in [ref] , where an alternative variable $y≡c_s k /aH$ was chosen as the evolution variable.].","intent_p":0.95,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":3,"sentences":7,"quotes":[{"arxiv_id":"astro-ph/0605679","title":"Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion","url":"/paper/astro-ph/0605679","section":"Around Horizon-crossings","sentence":"The cross-power spectrum around adiabatic horizon-crossing is approximately[([ref]) can be compared with (e.g.) Eq.(37) in [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"0704.0212","title":"Curvature and isocurvature perturbations in two-field inflation","url":"/paper/0704.0212","section":"Cross-correlations","sentence":"Actually one may verify that when setting $c_a = c_e$, ([ref]) reduces to Eq.(79) in [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"astro-ph/0106022","title":"Oscillations During Inflation and the Cosmological Density Perturbations","url":"/paper/astro-ph/0106022","section":"Comparison with Previous Results with $c_a = c_e$","sentence":"Our goal is to show that the field-theoretical perturbative approach taken in this note is essentially equivalent to previous “diagonalization\" method taken in [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":3,"sentences":4,"quotes":[{"arxiv_id":"0704.0212","title":"Curvature and isocurvature perturbations in two-field inflation","url":"/paper/0704.0212","section":"Cross-correlations","sentence":"This confirms previous result that cross-correlations among different perturbation modes are always negligible when modes are deep in side their respective sound-horizons [ref] , since there the system reduces to a collection of weakly-coupled oscillators.","intent_p":0.97,"contests_p":null},{"arxiv_id":"astro-ph/0106022","title":"Oscillations During Inflation and the Cosmological Density Perturbations","url":"/paper/astro-ph/0106022","section":"Cross-correlations","sentence":"This confirms previous result that cross-correlations among different perturbation modes are always negligible when modes are deep in side their respective sound-horizons [ref] , since there the system reduces to a collection of weakly-coupled oscillators.","intent_p":0.97,"contests_p":null},{"arxiv_id":"astro-ph/0605679","title":"Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion","url":"/paper/astro-ph/0605679","section":"Cross-correlations","sentence":"This confirms previous result that cross-correlations among different perturbation modes are always negligible when modes are deep in side their respective sound-horizons [ref] , since there the system reduces to a collection of weakly-coupled oscillators.","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":44,"sentences":53,"quotes":[{"arxiv_id":"astro-ph/0605679","title":"Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion","url":"/paper/astro-ph/0605679","section":"Conclusion and Discussion","sentence":"Previous investigations of the cross-correlations are based on diagonalizting the coupled equations of motion [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"astro-ph/0106022","title":"Oscillations During Inflation and the Cosmological Density Perturbations","url":"/paper/astro-ph/0106022","section":"Conclusion and Discussion","sentence":"Previous investigations of the cross-correlations are based on diagonalizting the coupled equations of motion [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"0704.0212","title":"Curvature and isocurvature perturbations in two-field inflation","url":"/paper/0704.0212","section":"Conclusion and Discussion","sentence":"Previous investigations of the cross-correlations are based on diagonalizting the coupled equations of motion [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"0804.3139","title":"Primordial fluctuations and non-Gaussianities in multi-field DBI inflation","url":"/paper/0804.3139","section":"Introduction","sentence":"Actually, non-gaussianities in multi-field models with non-canonical kinetic terms have been extensively investigated in [ref] (see also [ref] ).","intent_p":0.99,"contests_p":null},{"arxiv_id":"0805.1299","title":"Non-Gaussianity, Isocurvature Perturbation, Gravitational Waves and a No-Go Theorem for Isocurvaton","url":"/paper/0805.1299","section":"Introduction","sentence":"Actually, non-gaussianities in multi-field models with non-canonical kinetic terms have been extensively investigated in [ref] (see also [ref] ).","intent_p":0.99,"contests_p":null}]}],"unlabelled_sentences":89},"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. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/0908.4035"}}