Non-Gaussianity for a two component hybrid model of inflation

Alabidi, Laila

doi:10.1088/1475-7516/2006/10/015

Cited by 56 publications

(103 citation statements)

References 15 publications

Supporting

Mentioning

100

Contrasting

Order By: Relevance

“…In the following calculations we use the definitions Mcm dp p F i (p, τ 1 , τ 2 ) p+k p−k dp ′ p ′ G R j (p ′ , τ 1 , τ 2 ), (D. 21) for i and j from 1 to 3:…”

Section: D12 Amputated Diagrams For Large Internal Momentamentioning

confidence: 99%

“…those involving multiple fields, the curvature perturbation ζ is not constant after horizon exit. Therefore evolution after horizon exit might lead to non-Gaussian effects, which has been investigated in [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. These investigations have been done by solving classical equations of motion, which is assumed to be a good approximation to the quantum theory, because quantum effects are presumably negligible for wavelengths much longer than the horizon length (see [28] for a recent argument).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Classical approximation to quantum cosmological correlations

Meulen¹,

Smit²

2007

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

Abstract:We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study φ 3 theory on a de Sitter background for a massless minimally coupled scalar field φ. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale H are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.

show abstract

“…In the following calculations we use the definitions Mcm dp p F i (p, τ 1 , τ 2 ) p+k p−k dp ′ p ′ G R j (p ′ , τ 1 , τ 2 ), (D. 21) for i and j from 1 to 3:…”

Section: D12 Amputated Diagrams For Large Internal Momentamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Classical approximation to quantum cosmological correlations

Meulen¹,

Smit²

2007

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

show abstract

“…While simple single-field models predict negligible levels of non-Gaussianity [4,5], significant non-Gaussianity can be generated by different mechanisms, such as features in the inflaton potential [6], the curvaton scenario [7][8][9][10][11], modulated reheating/preheating [12][13][14][15][16][17], and an inhomogeneous end of inflation [18]. It is also possible to generate significant non-Gaussianity during multi-field inflation [19][20][21][22][23], for a review see [24]. For a complete review of primordial non-Gaussianity, see [25].…”

Section: Introductionmentioning

confidence: 99%

Influence of reheating on the trispectrum and its scale dependence

Leung¹,

Tarrant²,

Byrnes³

et al. 2013

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

We study the evolution of the non-linear curvature perturbation during perturbative reheating, and hence how observables evolve to their final values which we may compare against observations. Our study includes the evolution of the two trispectrum parameters, gNL and τNL, as well as the scale dependence of both fNL and τNL. In general the evolution is significant and must be taken into account, which means that models of multifield inflation cannot be compared to observations without specifying how the subsequent reheating takes place. If the trispectrum is large at the end of inflation, it normally remains large at the end of reheating. In the classes of models we study, it remains very hard to generate τNL f 2 NL , regardless of the decay rates of the fields. Similarly, for the classes of models in which gNL τNL during slow-roll inflation, we find the relation typically remains valid during reheating. Therefore it is possible to observationally test such classes of models without specifying the parameters of reheating, even though the individual observables are sensitive to the details of reheating. It is hard to generate an observably large gNL however. The runnings, n f NL and nτ NL , tend to satisfy a consistency relation nτ NL = (3/2)n f NL regardless of the reheating timescale, but are in general too small to be observed for the class of models considered.

show abstract

“…Indeed, there have been many attempts to calculate the level of non-Gaussianity in general multi-field models (e.g., [31][32][33][34][35][36][37][38][39][40][41][42]), as well as in two-field models (e.g., [43][44][45][46][47][48][49][50][51]). However, it has been very difficult to find models that produce large nonGaussianity, though some exceptions have been found such as in the curvaton model [52][53][54][55][56][57][58], hybrid and multibrid inflation (e.g., [59][60][61][62][63][64][65][66][67]), in certain modulated and tachyonic (p)re-heating scenarios (e.g., [68][69][70][71][72][73][74]), and in some quadratic small-field, two-field models by taking appropriate care of loop corrections [75,76]. Moreover, it has not been wholly clear why it is so diff...…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussianity in two-field inflation

2011

View full text Add to dashboard Cite

We derive semi-analytic formulae for the local bispectrum and trispectrum in general two-field inflation and provide a simple geometric recipe for building observationally allowed models with observable non-Gaussianity. We use the δN formalism to express the bispectrum in terms of spectral observables and the transfer functions, which encode the super-horizon evolution of modes. Similarly, we calculate the trispectrum and show that the trispectrum parameter τNL can be expressed entirely in terms of spectral observables, which provides a new consistency relation unique to two-field inflation. We show that in order to generate observably large non-Gaussianity during inflation, the sourcing of curvature modes by isocurvature modes must be extremely sensitive to a change in the initial conditions orthogonal to the inflaton trajectory and that the amount of sourcing must be non-zero. Under some minimal assumptions, we argue that the first condition is satisfied only when neighboring trajectories through the two-dimensional field space diverge during inflation. Geometrically, this means that the inflaton must roll along a ridge in the potential V for some time during inflation and that its trajectory must turn somewhat in field space. Therefore, it follows that under our assumptions, two-field scenarios with attractor solutions necessarily produce small nonGaussianity. This explains why it has been so difficult to achieve large non-Gaussianity in two-field inflation, and why it has only been achieved in a narrow class of models where the potential and/or the initial conditions are fine-tuned. Some of our conclusions generalize at least qualitatively to multi-field inflation and to scenarios where the interplay between curvature and isocurvature modes can be represented by the transfer function formalism.

show abstract

Non-Gaussianity for a two component hybrid model of inflation

Cited by 56 publications

References 15 publications

Classical approximation to quantum cosmological correlations

Classical approximation to quantum cosmological correlations

Influence of reheating on the trispectrum and its scale dependence

Non-Gaussianity in two-field inflation

Contact Info

Product

Resources

About