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In fluence of heavy modes on perturbations in multiple field inflation

This research explores the impact of heavy modes on perturbations in multiple field inflation models. The study investigates the behavior of trajectories and perturbations during turning processes, and the effects of soft and sharp turns on the trajectory evolution.

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In fluence of heavy modes on perturbations in multiple field inflation

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  1. Influence of heavy modes on perturbations in multiple field inflation Xian Gao (高显) Astroparticule et Cosmologie, Université Paris 7 (IAP & LPTENS) 13October, 2012 Kavli Institute for Theoretical Physics China with David Langlois and Shuntaro Mizuno, arXiv:1205.5275, and work in progress

  2. Single field inflation and beyond • The simplest models of single light scalar-field inflation remaincompatible with current observations. • Huge degeneracies: • Inflation is a (even not the only) paradigm. • Distinguishing alternative paradigms (bounce, cyclic, cosmic strings, string gas...): gravitational waves, non-Gaussianities, isocurvature modes, etc.[Talks by Senatore, Kleban, Ferreira, Wands et al.]

  3. Multiple and massive • Massive (M >= H) modesmay be allowed and play some role in multi-field models.[Talk by Yi Wang] • As long as there is a light (flat) direction in the multi-field potential, inflation occurs, while other directions may be heavy. • Perturbations feel the whole potential landscape, not only the light direction. A landscape of potentials

  4. Heavy modes? Integrate out? H • Naively, an effective theory for the light mode(s) is expected. • If there is a bending trajectory: The trajectory generally deviates from the light direction. The adiabatic mode can become temporarily heavy.The effective single-field description may break down. • Recent progress:Tolley & Wyman `09. Cremonini, Lalak & Turzynski '10, Achucarro, Gong, Hardeman, Palma, Patil `1.,Shiu & Xu `11, Watson et al '12. Chen & Wang `12, Pi & Sasaki....

  5. Heavy modes at work: Turning trajectory Multi-field effects manifest themselves only when the background trajectory is bending. We will describe a single turning process, by requiring (the minimal deviation from the standard scenario): 1) the turning process occurs in a finite time interval 2) the potential troughis asymptoticallystraightbefore and after the turn. Different from "constant turn" [Chen & Wang '09, '12]

  6. Single turn: basic picture

  7. Single turn: basic picture Intuitively, the trajectory deviatesfrom the light direction of the valley due to the centrifugal force.

  8. Single turn: basic picture Intuitively, the trajectory deviatesfrom the light direction of the valley due to the centrifugal force, and then starts to oscillate. [Shiu & Xu '11, Chen, '11, '12]

  9. Turning trajectory: a two-field example

  10. Turning trajectory: a two-field example The background trajectory is characterized by: • Velocity: • Direction:A simple approximate equation of motion for ψ(|ψ|<<1): • In general, the trajectory (adiabatic direction)tends to deviate from the light direction, with turning light direction θp serves as a driving force; • ψbehaves as a damped oscillator with frequency controlled by mh;

  11. A Gaussian toy model A toyGaussianansatz: "Energy scale" of the turn: μ = 1/Δt >> H The qualitative behaviors of the trajectory and the perturbations are sensitive to the ratio:μ/mh.

  12. Soft turn (μ<<mh) Before (-μt >> 1)and during (|μt| <≈ 1)the soft turn: Evolution of ψ=θ-θp Evolution of θ and θp

  13. Soft turn (μ<<mh) Before (-μt >> 1)and during (|μt| <≈ 1)the soft turn: Evolution of ψ=θ-θp Evolution of θ and θp

  14. Soft turn (μ<<mh) Before (-μt >> 1)and during (|μt| <≈ 1)the soft turn: Evolution of ψ=θ-θp Evolution of θ and θp

  15. Soft turn (μ<<mh) Before (-μt >> 1)and during (|μt| <≈ 1)the soft turn: Evolution of ψ=θ-θp Evolution of θ and θp

  16. Soft turn (μ<<mh) • Soft turn (μ<<mh): • If the turn is soft, the trajectory tightly follows the light direction, with tiny deviation just around the turning point. • The "softer" the turn is, the closer the background trajectory is to the light direction. • After the turn, the trajectory soon relaxes and re-coincides with the light direction. • There is no explicit oscillationwith the trajectory. • The adiabatic/entropic modes are approximately the light/heavy modes.

  17. Sharp turn (μ>≈mh) Evolution of ψ=θ-θp Evolution of θ and θp

  18. Sharp turn (μ>≈mh) Evolution of ψ=θ-θp Evolution of θ and θp

  19. Sharp turn (μ>≈mh) Evolution of ψ=θ-θp Evolution of θ and θp

  20. Sharp turn (μ>≈mh) Evolution of ψ=θ-θp Evolution of θ and θp

  21. Sharp turn (μ>≈mh) • Sharp turn (μ>≈mh): • Soon after the sharp turn, the trajectory starts to oscillate, with considerable amplitude. • The adiabatic/entropic-basis rapidly rotates. • The adiabatic/entropic modes get rapidly mixed with light/heavy modes. • The adibatic (curvature) mode has not necessarily to be light, which can be temporarily heavy around the turn. [Achucarro, Gong, Hardeman, Palma, Patil, '10. Shiu & Xu, '11]

  22. Adiabatic/entropic v.s. light/heavy after the turn Two possible decompositions: Adiabatic/entropic decomposition [Gordon, Wands, Bassett & Maartens '00, Groot Nibbelink & van Tent '01] Light/heavy decomposition kinematical feature potential feature • Adiabatic/entropic decomposition has special advantage, since the adiabatic mode is directly related to the curvature perturbation. • Light/heavy modes are directly related with the shape of the inflationary potential, which is (sometimes) more robust and simpler. • The final spectra for the curvature perturbation:

  23. Characteristic scales

  24. Characteristic scales light mode

  25. Characteristic scales light mode

  26. Characteristic scales light mode heavy mode

  27. Characteristic scales Turn

  28. Characteristic scales Turn Non-oscillatory Main oscillatory features Damped oscillatory features

  29. Perturbations A massless mode and a massive mode, in the dS approximation: withGaussian ansatz: We will solve both the full two-field system as well as the effective single light-field theory.

  30. Numerics: fixed mh

  31. Numerics: fixed mh The effective theory works quite well! Oscillation features

  32. Numerics: fixed mh The effective theory is not so good! Oscillation features

  33. Numerics: fixed mh The effective theory is too bad! Oscillation features

  34. Main message from this talk • Heavy field(s) may play a role in the early Universe. • Light/heavy decomposition may be more convenient. • Sharp turn may produce features in the spectra of light mode(s). • Effective single-field description may not be valid. • Probing the ultrahigh energy scale.

  35. Thank you for your attention!

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