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In fluence of heavy modes on perturbations in multiple field inflation

In fluence of heavy modes on perturbations in multiple field inflation. Xian Gao ( 高显 ) Astroparticule et Cosmologie, Université Paris 7 (IAP & LPTENS) 13 October , 2012 Kavli Institute for Theoretical Physics China.

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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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