Analysis of Multi-Field Inflation Models and Perturbations
Explore the dynamics and constraints of multi-field inflation models, focusing on the perturbations and fields' redefinition. Discover the impact of phase differences and adiabatic perturbations in the early universe's exponential expansion, shedding light on the observations and theoretical frameworks.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Multi T-Model Inflation Ryota Tozuka with Kei-ichi Maeda, Shuntaro Mizuno Waseda U. Kyoto U., Yukawa Inst.
Introduction Inflation exponential expansion at the early universe Observation(CMB) ??,?, Constrain to the Inflation model ? ?2 r 2 ? 3 41 exp ? + ?2Type 2 3? ns
Inflation from spontaneously broken conformal symmetry Kallosh, Linde 2013) Action Conformal Symm. ?? 1,1 Symm. ???= 1 2?????? ?2 1 2?????? +?2 ? 1 12? ? 4?2 ?2 2 6cosh? 6 6sinh? 6 = 12? + ? = ?2 ?2= 6 Constraint ghost free ? = 1 2? 1 2?????? 9? = ? Const. de Sitter
Inflation from spontaneously broken conformal symmetry Kallosh, Linde 2013) Action Conformal Symm. 2?????? ?2 1 2?????? +?2 ? 1 1 ? ? ?2 ?2 2 = 12? + 12? 36? 6cosh? ? = 6 ?2 ?2= 6 6sinh? Constraint ghost free ? = 6 ?2 1 2? 1 2?????? ? 1 e 2/3? ex ? = ? = ? ? + ?2 4 Starobinsky Type 2 ? =? ? ? 1 2? 1 2?????? ? ? 2tanh? = ? 2 6 T Type ? = ?2/12 1 ??= 2/?,
Multi T-Model Inflation Action (Conformal Symm.) 2 2 2 ? 1 2???????? ?? 1 2????????+?? 1 ?? 2 ?? ?? 22 2 ?? = 12? + 12? ?? 36 Constraint ghost free 2 ?? 2= ?? 2 ?? Micosh?? ??sinh?? ??= ??,??= ?? Action ? ? 2 1 2+?? ?? ?? 4tanh2?? = ? ??? 2?? 2 ?=1 ? 2 2= 6Mpl Coefficient of R ?? small ? ??? ? ?????? co ?? ? large ?=1
Metric specially flat gauge ??2= 1 2? ??2+ 2??,?????? + ?2????????? Inflaton ?? ??+ ??? ?,?,??? : perturbation (scalar) E.o.M. Perturbation Back Ground (BG) ?2 ?2+ ??,??????? ?3 ? ?? ?? ??+ 3? ??+ ??,??= 0 ? ??+ 3?? ??+ 1 ?3 ? ???= 0 Freidman linear Einstein Eq.
The initial condition (Bunch-Davies Vacuum) ? 2?3? ???;0 ???;0? = For 2-field case ? 2?3 ? 2?3e ?? ??1= ? [0,2?) : Phase difference ??2= In some case, the dynamics is depend on the phase difference
Analysis of the perturbation ??,?, Single-field Adiabatic perturbation Multi-field Adiabatic perturbation , Entropy perturbation redefinition of the perturbative fields : (C Gordon, D Wands, BA Bassett, R Maartens,2000) ? ?2 ??2 ?? perturbation adiabatic ?? ? ? ?? entropy ?? ?? ?? BG trajectory ?3 2?2 2,??,? ??1 ? = ?1 2+ ?2 2 ?? ?1
Example turn ?1= ?2= ?1= ?2= 10 10 (initial value ?1;0,?2;0) 3, ??=1 4??tanh2?? 2?? ?? ? We can classify the dynamics when the turn occurs: 1. ? 60 2. 2. ? ?? 3. ? < 60
Case 1. ? 60 ?1;0= 4,?2;0= 6 ?1,?2 = 4,6 ? = 60 ? = 0 Single-field like
Case 1. ? 60 Dynamics of the amplitude ? ?? ? = ??|?=60 ?? 0.966 ? 0.00165 ?3 2?2| |2 ? =
Case 2. ? 60 ?1;0= 4.57,?2;0= 5.43 ?1,?2 = 4.57,5.43 ? = 60 ? = 0 BG field turn around ?~60
Case 2. ? 60 ? = 0 ?? 0.855 ? 0.00167
Case 3. ? < 60 ?1;0= 4.7,?2;0= 5.3 ?1,?2 = 4.7,5.3 ? = 60 ? = 0 turn ?~40
Case 3. ? < 60 ? =? ? = 0 2 ?? 0.975 ? 0.00222 ? =? 4
Result Constraint of initial condition?1;0,?2;0 Case Case 1. 1. turn turn at sub horizon at sub horizon single single- -field Case Case 2. 2. turn around h turn around horizon Case Case 3. 3. turn at turn at Super horizon Super horizon field like like orizon crossing crossing ?? contour plot
Conclusion The dynamics is different when the turn occurs Almost of all the case, the entropy perturbation is generated at sub horizon (single-field like) ??=1 4??tanh2?? 2?? ?? ? Try the different parameter ??,?? constraint the model Calculate more than 3-field ? 2 2= 6Mpl ?? In progress ?=1
