1 / 20

Effects of a pre-inflation radiation-dominated epoch to CMB anisotropy

Effects of a pre-inflation radiation-dominated epoch to CMB anisotropy. I-Chin Wang ( 王怡青 ) NCKU( 成功大學 ) & Kin-Wang Ng( 吳建宏 ) ASIoP( 中研院物理所 ) Jan 8 , 2008. Outline. Motivation:. at l =2 WMAP data & Λ CDM model is not consistent. Our Model:.

denna
Download Presentation

Effects of a pre-inflation radiation-dominated epoch to CMB anisotropy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Effects of a pre-inflation radiation-dominated epoch to CMB anisotropy I-Chin Wang (王怡青) NCKU(成功大學) & Kin-Wang Ng(吳建宏) ASIoP(中研院物理所) Jan 8 , 2008

  2. Outline • Motivation: at l=2 WMAP data &ΛCDM model is not consistent • Our Model: we assume a pre-inflation radiation-dominated phase before inflation • Numerical results • Conclusion

  3. Wilkinson Microwave Anisotropy Probe (WMAP) about 2.73k Is

  4. Equation for inflation fluctuation

  5. Our model A ~ radiation component ΛCDM model B ~ vacuum energy only inflation phase inflation radiation-dominated Transition point for A=1 B=1 case radiation inflation

  6. Initial condition radiation-dominated when a is small the horizon crossing k mode

  7. The power spectrum is a smooth curve… A ~ radiation component B ~ vacuum energy But… A smooth power spectrum is obtained under two conditions (1) a(t) is a smooth transition function (2) initial a(t) can’t be too close to the phase transition point or it will lead to oscillations on power spectrum

  8. ai=0.0001 abrupt slope ai=0.0001<<at at=(A/B)1/4 Initial a is too close to phase transition point at=1 The choice of initial a is very important !

  9. A ~ radiation component Numerical results B ~ vacuum energy B=1 A=7, 5, 1 and 0.1 z ~ duration of inflation

  10. B=1 and A=7

  11. B=1 and A=1

  12. B=0.1 A=7, 5, 1 and 0.1

  13. Using WMAP3 data to the chi-square fitting of the CMB anisotropy spectrum Note the chi-square fitting for ΛCDM model is 47.09 in WMAP3 data Using WMAP1 data to the chi-square fitting of the CMB anisotropy spectrum Note the chi-square fitting for ΛCDM model is64.99 in WMAP1 data

  14. Using WMAP3 data to the chi-square fitting of the CMB anisotropy spectrum Note the chi-square fitting for ΛCDM model is 47.09 in WMAP3 data Using WMAP1 data to the chi-square fitting of the CMB anisotropy spectrum Note the chi-square fitting for ΛCDM model is64.99 in WMAP1 data

  15. Conclusions : (1) By adjusting the values of A( radiation component), B( vacuum energy ) and z( duration of inflation) , it can lead to a low l=2 value. It also can determine how many e-folds between phase transition point and today’s 60 e-folds . (2) One year WMAP data prefers our model slightly and the pre-inflation radiation-dominated phase was taking place as 67 e-folds from the end of inflation . 7 e-folds 60 e-folds (radiation-dominated) (3) For choosing initial value a(t) , If the initial value is too close to the transition point , it will lead to an oscillating power spectrum which is due to an improper choice of initial a(t) . But if the initial a is in the proper region (radiation-dominated region) then the power spectrum is almost the same and smooth. It’s initial condition insensitive. Therefore, the oscillation is from a improper choice of initial a ! Phase transition

  16. The value of A and B … • We choose B=1 and B=0.1 with A=7,5,1,0.1 to do the simulation . The value of B is from the constraint Where the slow-roll parameter is The vacuum energy that drives inflation is given by with and then No observational constraint for the value of A , it can from the particle physics model you choose . Therefore , the following simulations are (1) B=1 & A=7,5,1,0.1 and (2) B=0.1 & A=7,5,1,0.1

  17. e-folding The value of z correspond to an exponential expansion with the number of e-folding from the start of inflation given by The total e-folding is : From observation that

  18. Log (1/H) 4300Mpc-1 N z=7 The meaning of z : NCMB=60 Log (a) Transition point Pink line : radiation-dominated Red line : inflation (vacuum energy dominated) Log (1/H) N z=11 4300Mpc-1 NCMB=60 Log (a) Transition point

  19. Quantitative comparison … The chi-square fitting is the following The measured ith band power Theoretical value The width of the error bar in measurement We use this chi-square fitting method to do a comparison . e-folding The value of z correspond to an exponential expansion with the number of e-folding from the start of inflation given by The total e-folding is : From observation that

More Related