Quantum Noises and the Large Scale Structure

1. Quantum Noises and theLarge Scale Structure Wo-Lung Lee Physics Department, National Taiwan Normal University In collaboration with Chun-Hsien Wu, Kin-Wang Ng, Da-Shin Lee, and Yeo-Yie Charng Apr. 22 @ National Tsing Hua University

2. Introduction • The recent observational results of CMB anisotropy by the WMAP strongly support the ΛCDM model with early inflationary expansion • Although the result agrees with the generic predictions of inflationary scenario within a statistical error, it still suggests two unusual features: • the running spectral index • ananomalously low value of the quadrupole momentof the CMB

3. CMB Angular Power Spectrum Before WMAP

4. CMB Angular Power Spectrum by WMAP

5. CMB Angular Power Spectrum by WMAP

6. CMB Angular Power Spectrum by WMAP

7. Cosmic Variance • At large angular scales CMB experiments are limited by the fact that we only have one sky to measure and so cannot pin down the cosmic average to infinite precision no matter how good the experiment is.

8. Cosmic Variance • Mathematically, there are only 2l+1 samples of the power at each multipole. In fact, the current generation of experiments that measure the peaks are even more severely limited in that they measure only a small fraction of the sky and so have an even smaller number of samples at each multipole such that

9. Cosmic Variance • Given the large uncertainties due to thiscosmic variance, we might never know whether this constitutes a truly significant deviation from standard cosmological expectations.

10. Methods to Suppress the Large Scale Power By cosmic variance, it means that we simply live in a universe with a low quadrupole moment for no special reason. However, the low quadrupole moment can be treated as a physical effect that requests an explanation!!

11. Methods to Suppress the Large Scale Power By cosmic variance, it means that we simply live in a universe with a low quadrupole moment for no special reason. However, the low quadrupole moment can be treated as a physical effect that requests an explanation!! There are several methods that can generate small quadrupole moment. In principle, these methods can be classified into 3 categories: • Topology of the universe • Causality (Non-inflationary models) • Initial hybrid fluctuations

12. Methods to Suppress the Large Scale Power By cosmic variance, it means that we simply live in a universe with a low quadrupole moment for no special reason. However, the low quadrupole moment can be treated as a physical effect that requests an explanation!! There are several methods that can generate small quadrupole moment. In principle, these methods can be classified into 3 categories: • Topology of the universe • Causality (Non-inflationary models) • Initial hybrid fluctuations Quantum Colored Noise !!

13. Inflation & The Large Scale Structures • Inflation generates superhorizon fluctuations without appealing to fine-tuned initial setups. • Quantum fluctuations are generated and amplified during the accelerated expansion phase. These fluctuations remain constant amplitude after horizon crossing. • The majority of inflation models predict Gaussian, adiabatic, nearly scale-invariant primordial fluctuations

14. The Horizon-Crossings vs. Length Scales

15. Calculating Gauge-Invariant Fluctuations

16. Challenges to the Slow-Roll Inflation Scenario

17. Challenges to the Slow-Roll Inflation Scenario Slow-roll kinematics Quantum fluctuations

18. Challenges to the Slow-Roll Inflation Scenario Slow-roll kinematics Quantum fluctuations • Slow-roll conditions violated after horizon- crossing (Leach et al) • General slow-roll condition (Steward) • Multi-component scalar fields • etc …

19. Challenges to the Slow-Roll Inflation Scenario Slow-roll kinematics Quantum fluctuations • Slow-roll conditions violated after horizon- crossing (Leach et al) • General slow-roll condition (Steward) • Multi-component scalar fields • etc … • Stochastic inflation – classical fluctuations driven by a white noise (Starobinsky) or by a colored noise (Liguori et al) coming from high-k modes • Driven by a colored noise from interacting quantumenvironment (Wu et alJCAP02(2007)006)

20. Density Fluctuations of the Inflaton

21. Density Fluctuations of the Inflaton Long wavelength mean field High frequency fluctuation mode

22. Density Fluctuations of the Inflaton Long wavelength mean field High frequency fluctuation mode

23. The Forms of theWindow Function

24. White noise Scale-invariantspectrum The Forms of theWindow Function

25. White noise Scale-invariantspectrum No suppression on large scales The Forms of theWindow Function

26. The Forms of theWindow Function A smooth window function (Liguori et al astro-ph/0405544)

27. Colored noise low-l suppressed CMB spectrum The Forms of theWindow Function A smooth window function (Liguori et al astro-ph/0405544)

28. To mimic the quantum environment, we consider a slow-rolling inflaton coupled to a quantum massive scalar field σ, with a Lagrangian given by Quantum Noise & Density Fluctuation

29. To mimic the quantum environment, we consider a slow-rolling inflaton coupled to a quantum massive scalar field σ, with a Lagrangian given by Quantum Noise & Density Fluctuation • Approximate the inflationary spacetime by a de Sitter metric as

30. Langevin Equation for the Inflaton • Following the influence functional approach, we trace out  up to the one-loop level and thus obtain the equation of motion for , which is a semiclassical Langevin equation:

31. Langevin Equation for the Inflaton • Following the influence functional approach, we trace out  up to the one-loop level and thus obtain the equation of motion for , which is a semiclassical Langevin equation: Dissipation

32. Langevin Equation for the Inflaton • Following the influence functional approach, we trace out  up to the one-loop level and thus obtain the equation of motion for , which is a semiclassical Langevin equation: White Noise producesintrinsic inflaton quantum fluctuations with a scale-invariant power spectrum given by

33. Langevin Equation for the Inflaton • Following the influence functional approach, we trace out  up to the one-loop level and thus obtain the equation of motion for , which is a semiclassical Langevin equation: Colored Noise

34. Langevin Equation for the Inflaton • Following the influence functional approach, we trace out  up to the one-loop level and thus obtain the equation of motion for , which is a semiclassical Langevin equation:

35. Langevin Equation for the Inflaton • Following the influence functional approach, we trace out  up to the one-loop level and thus obtain the equation of motion for , which is a semiclassical Langevin equation:

36. Langevin Equation for the Inflaton • Following the influence functional approach, we trace out  up to the one-loop level and thus obtain the equation of motion for , which is a semiclassical Langevin equation:

37. The Linearized Langevin Equation

39. The Slow-Roll Condition

40. Start of inflation The Noise-driven Power Spectrum The noise-driven fluctuations depend upon the onset time of inflation and approach asymptotically to a scale-invariant power spectrum

41. Low CMB Quadrupole & the Onset of Inflation

43. The Hybrid Initial Spectrum

44. We have proposed a new source for the cosmological density perturbation which is passive fluctuations of the inflaton driven dynamically by a colored quantum noise as a result of its coupling to other massive quantum fields. The created fluctuations grow with time during inflation before horizon-crossing. Since the larger-scale modes cross out the horizon earlier, thus resulting in a suppression of their density perturbation as compared with those on small scales. By using current observed CMB data to constrain the parameters introduced, we find that a significant contribution from the noise-driven perturbation to the density perturbation is still allowed. Summary

45. Thank you for your attention.