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Quantum Noises and the Large 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. Introduction.
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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
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
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.
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
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.
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!!
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
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 !!
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
Challenges to the Slow-Roll Inflation Scenario Slow-roll kinematics Quantum fluctuations
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 …
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)
Density Fluctuations of the Inflaton Long wavelength mean field High frequency fluctuation mode
Density Fluctuations of the Inflaton Long wavelength mean field High frequency fluctuation mode
White noise Scale-invariantspectrum The Forms of theWindow Function
White noise Scale-invariantspectrum No suppression on large scales The Forms of theWindow Function
The Forms of theWindow Function A smooth window function (Liguori et al astro-ph/0405544)
Colored noise low-l suppressed CMB spectrum The Forms of theWindow Function A smooth window function (Liguori et al astro-ph/0405544)
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
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
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:
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
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
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
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:
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:
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:
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
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