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

Introduction The recent observational results of CMB anisotropy by the WMAP strongly support the ΛCDM model with early inflationary expansion 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: 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  an anomalously low value of the quadrupole moment of the CMB

CMB Angular Power Spectrum Before WMAP

CMB Angular Power Spectrum by WMAP

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. 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 2 l +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 Mathematically, there are only 2 l +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 this cosmic variance, we might never know whether this constitutes a truly significant deviation from standard cosmological expectations. Given the large uncertainties due to this cosmic 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 Topology of the universe Causality (Non-inflationary models) Causality (Non-inflationary models) Initial hybrid fluctuations Initial hybrid fluctuations

Quantum Colored Noise !! Quantum Colored Noise !! 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 Topology of the universe Causality (Non-inflationary models) Causality (Non-inflationary models) Initial hybrid fluctuations Initial hybrid fluctuations

Inflation & The Large Scale Structures Inflation generates superhorizon fluctuations without appealing to fine-tuned initial setups. 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. 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 The majority of inflation models predict Gaussian, adiabatic, nearly scale-invariant primordial fluctuations

The Horizon-Crossings vs. Length Scales

Calculating Gauge-Invariant 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- (Leach et al) crossing (Leach et al) General slow-roll condition (Steward) (Steward) Multi-component scalar fields etc …

Challenges to the Slow-Roll Inflation Scenario Slow-roll kinematics Quantum fluctuations Slow-roll conditions violated after horizon- (Leach et al) crossing (Leach et al) General slow-roll condition (Steward) (Steward) Multi-component scalar fields etc … Stochastic inflation – classical fluctuations driven by a white (Starobinsky) noise (Starobinsky) or by a colored (Liguori et al) noise (Liguori et al) coming from high-k modes Driven by a colored noise from interacting quantum environment (Wu et al ) (Wu et al JCAP02(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

The Forms of the Window Function

White noise Scale-invariant spectrum

The Forms of the Window Function White noise Scale-invariant spectrum No suppression on large scales No suppression on large scales

The Forms of the Window Function (Liguori et al ) A smooth window function (Liguori et al astro-ph/ )

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

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 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 To mimic the quantum environment, we consider a slow-rolling inflaton coupled to a quantum massive scalar field σ, with a Lagrangian given by Approximate the inflationary spacetime by a de Sitter metric as 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: 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: 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 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: 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: produces intrinsic inflaton quantum fluctuations with a scale-invariant power spectrum given by produces intrinsic inflaton quantum fluctuations with a scale-invariant power spectrum given by

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: 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: 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: 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: 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:

The Linearized Langevin Equation

The Slow-Roll Condition

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

Low CMB Quadrupole & the Onset of Inflation

The Hybrid Initial Spectrum

Summary 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. 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. 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. 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.

Thank you for your attention.