Quantum Noises and the Large Scale Structure

Quantum Noises and theQuantum Noises and theLarge Scale StructureLarge Scale Structure

Wo-Lung LeeWo-Lung Lee Physics Department, National Taiwan Normal UniversityPhysics Department, National Taiwan Normal University

In collaboration with Chun-Hsien Wu, Kin-Wang Ng, In collaboration with Chun-Hsien Wu, Kin-Wang Ng,

Da-Shin Lee, and Yeo-Yie CharngDa-Shin Lee, and Yeo-Yie Charng

Apr. 22 Apr. 22 @@ National Tsing Hua University National Tsing Hua University

IntroductionIntroduction

The recent observational results of CMB anisotropy by the WMAP The recent observational results of CMB anisotropy by the WMAP strongly support the strongly support the ΛΛCDM model with early inflationary expansionCDM model with early inflationary expansion

Although the result agrees with the generic predictions of inflationary Although the result agrees with the generic predictions of inflationary scenario within a statistical error, it still suggests two unusual features: scenario within a statistical error, it still suggests two unusual features: the running spectral indexthe running spectral index anan anomalously low value of the quadrupole momentanomalously low value of the quadrupole moment of the CMBof the CMB

CMB Angular Power Spectrum Before WMAPCMB Angular Power Spectrum Before WMAP

CMB Angular Power Spectrum by WMAPCMB Angular Power Spectrum by WMAP

Cosmic VarianceCosmic Variance

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


Mathematically, there are only 2Mathematically, there are only 2ll+1 samples of the power at each multipole. In +1 samples of the power at each multipole. In fact, the current generation of experiments that measure the peaks are even more 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 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 thateven smaller number of samples at each multipole such that


Given the large uncertainties due to thisGiven the large uncertainties due to this cosmic variancecosmic variance, , we might never know we might never know whether this constitutes a truly significant deviation from standard cosmological whether this constitutes a truly significant deviation from standard cosmological expectations.expectations.

Methods to Suppress the Large Scale PowerMethods to Suppress the Large Scale Power

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



There are several methods that can generate small quadrupole moment. In There are several methods that can generate small quadrupole moment. In principle, these methods can be classified into 3 categories:principle, these methods can be classified into 3 categories:

Topology of the universeTopology of the universe

Causality (Non-inflationary models)Causality (Non-inflationary models)

Initial hybrid fluctuationsInitial hybrid fluctuations

Quantum Colored Noise !!Quantum Colored Noise !!



There are several methods that can generate small quadrupole moment. In There are several methods that can generate small quadrupole moment. In principle, these methods can be classified into 3 categories:principle, these methods can be classified into 3 categories:

Topology of the universeTopology of the universe

Causality (Non-inflationary models)Causality (Non-inflationary models)

Initial hybrid fluctuationsInitial hybrid fluctuations

Inflation & The Large Scale StructuresInflation & The Large Scale Structures

Inflation generates superhorizon fluctuations without appealing to fine-tuned initial Inflation generates superhorizon fluctuations without appealing to fine-tuned initial setups. setups.

Quantum fluctuations are generated and amplified during the accelerated expansion Quantum fluctuations are generated and amplified during the accelerated expansion phase. These fluctuations remain constant amplitude after horizon crossing.phase. These fluctuations remain constant amplitude after horizon crossing.

The majority of inflation models predict The majority of inflation models predict Gaussian, adiabatic, nearly scale-invariantGaussian, adiabatic, nearly scale-invariant primordial fluctuationsprimordial fluctuations

The Horizon-Crossings vs. Length ScalesThe Horizon-Crossings vs. Length Scales

Calculating Gauge-Invariant FluctuationsCalculating Gauge-Invariant Fluctuations

Challenges to the Slow-Roll Inflation ScenarioChallenges to the Slow-Roll Inflation Scenario


Slow-roll kinematics Quantum fluctuations



Slow-roll conditions violated after horizon- crossing (Leach et al)(Leach et al) General slow-roll condition (Steward)(Steward) Multi-component scalar fields etc …



Slow-roll conditions violated after horizon- crossing (Leach et al)(Leach et al) General slow-roll condition (Steward)(Steward) Multi-component scalar fields etc …

Stochastic inflation – classical fluctuations driven by a white noise (Starobinsky)(Starobinsky) or by a colored noise (Liguori et al)(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 InflatonDensity Fluctuations of the Inflaton

Density Fluctuations of the InflatonDensity Fluctuations of the Inflaton

Long wavelength mean field High frequency fluctuation mode

The Forms of theThe Forms of the Window FunctionWindow Function


White noise Scale-invariant spectrum


White noise Scale-invariant spectrum

No suppression on large scalesNo suppression on large scales


A smooth window function (Liguori et al (Liguori et al astro-ph/0405544))


Colored noise low-l suppressed CMB spectrum

A smooth window function (Liguori et al (Liguori et al astro-ph/0405544))

Quantum Noise & Density FluctuationQuantum Noise & Density Fluctuation

To mimic the quantum environment, we consider a slow-rolling inflaton To mimic the quantum environment, we consider a slow-rolling inflaton coupled to a quantum massive scalar field coupled to a quantum massive scalar field σσ, with a Lagrangian given , with a Lagrangian given byby

Quantum Noise & Density FluctuationQuantum Noise & Density Fluctuation

To mimic the quantum environment, we consider a slow-rolling inflaton To mimic the quantum environment, we consider a slow-rolling inflaton coupled to a quantum massive scalar field coupled to a quantum massive scalar field σσ, with a Lagrangian given , with a Lagrangian given byby

Approximate the inflationary spacetime by a de Sitter metric asApproximate the inflationary spacetime by a de Sitter metric as

Langevin Equation for the InflatonLangevin Equation for the Inflaton

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

Dissipation



White Noise



producesproduces intrinsic inflaton quantum fluctuations intrinsic inflaton quantum fluctuations with a scale-invariant power spectrum with a scale-invariant power spectrum given by given by

Colored Noise



The Linearized Langevin EquationThe Linearized Langevin Equation

The Slow-Roll ConditionThe Slow-Roll Condition

The Noise-driven Power SpectrumThe Noise-driven Power Spectrum

Start of inflationThe 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 InflationLow CMB Quadrupole & the Onset of Inflation

The Hybrid Initial SpectrumThe Hybrid Initial Spectrum

SummarySummary

We have proposed a new source for the cosmological density We have proposed a new source for the cosmological density perturbation which is passive fluctuations of the inflaton driven perturbation which is passive fluctuations of the inflaton driven dynamically by a colored quantum noise as a result of its coupling to dynamically by a colored quantum noise as a result of its coupling to other massive quantum fields.other massive quantum fields.

The created fluctuations grow with time during inflation before horizon-The created fluctuations grow with time during inflation before horizon-crossing. Since the larger-scale modes cross out the horizon earlier, crossing. Since the larger-scale modes cross out the horizon earlier, thus resulting in a suppression of their density perturbation as thus resulting in a suppression of their density perturbation as compared with those on small scales.compared with those on small scales.

By using current observed CMB data to constrain the parameters By using current observed CMB data to constrain the parameters introduced, we find that a significant contribution from the noise-driven introduced, we find that a significant contribution from the noise-driven perturbation to the density perturbation is still allowed.perturbation to the density perturbation is still allowed.

Thank you for your attention.Thank you for your attention.

Quantum Noises and the Large Scale Structure

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