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暗能量、残余引力波、 CMB 极化Dark energy, relic GW and CMB polarization

张杨 (Yang Zhang) 中国科学技术大学 (USTC)天体物理中心 (CFA)

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Outline Of Topics

• 一、 Cosmic Dark Energy• 二、 Relic Gravitational Waves• 三、 CMB Polarizations by RGW

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一、 Cosmic Dark Energy

-- the effective YM condensate model

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Observational Evidence for Accelerating Expansion

• SN Ia 型超新星• Riess(1998)• Permutter(1999)• Tonry(2003), z=0.3~1.3, 8 new• Knop(2003), z=0.36-0.86, 11 new• CMB anisotropies (WMAP)• Large scale structure etc.

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Models for Dark Energy:

1. Cosmological constant: Λ

2. Effective gravity: L = R + bR lnR +…

3. scalar field ： quintessence, k-essence, etc

4. Bag-Model (T.D.Lee) φ =const.

5. Effective Yang-Mills condensate

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Coincidence Problem ：

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strategy:

construct a tracking solution,

the present state is insensitive to the initial conditions.

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Effective Yang-Mills condensate:

Idea: What if the Universe is filled with quantum effective YM condensate as the ground state?

The universe is quite similar to the QCD vacuum in hadrons, to which the quantum effective Yang-Mills condensate contributes.

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Recall : MIT Bag Constant :

Idea: Quarks inside hadrons feel a vacuum with ρ=B, p= -B, where B is MIT Bag constant.

QCD vacuum in hadrons can be phenomenologically described by the B, to which the gluon condensate contributes.

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Interesting features:

quantum effective—1-loop contribution;gauge invariance; Lorentz invariance;correct trace anomaly;

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Observe that:

the effective YM condensate behaves as

at high energies, py → ρy /3, radiation

at low energies, py →-ρy , dark energy

This will lead to the scaling behavior, and the track solution.

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Friedmann equation:

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Non-interaction:

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Interaction with matter:

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The model 1 :

i.e. the YM condensate decays into matter at the rate Г.

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Remark:

A tracker solution exists for a wide range of the initial YM energy density;

The present state ΩΛ≈0.73, Ωm≈0.27

is realized naturally as a result of evolution;

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wy =ρy/py goes from 1/3 crosses over -1,and settles down to w< -1;

Other choices of Г/H also yield similar evolution behavior; ρm levels off;

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The asymptotic behavior of the tracker solution with

Ωy →0.73, Ωm→ 0.27, as t → ∞It is a fixed point, and it is stable .

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Phase graph for trajectories:

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The model 2:

i.e. the matter decays into the YM condensate at a rate Г.

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Remark: similar to the model 1

wy =ρy/py also goes from 1/3, and approaches to -1, but does not go to w< -1;

ρm does not level off.

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Interaction with both Matter and Radiation:

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Taking, for instance, the couplings as :

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Remark: similar to the previous models.

Both ρm and ρ r level off.

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The past history of the Universe is similar to the standard Big Bang model,

and yet the future Universe is a steady one, quite similar to the Steady State Model (Bondi, Gold, Hoyle, 1948).

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Section Summary:

The effective YM condensate dark energy model can solve the coincidence problem

for generic interactions with matter and radiation,

and for a wide range of initial values of YM density.

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二、 Relic GW

--- in the accelerating universe driven by dark energy

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How does the dark energy affect the spectrum of relic GW ？

We have obtained the exact spectrum h(t,k) of relic GW

in the accelerating Universe

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GW: transverse and traceless

wave equation:

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the spectrum is defined by

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the initial condition:

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which can be fixed by CMB anisotropies on large scales:

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various stages of expansion

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Now add the accelerating stage:

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connecting condition:

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The scale factor a(t) depends the dark energy

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Influence of the index β

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Probed by 2nd run of LIGO

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To be probed by next generation LISA

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The influence of dark energy:

h( k,τ) Ωm/ΩΛ

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The spectral energy density constrained by:

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In high frequency range:

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Reheating enhances the amplitude in the high frequency range:

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Very high frequencies

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section summary:

• Amplitude of RGW is modified by : h(k,τ) Ωm/ΩΛ ； The model ΩΛ=0.65 is ~50% higher than ΩΛ=0.70; ----- an effect detectable.• Spectrum is sensitive to the inflationary models. β =>-1.8 is ruled out by LIGO;

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•Nucleosynthesis bound puts β =-1.9 in danger;The model β =<-2.0 is still robust.Reheating enhances the high frequency amplitude, which may be detectable.

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三、 CMB Polarizations induced by RGW

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• Magnetic type of CMB polarization can only be produced by GW.

----This gives a way to detect GW on large scales.

We have obtained the analytic expressions for the CMB polarization spectra .

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Sachs-Wolfe term:

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In Polnarev’s method the Bolzmann’s equation reduces to :

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The polarization spectra of CMB:

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As a source, GW is given by:

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Polarizations are generated via Thompson Scattering during the decoupling.

It is described by the optical depth, or more conveniently, by the visibility function V(t).

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The visibility function is usally modeled by a Gaussian function, but we model it by two pieces of half-Gaussian curves:

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V(t) depends on the baryon very sensitively:

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Integration to yield β:

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where

This is because we have modeled the visibility function V as consisting of two half-gaussian pieces:

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The resulting analytic spectra:

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The electric polarization spectrum:

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The magnetic polarization spectrum:

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Dependence on baryon density Ωb:

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Dependence on dark energy ΩΛ:

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Dependence on primordial index nT:

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To be detected:

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works on the topics Gen. Rel. Grav. 34, 2155 (2002) Gen. Rel. Grav. 35; 689 (2003) Chin.Phys.Lett.20, 1899 (2003) Chin.Phys.Lett. 21, 1183 （ 2004 ） Class. Quant. Grav. 22, 1383 （ 2005 ） Chin. Phys. Lett. 22, 1817 （ 2005 ） Chinese Astron and Astrophys 29, 250 （ 2005 ） Class. Quant. Grav. 23, 3783 （ 2006 ） Class. Quant. Grav. 23, 3405 （ 2006 ） PRD.73, 123509 (2006) PRD.74, 043503 (2006) Phys.Lett.B64, 69    (2006).

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谢 谢 ! Merci !