Physics Primer: The CMB


The Cosmic Microwave Background (CMB) 宇宙微波背景(CMB

For a helpful quick overview of the CMB, click here.



The microwaves of the CMB which we detecttoday are the redshifted form of the very "first light" that radiatedin the universe. Astronomers date this "first light" to about 370,000years after the big bang. In the immediate aftermath of the big bang, theuniverse consisted of an extremely hot dense plasma of ionized gas in whichphotons (light particles) were continually scattered by the free electrons inthe plasma, trapped as in a fog, so that the universe was completely dark.Eventually the universe cooled to a temperature at which the positive ions andelectrons were able to combine to form neutral atoms (called the "epoch ofrecombination"), so that photons no longer were scattered and light couldtravel freely through space. Cosmologists accordingly refer to this moment whenthe universe became transparent as both the "epoch of last scatter"and the "first light." The expansion of space caused this emittedcosmic radiation to gradually cool off from an original temperature of 3000K totoday's 2.7K (-450 degrees F) as the radiation was increasingly redshifted tothe microwave frequency -- the CMB.


CMB Temperature


 So far we hav only talked about the frequencyor wavelength of the cosmic radiation / light. So what does temperature has todo with it? How can we talk about the temperature of a ray of light?


Recall from lesson 3 (Unit Analysis), theenergy formula we have introduced:



where k is called Boltzmann's constant andT is a temperature measured in Kelvins. Then, if we use Planck's constant, wecan relate the frequency to the temperature:




This is a very "rough" estimateformula that is only partially correct and doesn't allow us to obtain a preciseresult. However, it does capture the physical connection between frequency andtemperature, and it also gives us a correct estimate of the scale.


The CMB radiation extends over a wholespectrum, but for this problem we'll approximate it to ν=160 GHz. Also, we knowthe values for the two constants h=6×10−34 Js and k=1.3×10−23 J/K. 

CMB辐射延伸到整个频谱,但对这个问题我们将近似它ν= 160 GHz。同时,我们知道这两个常数h =6×10−34 JSK = 1.3×10−23  J / K.的概念。

The CMB radiation is not overall spatiallyuniform – the radiation coming from different points in the sky can haveslightly different frequencies, and by association, different temperatures. Ifwe were to map the differences compared to the average temperature of 2.7 K, wewould get this picture of the fluctuations:

CMB辐射在空间上不是均匀的,天空中不同点的辐射会有轻微的不同频率,并且通过不同的温度关联。如果我们将这些差异与平均温度2.7 K进行比较,我们就可以得到这幅波动图:


Image of full-sky map of CMB from WMAP9-year data (2012) [NASA/WMAP]

WMAP 9年数据(2012)[NASA/WMAP]的全天空地图图像

The red and blue “spots” (also calledanisotropies) are the temperature fluctuations compared to the average. Theanisotropies represent compressed and rarefacted regions in the otherwiseuniform ionized gas of the early universe. The red hot spots (compressed) areregions with particles of slightly higher velocity (yielding slightly shorterwavelength radiation) and the cold blue spots (rarefacted)are regions with particles of slightly lower velocity (yielding radiation withslightly longer wavelength). These temperature fluctuations are tiny, of theorder of a part per million.            


The Concordance Model of RelativisticCosmology


Cosmological parameters include cosmiccurvature (the geometry of space at the largest scale – frequently labeled “thegeometry of the universe”), dark energy, ordinary (baryonic) matter, and darkmatter. Varying these parameters in numerical simulations imposes constraintson the observational data coming from the CMB, Type Ia supernovae, galaxyclusters, and from other studies.             


Let’s take as an example the geometry ofthe universe. As you learned in Lesson 4, according to Einstein’s generaltheory of relativity, the geometry of the universe is related to the total massΩm and total energy ΩΛ in the universe.


In relativistic cosmology, there are threepossibilities for the geometry of the universe depending on the relationbetween the total energy and the total mass:


l        Flat geometry (zero cosmiccurvature) with ΩmΛ=1 (the universe can be eitherinfinite or finite for a flat space)

l        平面几何(零宇宙曲率)与ΩmΛ=1(宇宙可以是无限或有限的平面空间)             

l        Open geometry (negative cosmiccurvature) with ΩmΛ<1 (the universe can be eitherinfinite or finite for a negatively-curved space) 

l        开放几何(负宇宙曲率)与ΩmΛ<1(宇宙可以是无限或有限的负曲率空间)             

l        Closed geometry (positivecosmic curvature) with Ωm+ΩΛ>1 (the universe is finite for apositively-curved space) 

l        封闭几何(正宇宙曲率)与ΩmΛ>1(宇宙是有限的正曲率空间)

The curvature, matter, and energyparameters have all been constrained by independent studies – most notably bystudies of the CMB, studies of Type Ia supernovae, and studies of baryonacoustic oscillation (BAO) signals from galaxy clusters – in the past decade.These parameter constraints all converge to a particular cosmological model –the concordance model of cosmology (Lambda-CDM Model) – which is indicated bythe gray ellipses (the intersection of the orange CMB line, blue Supernovaeellipses, and the green BAO line) in Figure 3.



Image source: Supernova Cosmology Project,Lawrence Berkeley National Laboratory


The concordance model of cosmology maintainsthat the universe is flat (observe that the gray ellipses fall along the linelabeled “Flat” in the figure), is expanding at an accelerating rate, is about13.8 billion years old, and is made up of about 68% dark energy, 27% darkmatter, and 5% ordinary (baryonic) matter.


CMB Simulation using NASA's CMB Analyzer


Try out this "Build a Universe"tool from NASA which enables you to adjust different cosmological parametersand observe the effect on the geometry and age of the universe, and on theappearance of the CMB: click here. On the page, be sure to read theinstructions and the information provided about the angular power spectrumgraph, and about the "ingredients" of the universe and "otherproperties" of the universe that you will be adjusting, and then click on"Make full screen in new window" to use the CMB Analyzer.