Final Report on theMeasurement of the temperature of theCosmic Microwave BackgroundToward fulfilling the requirements of PHY 210Srivas PrasadIn this report, I present the results of my investigations of the temperature of the cosmicmicrowave background using the apparatus developed for this purpose in the PHY 210laboratories.Background informationThe CMB is a practically isotropic radiation in the microwave region that is observedalmost completely uniformly in all directions. This radiation is understood to be the radiationemitted by the universe at an early period of its history. It then gives us a snapshot of the universeat this early period - only three hundred thousand years old. This is the time when the universefinally became cold enough for neutral atoms to form from their nucleons and electrons, about3000 K. Before this time / temperature, any neutral atoms formed could immediately be re-ionizedby the high-energy radiation. Once a low enough temperature is reached, ions and electrons caneffectively combine to form neutral atoms. As such, the universe is no longer opaque to radiation –as atoms become neutral, matter and radiation decouple, so that photons no longer keep scatteringoff the ions. When we examine the CMB, we look back to the time when light last interactedsignificantly with matter. In other words, the microwave background is really the light off the lastscatterings, and gives the so-called Surface of Last Scattering. As the universe expands and cools,the wavelength of this light increases by stretching out, so that the radiation is red-shifted, into themicrowave region.The isotropy of this radiation is quite remarkable – it exhibits a constancy of temperature towithin one part in a thousand in all directions. Further, the spectrum corresponds almost perfectlyto that of a blackbody at that temperature. As such, the first observations of the background lentstrong support to the Big Bang picture of cosmology. More recently, attention has focused onmeasuring the anisotropy of the microwave background, which gives invaluable information onthe conditions of the early universe, including its geometry, the fluctuations that eventually spawntoday’s galaxies, its expansion rate, nature of dark matter, and so on.Black BodyIt is useful here to elaborate somewhat on the theory of the Black Body.A perfect black body is a perfect absorber of light, so that it reflects none of it. Following thegeneral principle of good absorbers also being good emitters, such a black body also re-emits theabsorbed energy. In steady state, the black body re-emits all the absorbed energy in a spectrum thatdepends only on the temperature of the black body. In particular, the wavelength of maximumintensity depends on the temperature, in a relation given by Wein’s Displacement Law:Tλmax = a, a = 0.29 cm K approxHence, as the temperature of a body is raised it radiates energy as shorter and shorter wavelengths.It is important to note, that anisotropy notwithstanding, the CMB behaves as an almost perfectBlack body. Indeed, it is a better approximation to the blackbody than any made in the lab.Planck’s Law:A result of central importance in the theory of the black body is the celebrated Planck’s Law,which relates the energy density to the temperature and the frequency. It is this formula thatresolves the old problem of Black Body Radiation, viz. the apparently infinite energy that shouldbe radiated.here,T – temperature, n -- frequency, h – Planck’s constant, c – Speed of Light, k – Boltzmann’sConstantA low temperature approximation of this formula consists of a leading order series expansion,givingThis approximation is sufficiently precise for our purposes: at 10 GHz, the frequency of ourobservations, the relative error of this approximation is ~ 0.0008 at 300 K, 0.06 at 4 K.It is a matter of some concern that this relative error actually rises with the decrease oftemperature; however, for our purposes this level of precision is tolerable. To reduce this effect ofdecreasing the temperature, observations can be made at a different frequency.Experimental Procedure and Related Issues:For this measurement of the CMB temperature, the equipment consists of a receiver for 10 GHzwhich receives the signal, a series of amplifiers that amplify the signal, which is then converted toa voltage reading (a few milli Volt typically) on screen.Based on the approximation to Planck’s Law derived above, we expect the voltage – temperatureplot to be linear, so that the slope yields the change in voltage per rise in temperature. As such, bymeasuring the voltage readings for black bodies at different temperatures, we can obtain this line.Then, by obtaining the voltage reading for the microwave background, we can find thecorresponding temperature from the best-fit line.We use voltage readings for black bodies at room temperature, liquid nitrogen 77 K, and liquidhelium at 4.2 K.Absorbers: For this procedure to work, we need to ‘see’ the temperature spectra of a blackbody.As such, the receiver must be pointed at a black body at the different temperatures. For thispurpose, we use different commercially available microwave absorbers. By maintaining theseabsorbers at a certain temperature, we can thus observe the black body spectrum at thattemperature.In this experiment we used three types of absorbers – an absorber that works at a broader range offrequencies and has low coefficient of reflection, one that is optimal for the 10 GHz but has ahigher coefficient of reflection at glancing incidence, and an absorber of the same material as thefirst type but which is corrugated, reducing the angle of incidence and increasing the effectivesurface of absorber seen by the receiver.It was observed that to the degree of precision attained by this experiment, the precise type ofabsorber had no significant effect. One assumes that the second absorber works better at 10 GHzbut this effect is counterbalanced by its comparative ineffectiveness at glancing incidences.Minimize external light: In addition to reducing reflection by using high quality absorbers, it isdesirable to minimize the external light impinging on the system, so that the black body spectrumpredominates. To this effect, the receiver-absorber setup was wrapped in reflecting aluminum foil.It is noted that the use of high quality commercial absorbers partially negates the need for suchfoil, though the foil still makes a measurable