PHYS 210Spring 2006Experimental CosmologyThe goal of Cosmology is to understand the physical history of our Universe, how it formed anddeveloped, why does it have certain characteristics and how will it evolve in the future.Cosmology draws heavily on particle physics and astronomical observations. We will discussjust one such observation, the Cosmic Microwave Background (CMB).1. Black Body RadiationBlack body radiation is a simple consequence of equipartition of thermal energy. At atemperature T each degree of freedom, including each quantum mode of electromagnetic field,has an average thermal energy equal to kT/2. It can be shown that the energy density as afunction of temperature is given by118),(/33−=kThechTuννπν.The spectrum of the radiation is shown on the right for atemperature of 2 K. The frequency of the maximum energydensity depends linearly on the temperature,)(GHz59maxKT=ν. For example, at room temperature(~300 K) the maximum occurs at about 2×1013 Hz orwavelength of 17 µm, in the far infrared and at 6000 K,which is the temperature of the Sun, the peak is in thevisible range. At low frequencies, when hν/kT`1, theenergy density is proportional to the temperature. As the name suggests, the black body radiationis only emitted by “black”, i.e. not transparent objects, which absorb and emit the radiation inequilibrium with their own temperature. The black body radiation can be used for non-contacttemperature measurements. Infrared thermometers based on this principle are easily available.2. Evolution of the UniverseThe universe started in a very hot and dense state immediately after the Big Bang. In thisstate photons as well as all other particles were thermal equilibrium. Eventually the Universeexpanded and cooled until the electrons and protons combined into neutral atoms and theUniverse became transparent to light. The black body radiation photons that existed at that time,about 390,000 years after the Big Bang, continued to propagate freely through the Universe. Asthe Universe continued to expand the wavelength of the photons increased and their temperaturedropped. Today, after 13.7 billion years, the temperature of the cosmic black body radiation is2.7K. The radiation is nearly uniform in all directions, but not perfectly so. Small temperaturefluctuations, about 1 part in 104, exist due to initial density fluctuations that eventually developedinto stars and galaxies that we see today. In fact, the spectrum of these fluctuations, recentlymeasured with exquisite precision by the Wilkinson Microwave Anisotropy Probe constructed atPrinceton, tells us a lot about the properties of our Universe.3. Measurement of the microwave radiationRadiation in this range is measured using electronic technology. However, because thewavelength of the radiation is very short (millimeters to centimeters), great care is needed inconstruction of the electronics. Every piece of wire becomes an inductor or an antenna.Fortunately, microwave technology is fairly mature and compact amplifiers, filters and othercomponents are easily available commercially. We will use a simple combination of thesecomponents to measure the energy density of the radiation at 10 GHz. At this frequency, theenergy is directly proportional to the temperature. However, one has to take into account theamplifier noise, reflection of microwaves and other systematic uncertainties. By carefulcalibration of the detector at several temperatures one can make an absolute measurement of thepresent temperature of the