Cosmic Background Radiation Temperature Anisotropy : Position of First Doppler Peak

The purpose of the Cosmic Background Radiation (CBR) experiments is to measure the temperature anisotropy via the autocorrelation function. The partial wave l1 corresponding to the first Doppler peak caused by baryonphoton oscillations at the surface of last scattering depends on the present density Ω0 and the cosmological constant contribution ΩΛ. We discuss this dependence on the basis of perspicuous figures. Typeset using REVTEX 1 I. CBR TEMPERATURE ANISOTROPY. Although the Cosmic Background Radiation (CBR) was first discovered over thirty years ago [1], the detection of its temperature anisotropy waited until 1992 when the Cosmic Background Explorer (COBE) satellite provided its impressive experimental support [2,3] for the Big Bang model. In particular, the COBE results were consistent with a scale-invariant spectrum of primordial scalar density perturbations [4–7] such as might be generated by quantum fluctuations during an inflationary period. [8–10] This discovery of temperature anisotropy in the CBR has inspired many further experiments which will be sensitive to smaller angle anisotropies than the COBE satellite was (about 1). NASA has approved the flight of a satellite mission, the Microwave Anisotropy Probe (MAP) in the year 2000 and ESA has agreed to a more accurate later experiment called the Planck Surveyor. The expected precision of these measurements implies that the angular dependence of the temperature anisotropy will be known sufficiently well that the location of the first accoustic (Doppler) peak, and possibly subsequent ones, will be resolved. Although the hot big bang theory is supported by at least three major triumphs: the expansion of the universe, the cosmic background radiation and the nucleosynthesis calculations, it leaves unanswered several questions. The most important unanswered questions are the horizon and flatness issues. When the CBR last scattered, the age of the universe was about 100,000 years compared to its present age of some 10 billion years. As we shall see, the horizon size at the recombination time subtends now an angle of about (1/208) of π radians. On the celestial sphere there are therefore approximately 40,000 causally disconnected regions. Nevertheless, these different regions have a uniform CBR temperature to an accuracy of better than one part in 10. This is the horizon problem. The flatness problem may be understood from the cosmological equation k R2 = (Ω− 1) 2 R2 (1)