L~TTI~,RF, AL NUOV0 CIMENTO VOL. 36, ~. 7 12 l~ebbraio 1983 The Quark-Hadron Phase Transition and the Temperature of the MW Background Radiation. S. A. BO~O~TTO IstitutO di ~isica (( G. Galilei ,) - Via Marzolo, 8 - 35100 Padova Istituto ~Vazionale di ~isica Nucleate - Sezione di Padova International School ]or Advanced Studies Strada Costiera 11, 34014 Miramare, Trieste l~. LUCCHIN Istituta di ~isiea (( G. Galilei ~ - Via Marzolo, 8, 35100 Padova S. I~ATAR~SE International School /or Advanced Studies Strada Costiera 11, 34014 Miramare, Trieste (ricevuto il 60ttobre 1982) PACS. 98.80. - Cosmology. Summary. - It is shown that the temperature of the 3~W background radiation might be directly connected with the details of the quark-hadron phase transition. In fact at temperatures just above 10 GeV the Universe has no room to contain the present baryon number in hadron form. This temperature migh~ be smaller even by a large factor, if a part of the present entropy originated at red-shift ~ 10--100. In this note we want to suggest that the cosmological transition from quark matter into hadron matter might have played a nonncgligible role in defining the present structure of the Universe. It is mostly believed that this transition took place when the temperature of the Universe ranged about 200 ~eV (1.7). This belief is based on perturbative computations (4,5) and on lattice numerical evaluations (v). However, it (i) R. V. WAGONERand G. STEIGMAN: Phys. Rev. D, 20, 825 (1979). (~) F. KARSCH and H. SATZ: Phys. Rev. D, 21, 1168 (1980); 22, 480 (1980). (8) K.A. OLIVE: Nucl. Phys. B, 190, 483 (1981). (4) 5. I. K~eUSTX: Nucl. Phys. B, 148, 461 (1979). (5) O. K. "R'ALASHNIKOV and V. V. KLI~OV: Phys. Lett. B, 88, 328 (1979). (e) D. J. GROSS, R. D. PISARSKI, L. G. YAFFE: Rev. Mod. Phys., 53, 43 (1981). (T) J. E~G~LS, F. KA~SO~ and H, SATZ: Phys. Left. B, 101~ 89 (1981), ~7~