Analytic solutions for the energy density and the temperature of the QGP in the early Universe

Year 2019, Volume: 2 Issue: 2, 52 - 58, 24.02.2020

Gaber Faisel Amr Abd Al-rahman Youssef Hamid Alzakı

Abstract

After the Big Bang and at a time estimated to be a millionth of a second, the Universe was in a phase that filled
with quark-gluon plasma. Due to the high temperature, the strong coupling constant that describes the strength of the strong force
acting on the quarks and the gluons, was so small. As a result, quarks and gluons inside the plasma behaved as an ideal gas of
gluons and massless quarks that weakly interact with each others. Hence,  one can describe the characteristics of the plasma by the
equations of states which relate energy density and pressure to its temperature as in the MIT bag model. Having these equations of
states, one can solve Friedmann equations of the general relativity. In this work, we derive the analytic solutions for the
Friedmann differential equations governing the time evolution of the energy density and the temperature of the quark-gluon plasma
in that era of the early Universe adopting the MIT bag model.

Keywords

quark-gluon plasma, Early Universe

References

• A. Einstein et al, The Principle of Relativity, Dover, New York, 1952.
• Robert J. A. Lambourne, Relativity, Gravitation and Cosmology, Cambridge University Press, Cambridge,2010.
• A. R. Liddle and D. H. Lyth, Cosmological inflation and large-scale structure, Cambridge UniversityPress, Cambridge, 2010.
• E. W. Kolb and M. Turner, The Early Universe, Addison-Wesley, Boston, 1990.
• S. Weinberg, Gravitation and Cosmology, John Wiley and Sons, Inc, Hoboken, New Jersey 1972.
• T. Padmanabhan, Theoretical Astrophysics, Cambridge Univ. Press, Cambridge, 2000.
• Fritzsch, H. Gell-Mann and M. Leutwyler, H., Advantages of the Color Octet Gluon Picture. Phys.Lett. B 47,1973,365-368.
• Gross, D.J.and Wilczek, F., Ultraviolet Behavior of Nonabelian Gauge Theories, Phys. Rev. Lett.30,1973, 1343-1346.
• Politzer, H.D., Reliable Perturbative Results for Strong Interactions? Phys. Rev. Lett. 30, 1973, 1346-1349.
• Collins, J.C. and Perry, M.J., Neutrons or Asymptotically Free Quarks? Phys. Rev. Lett. 34, 1975,1353.
• Cabibbo, N. and Parisi, G., Exponential hadronic spectrum and quark liberation. Phys. Lett. B59,1975, 67-69.
• A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn and V.F. Weisskopf, A New Extended Model ofHadrons, Phys. Rev. D 9, 1974, 3471-3495.
• S.M.Sanches, F.S.Navarra and D.A.Fogaa, The quark gluon plasma equation of state and the expansionof the early Universe, Nucl. Phys. A , 937, 2015, 1-16.
• D.A. Fogaa, L.G. Ferreira Filho and F.S. Navarra, Non-linear waves in a Quark Gluon Plasma, Phys.Rev. C 81,2010, 055211.
• T. Kalaydzhyan and E. Shuryak, Gravity waves generated by sounds from big bang phase transitions,Phys. Rev. D 91, no. 8, 2015, 083502.
• U. Ornik and R. M. Weiner, Expansion of the Early Universe and the Equation of State, Phys. Rev. D36, 1987, 1263.