Quantum origin of a hot universe

We present the results on the quantum birth of a hot FRW universe in de Sitter vacuum from a quantum fluctuation which contains radiation and strings or some quintessence with the equation of state p = -ε/3.a The presence of radiation results in quantum tunnelling from a discrete energy level with a non-zero quantized temperature. Energy levels have non-zero width corresponding to temperature fluctuations. The observational constraint on the CMB anisotropy selects the admissible range of the model parameters. For the GUT scale initial de Sitter vacuum, the lower limit on temperature at the start of classical evolution is close to the values predicted by theories of reheating, while an upper limit is far from the threshold for a monopole rest mass. The probability of quantum birth from a level of non-zero energy is much bigger than the probability of quantum birth from nothing. The presence of material with p = -ε/3 mimics a positive curvature term which makes possible quantum tunnelling for an open and a flat universe. Most plausible case is a flat universe arising from an initial fluctuation with a small admixture of radiation and strings with the negative deficit angle