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Y. Tomozawa, “The Origins of Cosmic Rays and Quantum Effects of Gravity,” In: F. Mancini, Ed., Quantum Field Theory, Ersever Science Publishers B. V., Amsterdam, 1986, p. 241.

has been cited by the following article:

• TITLE: Ankle Phenomenon in the Cosmic Ray Energy Spectrum

  AUTHORS: Yukio Tomozawa

  KEYWORDS: Cosmic Rays; Cosmology; Knee Energy; Inflation

  JOURNAL NAME: Journal of Modern Physics, Vol.4 No.3, March 22, 2013

  ABSTRACT: The author has suggested that the knee phenomenon in the cosmic ray energy spectrum at 3 PeV can be explained as a split between a radiation-dominated expansion and a matter-dominated expansion of an expanding heat bath. The model proposed in 1985, in fact, predicted that high energy cosmic rays are emitted from AGN, massive black holes, in agreement with recent data from the Pierre Auger Observatory. Similarly, the ankle phenomenon at 3 EeV is shown to be explained by a split between inflational expansion and ordinary material expansion of the expanding heat bath, not unlike that in the expansion of the universe. All the spectral indicies in the respective regions of the energy spectra agree with the theoretical calculation from the respective expansion rates. It is shown that the ankle energy is approximately equal to the threshold energy of cosmic ray production of an electron positron pair on the cmb photon.