Derivation of Weinberg's Relation in a Inflationary Universe

Authors: Ioannis Iraklis Haranas

We propose a derivation of the empirical Weinberg relation for the mass of an elementary particle and in an inflationary type of universe. Our derivation produces the standard well known Weinberg relation for the mass of an elementary particle, along with an extra term which depends on the inflationary potential, as well as Hubble's constant. The derivation is based on Zeldovich's result for the cosmological constant Λ, in the context of quantum field theory. The extra term can be understood as a small correction to the mass of the elementary particle due to inflation. This term also enables us to calculate, the initial value of the field φO for two kinds of potentials chosen, which makes Weinberg's relation possible. Closed and flat and open universes give the mass of the particles close to the mass of a pion, 140 MeV/c2 or as the one also predicted by Weinberg's relation.

Comments: 7 pages. Published Romanian Astronomical Journal, Vo. 13 No. 2, pp.111-117

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Submission history

[v1] 18 Feb 2010

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