## 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 φ_{O} 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/c_{2} 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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