Cosmological Relativity: Determining the Universe by the Cosmological

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3 Cosmological Redshift

Having the metric tensor we may now ﬁnd the redshift of light emitted in the cosmos. As usual, at two points 1 and 2 we have for the wave lengths:

λ2 ds (1) g11 (1) = = . (4) λ1 ds (2) sg11 (2)

Using now the solution for g11 in Eq. (4) we obtain

2 2 λ2 1+ r2/a = 2 2 . (5) λ1 s1+ r1/a For a sun-like body located at the coordinates origin, and an observer at a distance r from the center of the body, we then have r2 = r and r1 = 0, thus

2 2 λ2 r (1 − Ω) r = 1+ 2 = 1+ 2 2 (6) λ1 r a r c τ for the cosmological contribution to the redshift. If, furthermore, r ≪ a we then have 2 2 λ2 r (1 − Ω) r =1+ 2 =1+ 2 2 , (7) λ1 2a 2c τ to the lowest apprixomation in r2/a2, and thus 2 2 λ2 r (1 − Ω) r z = − 1= 2 = 2 2 . (8) λ1 2a 2c τ From Eqs. (6)–(8) it is clear that Ω cannot be larger than one since otherwise z will be negative, which means blueshift, and as is well known nobody sees such a thing. If Ω = 1 then z = 0, and for Ω < 1 we have z > 0. ThecaseofΩ=1is also implausible since the light from stars we see is usually redshifted more than the redshift due to the gravity of the body emitting the radiation, as is evident from our sun, for example, whose emitted light is shifted by only z =2.12×10−16 [17].

2 4 Conclusions

One can thus conclude that the theory of cosmological general relativity pre- dicts that the universe is inﬁnite and expands from now on forever. As is well known the standard FRW model does not relate the cosmological redshift to the kind of the universe. Our conclusion is also in full agreement with the measurements recently obtained by the High-Z Supernovae Team and the Suprenovae Cosmology Project [18-24].

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