ABSTRACT There are three main mechanisms to cause the red shift of spectrum in physics. The first is gravity which is related to mass. The second is the Compton scattering which is related to the energy transformation of photon. The third is the Doppler’s effect which is related to velocity. The basic formula used to calculate the relation of red shift and distance of Ia supernova in cosmology is which is related to the scalar factor of the R-W metric. It is completely different from the Doppler formula of red shift which is related to velocity factor . This kind of inconsistency is not allowed in physics. Because of , when became larger and larger with time increase, z became smaller and smaller, means that space expansion leads to red shift becoming smaller. At present time, we have and , means that there is no red shift for the light emitted from distance celestial bodies at present. The results obviously violate the Hubble law! It is proved strictly in mathematics that the formula is untenable unless constant and . The further study reveals that the essential reason of the mistake is that the R-W metric violates the principle of light’s speed invariable. The time delay caused by relativity velocity between light’s source and observer is neglected. Besides, there exists the problem of time misalignment between theoretical calculation and practical observations in the original documents of Ia supernova projects. So the formula used to calculate the relation between red shift and distance of Ia supernova is wrong and the deduced conclusion about dark energy and the accelerating expansion of the universe are incredible. It is proved in this paper that based on the Doppler’s formula and the method of numerical calculation, the relation of red shift and distance of Ia supernova can be explained well. The hypotheses of dark energy and the accelerating expansion of the universe are completely unnecessary in cosmology.
Cite this paper
X. Mei and P. Yu, "The Formula to Calculate the Red Shift-Distance Relation of Ia Supernova in Cosmology Has Essential Mistakes —The Calculation of Cosmological Red Shift Should Use the Doppler Formula Directly," International Journal of Astronomy and Astrophysics, Vol. 2 No. 3, 2012, pp. 183-193. doi: 10.4236/ijaa.2012.23023.
 S. Perlmutter, et al., “Measurements of Ω and Λ from 42 High-Redshift Supernovae,” The Astrophysical Journal, Vol. 517, No. 2, 1999, pp. 517, 565. doi:10.1086/307221
B. Leibundgut, et al., “Observational Evidence from Su-pernovae for an Accelerating Universe and a Cosmological Constant,” The Astronomical Journal, Vol. 116, No. 3, 1998, p. 1009. doi:10.1086/300499
E. W. Kolb and M. S. Turner, “The Early Universe,” Addison-Wesley Publishing Company, Boston, 1990, p. 39.
S. M Carroll and W. H. Press, “The Cosmology Con-stant,” Annual Review of Astronomy and Astrophysics, 1992, Vol. 30, p. 409.
X. Mei, “The R-W Metric Has No Constant Curvature When Scalar Factor R(t) Changes with Time,” Interna- tional Journal of Astronomy and Astrophysics, Vol. 1, 2011, pp. 177-182.
X. Mei and P. Yu, “Revised Newtonian Formula of Grav-ity and Equation of Cosmology in Flat Space-time Transformed from Schwarzschild Solution,” International Journal of Astronomy and Astrophysics, Vol. 2, No. 1, 2012, pp. 6-18.