Redshift and the Hubble Constant in Conformally Flat Spacetime
Abstract
In conformally flat space-time (CFS), the cosmological redshift consists of a Doppler component, calculated using the radial recession velocity of the Friedmann-Robertson-Walker (FRW) coordinates, with respect to the CFS coordinates, and a gravitational component. It is shown that, for all forms of the FRW scaling factor R(t), where t is the FRW time coordinate, the fundamental formula for the total cosmological redshift z, namely, (1 + z) = R(t_0_)/R(t), is confirmed by calculations in CFS coordinates. Redshift-distance relations expressed in terms of the CFS absolute radial distance coordinate, instead of the more usual FRW elapsed time (t_0_ - t), are derived for the standard open three- dimensional space dust model. Attention is drawn to cataclysmic consequences resulting from any departure of the cosmological constant from zero. The product of the Hubble constant and the present age of the universe is substantially increased in the CFS description, its precise value depending only on the present age of the universe normalized to the characteristic scale length of the open three-dimensional space curvature. More precise observational determinations of the Hubble constant and the present age of the universe are needed to verify the correctness or otherwise of the CFS physical interpretation.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- October 1994
- DOI:
- 10.1086/174741
- Bibcode:
- 1994ApJ...434..397E
- Keywords:
-
- Coordinate Transformations;
- Cosmology;
- Doppler Effect;
- Gravitation;
- Hubble Constant;
- Red Shift;
- Relativity;
- Universe;
- Distance;
- Radial Velocity;
- Time;
- Astrophysics;
- COSMOLOGY: THEORY;
- GALAXIES: DISTANCES AND REDSHIFTS