![]() Nevertheless, introducing the conformal time into the FLRW metric is commonly viewed as a mathematical concept different from the physical cosmic time. The conformal metrics have also other exceptional properties and open space for new cosmological models as the Conformally Flat Space-Time Cosmology, Conformal Gravity or the Conformal Cyclic Cosmology. This metric is particularly interesting, because it leaves the Maxwell’s equations unchanged from their form in the Minkowski spacetime. The new time coordinate is called the conformal time and the metric utilizing this time is called the conformal metric. Firstly, this metric evolves in time according to the so-called conformal transformation, properties of which are intensively studied in GR in recent years. Introducing the same scale factor for time and space coordinates has also other advantages. Where g 00( e) and g 00( r) are the time components of the metric tensor g αβ for the emitter and receiver, respectively. This option has a clear advantage, because the cosmological redshift will be defined by the same formula as the gravitational redshift In this case, another function is considered in the metric tensor g αβ, which describes the evolution of the time component g 00.Īmong many possibilities how to define this function, the simplest way is to assume that the time and scale factors are defined by the same function a( t). Therefore, some authors pointed out to other alternative theories admissible in GR and introduced more general metrics for describing isotropic homogeneous Universe evolving in time. This is somewhat strange and surprising, because other solutions in GR such as the well-known Schwarzschild solution involve distortions in space and time together. In contrast to the space coordinates, the time coordinate is assumed to be invariable during the Universe history. Hence, the redshift of distant galaxies would be observed even in the case, when the Universe is not expanding anymore at the present epoch. Where z is the redshift, and a( e) and a( r) are the scale factors for the emitter and receiver, respectively. The redshift is not related to the speed of the expansion as for the Doppler effect but to the ratio between sizes of the space, in which the photons were emitted and received. At present, the Universe is described by the so-called Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, which introduces the scale factor a( t) for describing the space expansion. ![]() However, the intuitive idea of the redshift as the Doppler effect was later abandoned. This observation (called the Hubble-Lemaitre law) was interpreted as the Doppler effect produced by galaxies moving away from the Earth due to the Universe expansion. The possibility that the Universe is really dynamic but not static was later supported by Lemaitre and Hubble, who observed a systematic redshift of nearby galaxies, which was roughly proportional to their distance. Obviously, adopting the conformal FLRW metric for describing the evolution of the Universe has many fundamental cosmological consequences.įriedmann applied the Einstein equations of General Relativity (GR) for describing the Universe and firstly showed that the space filled by uniformly distributed matter might evolve in time. Hence, the discovery of the supernova dimming actually revealed a failure of the FLRW metric and introducing dark energy was just an unsuccessful attempt to cope with the problem within this false metric. By contrast, the conformal FLRW metric fits data well with no need to introduce any new free parameter. The standard FLRW metric produces essential discrepancy with the SNe Ia observations called the ‘supernova dimming’, and dark energy has to be introduced to comply theoretical predictions with data. The correctness of the proposed conformal metric is convincingly confirmed by Type Ia supernovae (SNe Ia) observations. Consequently, the cosmological time must be identified with the conformal time and the standard FLRW metric must be substituted by its conformal version. ![]() Therefore, the cosmic time runs differently at high redshifts than at present. It is proved that the change in the frequency of redshifted photons is always connected with time dilation, similarly as for the gravitational redshift. The paper shows that the commonly used Friedmann-Lemaitre-Robertson-Walker (FLRW) metric describing the expanding Universe must be modified to properly predict the cosmological redshift. Institute of Geophysics, Czech Academy of Sciences, Prague, Czechia. ![]()
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