Two Approaches to Interpretation of Hubble Diagram

Supernovae of type Ia are used as standard candles in modern cosmology, they serve to testcosmological models. Interpretation of the Hubble diagram based on the standard cosmologicalmodel led cosmologists to conclusion that the Universe is filled mostly with cosmic dust andmysterious dark energy.In this paper we present exact solutions of the Friedmann equation in standard cosmologyand conformal cosmology. The theoretical curves interpolating the Hubble diagram for thelatest supernova data are expressed in an analytical form. The functions belong to the classof meromorphic Weierstrass functions. Both approaches describe the modern Hubble diagramwith the same accuracy. Physical interpretation from the standpoint of conformal cosmologyis preferable, since supernova data are described without using a Λ-term. In the standardcosmology, the Hubble diagram is described by some characteristics: a Hubble parameter (),a deceleration (), and a jerk (). As calculations show, the deceleration parameter changesits sign during the evolution of the Universe, the -parameter remains constant. In the modernera, the Universe expands with acceleration, and in the past its acceleration was negative. Thechange in the sign of acceleration, without a clear physical reason, puzzles cosmologists.It seems obvious to us that to study objects dislocated from us at distances of billions oflight years, we should not use the coordinate time customary for work in laboratories, butthe conformal time. In conformal coordinates, the behavior of photons is described as in theMinkowski space. The time intervals d and d are different, they are related by the scale factor:d = d. The conformal luminosity distance is longer than the standard luminosity distance,which is manifested when observing distant stellar objects. As a result, the effective magnitudevalue - the redshift relationship, on which the Hubble diagram is constructed, will be different.Using the conformal Friedmann equation, we introduce the conformal parameters (), (),(). All parameters remain positive during the evolution of the Universe. The scale factorgrows with deceleration. The Universe does not experience a jerk.