Narrow Results

The validity of Hubble's law defies the determination of the center of the big bang expansion, even if it exists. Every point in the expanding universe looks like the center from which the rest of the universe flies away. In this paper, we show that the distri- bution of apparently circular galaxies is not uniform in the sky and that there exists a special direction in the universe in our neighborhood. The data is consistent with the assumption that the tidal force due to the mass distribution around the universe center causes the deformation of galactic shapes depending on its orientation and location relative to the center and our galaxy. Moreover, the CMB dipole data can also be associated with the center of the universe expansion, if the CMB dipole at the center of our supercluster is assumed to be due to Hubble flow. The location of the center is estimated from the CMB dipole data. The direction to the center from both sets of data is consistent and the distance to the center is computed from the CMB dipole data.

Aims: In this work, we address the issue of peculiar velocity measurement in a perturbed Friedmann universe using the deviations from measured luminosity distances of standard candles from background FRW universe. We want to show and quantify the statement that in intermediate redshifts ($0.5<z<2$), deviations from the background FRW model are not uniquely governed by peculiar velocities. Luminosity distances are modified by gravitational lensing. We also want to indicate the importance of relativistic calculations for peculiar velocity measurement at all redshifts. Methods: For this task, we discuss the relativistic correction on luminosity distance and redshift measurement and show the contribution of each of the corrections as lensing term, peculiar velocity of the source and Sachs–Wolfe effect. Then, we use the SNe Ia sample of Union 2, to investigate the relativistic effects, we consider. Results: We show that, using the conventional peculiar velocity method, that ignores the lensing effect, will result in an overestimate of the measured peculiar velocities at intermediate redshifts. Here, we quantify this effect. We show that at low redshifts the lensing effect is negligible compare to the effect of peculiar velocity. From the observational point of view, we show that the uncertainties on luminosity of the present SNe Ia data prevent us from precise measuring the peculiar velocities even at low redshifts ($z<0.2$).

This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime within the Lambda Cold Dark Matter ($\mathrm{\Lambda }$CDM) model. Using the radial free motion solutions, we provide two methods for characterizing the geodesics and defines a general formula that encapsulates all possible solutions, determined by two initial conditions. We show that the past light cone, event horizon, and particle horizon, can be considered as special cases of this overarching formula. Furthermore, the paper explores the free geodesics within the currently accepted cosmological model based on the recent Planck results, thoroughly examining the various possible geodesic scenarios.