Cosmology under Milne's shadow

Based on the magnitude--redshift diagram for the sample of supernovae Ia analysed by Perlmutter et al. (1999), Davis & Lineweaver rule out the special relativistic interpretation of cosmological redshifts at a confidence level of 23 sigma. Here, we critically reassess this result. Special relativity is known to describe the dynamics of an empty universe, by means of the Milne kinematic model. Applying only special-relativistic concepts, we derive the angular diameter distance and the luminosity distance in the Milne model. In particular, in this model we do not use the underlying metric in its Robertson-Walker form, so our exposition is useful for readers without any knowledge of general relativity. We do however, explicitly use the special-relativistic Doppler formula for redshift. We apply the derived luminosity distance to the magnitude--redshift diagram for supernovae Ia of Perlmutter et al. (1999) and show that special relativity fits the data much better than that claimed by Davis & Lineweaver. Specifically, using these data alone, the Milne model is ruled out only at a 2 sigma level. Although not a viable cosmological model, in the context of current research on supernovae Ia it remains a useful reference model when comparing predictions of various cosmological models.Comment: 5 pages, 1 figure; a didactic article; matches the version accepted for publication in PAS

Kurtosis in Large-Scale Structure as a Constraint on Non-Gaussian Initial Conditions

We calculate the kurtosis of a large-scale density field which has undergone weakly non-linear gravitational evolution from arbitrary non-Gaussian initial conditions. It is well known that the weakly evolved {\twelveit skewness} is equal to its initial value plus the term induced by gravity, which scales with the rms density fluctuation in precisely the same way as for Gaussian initial conditions. As in the case of skewness, the evolved {\twelveit kurtosis} is equal to its initial value plus the contribution induced by gravity. The scaling of this induced contribution, however, turns out to be qualitatively different for Gaussian versus non-Gaussian initial conditions. Therefore, measurements of the kurtosis can serve as a powerful discriminating test between the hypotheses of Gaussian and non-Gaussian nature of primordial density fluctuations.Comment: uuencoded compressed tar file including postscript text (17 pages) and 2 postscript figures, submitted to MNRA

Is space really expanding? A counterexample

In all Friedman models, the cosmological redshift is widely interpreted as a consequence of the general-relativistic phenomenon of EXPANSION OF SPACE. Other commonly believed consequences of this phenomenon are superluminal recession velocities of distant galaxies and the distance to the particle horizon greater than c*t (where t is the age of the Universe), in apparent conflict with special relativity. Here, we study a particular Friedman model: empty universe. This model exhibits both cosmological redshift, superluminal velocities and infinite distance to the horizon. However, we show that the cosmological redshift is there simply a relativistic Doppler shift. Moreover, apparently superluminal velocities and `acausal' distance to the horizon are in fact a direct consequence of special-relativistic phenomenon of time dilation, as well as of the adopted definition of distance in cosmology. There is no conflict with special relativity, whatsoever. In particular, INERTIAL recession velocities are subluminal. Since in the real Universe, sufficiently distant galaxies recede with relativistic velocities, these special-relativistic effects must be at least partly responsible for the cosmological redshift and the aforementioned `superluminalities', commonly attributed to the expansion of space. Let us finish with a question resembling a Buddhism-Zen `koan': in an empty universe, what is expanding?Comment: 12 pages, no figures; added Appendix with a calculation of the cosmological redshift in `private space

The kinematic component of the cosmological redshift

It is widely believed that the cosmological redshift is not a Doppler shift. However, Bunn & Hogg have recently pointed out that to settle properly this problem, one has to transport parallelly the velocity four-vector of a distant galaxy to the observer's position. Performing such a transport along the null geodesic of photons arriving from the galaxy, they found that the cosmological redshift is purely kinematic. Here we argue that one should rather transport the velocity four-vector along the geodesic connecting the points of intersection of the world-lines of the galaxy and the observer with the hypersurface of constant cosmic time. We find that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula. Instead, for small redshifts it coincides with the well known non-relativistic decomposition of the redshift into a Doppler (kinematic) component and a gravitational one. We perform such a decomposition for arbitrary large redshifts and derive a formula for the kinematic component of the cosmological redshift, valid for any FLRW cosmology. In particular, in a universe with Omega_m = 0.24 and Omega_Lambda = 0.76, a quasar at a redshift 6, at the time of emission of photons reaching us today had the recession velocity v = 0.997c. This can be contrasted with v = 0.96c, had the redshift been entirely kinematic. Thus, for recession velocities of such high-redshift sources, the effect of deceleration of the early Universe clearly prevails over the effect of its relatively recent acceleration. Last but not least, we show that the so-called proper recession velocities of galaxies, commonly used in cosmology, are in fact radial components of the galaxies' four-velocity vectors. As such, they can indeed attain superluminal values, but should not be regarded as real velocities.Comment: 10 pages, 1 figure; matches the version published in MNRA

Towards the optimal window for the 2MASS dipole

A comparison of the 2MASS flux dipole to the CMB dipole can serve as a method to constrain a combination of the cosmological parameter Omega_m and the luminosity bias of the 2MASS survey. For this constraint to be as tight as possible, it is necessary to maximize the correlation between the two dipoles. This can be achieved by optimizing the survey window through which the flux dipole is measured. Here we explicitly construct such a window for the 2MASS survey. The optimization in essence reduces to excluding from the calculation of the flux dipole galaxies brighter than some limiting magnitude K_min of the near-infrared K_s band. This exclusion mitigates nonlinear effects and shot noise from small scales, which decorrelate the 2MASS dipole from the CMB dipole. Under the assumption of negligible shot noise we find that the optimal value of K_min is about five. Inclusion of shot noise shifts the optimal K_min to larger values. We present an analytical formula for shot noise for the 2MASS flux dipole, to be used in follow-up work with 2MASS data. The misalignment angle between the two dipoles is a sensitive measure of their correlation: the higher the correlation, the smaller the expectation value of the angle. A minimum of the misalignment is thus a sign of the optimal gravity window. We model analytically the distribution function for the misalignment angle and show that the misalignment estimated by Maller et al. is consistent with the assumed underlying model (though it is greater than the expectation value). We predict with about 90% confidence that the misalignment will decrease if 2MASS galaxies brighter than K_min = 5 mag are excluded from the calculation of the flux dipole. This prediction has been indirectly confirmed by the results of Erdogdu et al. (ABRIDGED)Comment: 14 pages, 3 figures. Significantly expanded version, with added sections on shot noise and likelihood for beta, as well as an appendix with a derivation of the distribution for the misalignment angle relaxing the small-angle assumptio