All possible transformations from the Robertson-Walker metric to those conformal to the Lorentz-Minkowski form are derived. It is demonstrated that the commonly known family of transformations and associated conformal factors are not exhaustive and that there exists another relatively less well known family of transformations with a different conformal factor in the particular case that K = -1. Simplified conformal factors are derived for the special case of maximally-symmetric spacetimes. The full set of all possible cosmologicallycompatible conformal forms is presented as a comprehensive table. A product of the analysis is the determination of the set-theoretical relationships between the maximally symmetric spacetimes, the Robertson-Walker spacetimes, and functionally more general spacetimes. The analysis is preceded by a short historical review of the application of conformal metrics to Cosmology.

Rudimentary acoustical measurements performed inside six diverse ancient structures revealed that each sustained a strong resonance at a frequency between 95 and 120 Hz, despite major differences in chamber shapes and sizes. The resonant modal patterns all featured strong antinodes at the outer walls, with appropriately configured nodes and antinodes interspersed toward the central source. In some cases, interior and exterior rock drawings resembled these acoustical patterns. Since the resonance frequencies are well within the adult male voice range, one may speculate that some forms of human chanting, enhanced by the cavity resonance, were invoked for ritual purposes.

A classical electromagnetic zero-point field (ZPF) analogue of the vacuum of quantum field theory has formed the basis for theoretical investigations in the discipline known as random or stochastic electrodynamics (SED) wherein quantum measurements are imitated by the introduction of a stochastic classical background EM field. Random EM fluctuations are assumed to provide perturbations which can mimic some quantum phenomena while retaining a purely classical basis, e.g. the Casimir force, the Van-der-Waals force, the Lamb shift, spontaneous emission, the RMS radius of the harmonic oscillator, and the radius of the Bohr atom. This classical ZPF is represented as a homogeneous, isotropic ensemble of plane waves with fixed amplitudes and random phases. Averaging over the random phases is assumed to be equivalent to taking the ground-state expectation values of the corresponding quantum operator. We demonstrate that this is not precisely correct by examining the statistics of the classical ZPF in contrast to that of the EM quantum vacuum. We derive the distribution for the individual mode amplitudes in the ground-state as predicted by quantum field theory (QFT) and then carry out the same calculation for the classical ZPF analogue, showing that the distributions are only in approximate agreement, diverging as the density of k states decreases. We introduce an alternative classical ZPF with a different stochastic character, and demonstrate that it can exactly reproduce the statistics of the EM vacuum of QED. Incorporated into SED, this new field is shown to give the correct (QM) distribution for the amplitude of the ground-state of a harmonic oscillator, suggesting the possibility of developing further successful correspondences between SED and QED.Comment: 18 page

Abstract.We test the Yilmaz theory of gravitation by working out the corresponding Friedmanntype equations generated by assuming the Friedmann-Robertson-Walker cosmological metrics. In the case that space is flat the theory is consistent only with either a completely empty universe, or with a negative energy vacuum that decays to produce a constant density of matter. In both cases the total energy remains zero at all times, and in the latter case the acceleration of the expansion is always negative. To obtain a more flexible and potentially more realistic cosmology the equation of state relating the pressure and energy density of the matter creation process must be different from the vacuum, as for example is the case in the steady-state models of Gold, Bondi, Hoyle and others. The theory does not support the Cosmological Principle for curved space 0 K ≠ cosmological metrics.

The current concordance model of cosmology is dominated by two mysterious ingredients: dark matter and dark energy. In this paper, we explore the possibility that, in fact, there exist two dark-energy components: the cosmological constant Λ, with equation-of-state parameter wΛ=−1, and a 'missing matter' component X with wX=−2/3, which we introduce here to allow the evolution of the universal scale factor as a function of conformal time to exhibit a symmetry that relates the big bang to the future conformal singularity, such as in Penrose's conformal cyclic cosmology. Using recent cosmological observations, we constrain the present-day energy density of missing matter to be ΩX,0=−0.034 ± 0.075. This is consistent with the standard ΛCDM model, but constraints on the energy densities of all the components are considerably broadened by the introduction of missing matter; significant relative probability exists even for ΩX,0 ∼ 0.1, and so the presence of a missing matter component cannot be ruled out. As a result, a Bayesian model selection analysis only slightly disfavours its introduction by 1.1 log-units of evidence. Foregoing our symmetry requirement on the conformal time evolution of the universe, we extend our analysis by allowing wX to be a free parameter. For this more generic 'double dark energy' model, we find wX = −1.01 ± 0.16 and ΩX,0 = −0.10 ± 0.56, which is again consistent with the standard ΛCDM model, although once more the posterior distributions are sufficiently broad that the existence of a second dark-energy component cannot be ruled out. The model including the second dark energy component also has an equivalent Bayesian evidence to ΛCDM, within the estimation error, and is indistuingishable according to the Jeffreys guideline.