Two phenomenological models of Λ, viz. $\Lambda \sim (\dot{a}/a)^{2}$
 and $\Lambda \sim \ddot{a}/a$
 are studied under the assumption that G is a time-variable parameter. Both models show that G is inversely proportional to time as suggested earlier by others including Dirac. The models considered here can be matched with observational results by properly tuning the parameters of the models. Our analysis shows that $\Lambda \sim \ddot{a}/a$
 model corresponds to a repulsive situation and hence correlates with the present status of the accelerating Universe. The other model $\Lambda \sim (\dot{a}/a)^{2}$
 is, in general, attractive in nature. Moreover, it is seen that due to the combined effect of time-variable Λ and G the Universe evolved with acceleration as well as deceleration. This later one indicates a Big Crunch.

Higher Dimensional Dark Energy Investigation with Variable Λ and G

Time variable $\Lambda$ and $G$ are studied here under a phenomenological model of $\Lambda$ through an ($n+2$) dimensional analysis. The relation of Zeldovich (1968) $|\Lambda| = 8\pi G^2m_p^6/h^4$ between $\Lambda$ and $G$ is employed here, where $m_p$ is the proton mass and $h$ is Planck's constant. In the present investigation some key issues of modern cosmology, viz. the age problem, the amount of variation of $G$ and the nature of expansion of the Universe have been addressed.

Higher Dimensional Dark Energy Investigation with Variable $\Lambda$ and $G$

A paper by Harmut Traunmuller [1] showed from statistical studies of observational data that the most adequate equation to represent observations on magnitude and redshift from 892 type 1a supernovae is $\mu = 5\,log[(1+z)\,ln(1+z)] + const.$ Comparing the Hubble diagram calculated from the observed redshift data of 280 supernovae with Hubble diagrams inferred on the basis of two cosmological models in the range of z = 0.0104 to 8.1, Laszlo Marosi [2] found in a quite independant study that the best fit function to represent observations is $\mu= 44.109769 \,z^{0.059883}$. Noting that differences between the different cosmological models become more pronouced in a photon time-of-fligth $t_s$ vs. $z$ representation, he also noted that the best equation to account for observations may also be written $z = -1+e^{2.024\,\,10^{-18} \,\,ts}$. In the light of these observational data, we compare the theoretical Hubble diagram obtained with the flat $\Lambda CDM$ model to the ones we have obtained few years ago [3, 4, 5] from a model that we call here the "light model" for the sake of clarity. Our conclusions are that values calculated on the basis of the $\Lambda CDM$ model exhibit poor agreement with the presently available data while the light model agrees exactly with observations and conclusions of statistical studies [1] and [2] (independently of the values of $\Omega_k$, $\Omega_M$ or $\Omega_{\Lambda}$). Our model giving no accelerating expansion of the universe, we conclude that this latter is not necessary and that models can exist which lead exactly to observations without having to consider any accelerating expansion of the universe. In an Appendix, we discuss some aspects of the model and we present a brief overview of some of its key results.

Analysis of the Hubble diagram of type SNe Ia supernovae and of gamma-ray bursts. A comparison between two models

A strictly linear evolution of the cosmological expansion scale factor is a characteristic feature in several classes of alternative gravity theories as also in the standard (big-bang) model with specially chosen equations of state of matter. Such an evolution has no free parameters as far as the classical cosmological tests are concerned and should therefore be easily falsifiable. In this article we demonstrate how such models present very good fits to the current supernovae 1a data. We discuss the overall viability of such models.

Linear Coasting in Cosmology and SNe Ia

In this paper we present higher dimensional cosmological model of the universe with the decaying vacuum energy density in the realm of model with a time varying gravitational constant. We have shown that our model admits the usual higher dimensional de Sitter solution and the other solutions characterized by the constant ratio between matter density and the total energy density. Our work is the generalization of the work obtained earlier by Carneiro (Proceedings of the MG10 Meeting held at Brazilian Center for Research in Physics (CBPF), Rio de Janeiro, Brazil, 20–26 July, 2003) in four dimensional space-time.

B. P. Butey

Papers

Higher Dimensional Cosmological Model of the Universe with Decaying Λ Cosmology with Varying G