Realistic Inhomogeneous Universe Research Articles

CONSTRAINTS ON NEUTRINO MASSES FROM THE LENSING DISPERSION OF TYPE Ia SUPERNOVAE

ABSTRACT We investigate how accurately the total mass of neutrinos is constrained from the magnitude dispersion of SNe Ia due to the effects of gravitational lensing. For this purpose, we use the propagation equation of light bundles in a realistic inhomogeneous universe and propose a sample selection for supernovae to avoid difficulties associated with small-scale effects such as strong lensing or shear effects. With a fitting formula for the nonlinear matter power spectrum taking account of the effects of massive neutrinos, we find that in our model it is possible to obtain the upper limit for future optical imaging surveys with the Wide-Field InfraRed Survey Telescope and Large Synoptic Survey Telescope. Furthermore, we discuss how far we need to observe SNe Ia and to what extent we have to reduce the magnitude error except for lensing in order to realize the current tightest limit .

The magnitude-redshift relation in a realistic inhomogeneous universe

The light rays from a source are subject to a local inhomogeneous geometry generated by inhomogeneous matter distribution as well as the existence of collapsed objects. In this paper we investigate the effect of inhomogeneities and the existence of collapsed objects on the propagation of light rays and evaluate changes in the magnitude-redshift relation from the standard relationship found in a homogeneous FRW universe. We give the expression of the correlation function and the variance for the perturbation of apparent magnitude, and calculate it numerically by using the non-linear matter power spectrum. We use the lognormal probability distribution function for the density contrast and spherical collapse model to truncate the power spectrum in order to estimate the blocking effect by collapsed objects. We find that the uncertainties in Ωm is ∼ 0.02, and that of w is ∼ 0.04 . We also discuss a possible method to extract these effects from real data which contains intrinsic ambiguities associated with the absolute magnitude.

Lagrangian theory of structure formation in relativistic cosmology: Lagrangian framework and definition of a nonperturbative approximation

In this paper, we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate its implications by functionally evaluating relevant variables, and we address the singularity problem. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to put into practice nonperturbatively, e.g., problems of structure formation, backreaction problems, nonlinear properties of gravitational radiation, and light propagation in realistic inhomogeneous universe models. With this model we also provide the key building blocks for initializing a fully relativistic numerical simulation.

Ricci focusing, shearing, and the expansion rate in an almost homogeneous Universe

The Universe is inhomogeneous, and yet it seems to be incredibly well-characterised by a homogeneous relativistic model. One of the current challenges is to accurately characterise the properties of such a model. In this paper we explore how inhomogeneities may affect the overall optical properties of the Universe by quantifying how they can bias the redshift-distance relation in a number of toy models that mimic the real Universe.The models that we exploreare statistically homogeneous on large scales. We find that the effect of inhomogeneities is of order of a few percent, which can be quite important in precise estimation of cosmological parameters. We discuss what lessons can be learned to help us tackle a more realistic inhomogeneous universe.

Distance-Redshift Relation in a Realistic Inhomogeneous Universe

We investigate the distance-redshift relation in a realistic inhomogeneous universe where the mass distribution is described by the mass function of Sheth and Tormen. It is found that the derived distance deviates systematically from the standard distance up to 10% depending on the choice of the lowest halo mass in which baryonic matter condensed to form luminous object such as galaxies. Remarkably the derived distance is well approximated by the Dyer-Roeder distance if we choose the clumpiness parameter \alpha calculated by our model.We also discuss the effect of inhomogeneities in the determination of dark energy parameter in the supernovae observation, and find that this effect must be taken into account for the future high redshift supernovae observation.

Effect of inhomogeneities on the luminosity distance-redshift relation: Is dark energy necessary in a perturbed universe?

The luminosity distance-redshift relation is one of the fundamental tools of modern cosmology. We compute the luminosity distance-redshift relation in a perturbed flat matter-dominated Universe, taking into account the presence of cosmological inhomogeneities up to second order in perturbation theory. Cosmological observations implementing the luminosity distance-redshift relation tell us that the Universe is presently undergoing a phase of accelerated expansion. This seems to call for a mysterious Dark Energy component with negative pressure. Our findings suggest that the need of a Dark Energy fluid may be challenged once a realistic inhomogeneous Universe is considered and that an accelerated expansion may be consistent with a matter-dominated Universe.

On the Validity of the Cosmological Lens Equation in General Relativity

We present a simple derivation of the cosmological lens equation within the framework of general relativity by investigating the propagation of light ray in the realistic inhomogeneous universe. The equation gives a natural generalization of the conventional lens equation used in the previous studies and allows us to clarify the conditions for the validity of the conventional equation.

General Relativistic Description of a Realistic Inhomogeneous Universe

Recent development of the observational cosmology indicates the necessity of general relativistic treatment of our universe. In this paper we present a possible approach to the construction of a realistic inhomogeneous universe starting from the first principle of general relativity. The approach does not assume that the density contrast is small and gives a method using a spatial averaging to calculate the effect that local inhomogeneities determine the global geometry. It clarifies the conditions under which the homogeneous and isotropic geometry appears in the global scale as the result of the averaging

General Relativistic Description of a Realistic Inhomogeneous Universe

Recent development of the observational cosmology indicates the necessity of general relativistic treatment of our universe. In this paper we present approach to the construction of a realistic inhomogeneous universe starting from the first principle of general relativity. The approach does not assume that the density contrast is small and gives a method using a spatial averaging to calculate the effect that local inhomogeneities determine the global geometry. It clarifies the conditions under which the homogeneous and isotropic geometry appears in the global scale as the result of the averaging. Our approach allows one to calculate the back reaction by local inhomogeneities on the cosmic expansion and we express explicitly the deviation from Friedman-Lemaitre-Robertson-Walker (FLRW) geometry in terms of local inhomogeneities. We discuss also the condition for the applicability of the Newtonian approximation in the cosmological situation. As an application of the present formalism, the propagation of light rays in such an inhomogeneous universe is considered and the distance-redshift relation is derived which would play a fundamental role in the observational cosmology. On the basis of the derived relation we discuss the validity of the Dyer-Roeder distance.

A New Description for a Realistic Inhomogeneous Universe in General Relativity

A new approximation scheme is proposed to describe a realistic inhomogeneous universe in general relativity. This scheme improves the former one and allows one to treat more general situations where the local effect due to self-gravity of the matter dominates the effect of cosmic expansion. A new statistical way of averaging spacetime is also discussed.

A New Description for a Realistic Inhomogeneous Universe in General Relativity

A new approximation scheme is proposed to describe a realistic inhomogeneous universe in general relativity. This scheme improves the former one and allows one to treat more general situations where the local effect due to self-gravity of the matter dominates the effect of cosmic expansion. A new statistical way of averaging spacetime is also discussed

Light propagation and the distance-redshift relation in a realistic inhomogeneous universe.

The propagation of light rays in a clumpy universe constructed by cosmological version of the post-Newtonian approximation was investigated. It is shown that linear approximation to the propagation equations is valid in the region where zeta is approximately less than 1 even if the density contrast is much larger than unity. Based on a gerneral order-of-magnitude statistical consideration, it is argued that the linear approximation is still valid where zeta is approximately greater than 1. A general formula for the distance-redshift relation in a clumpy universe is given. An explicit expression is derived for a simplified situation in which the effect of the gravitational potential of inhomogeneities dominates. In the light of the derived relation, the validity of the Dyer-Roeder distance is discussed. Also, statistical properties of light rays are investigated for a simple model of an inhomogeneous universe. The result of this example supports the validity of the linear approximation.