Krzysztof Bolejko

Inhomogeneous cosmological models: exact solutions and their applications

Recently, inhomogeneous generalizations of the Friedmann?Lema?tre?Robertson?Walker (FLRW) cosmological models have gained interest in the astrophysical community and are more often employed to study cosmological phenomena. However, in many papers the inhomogeneous cosmological models are treated as an alternative to the FLRW models. In fact, they are not an alternative, but an exact perturbation of the latter, and are gradually becoming a necessity in modern cosmology. The assumption of homogeneity is just a first approximation introduced to simplify equations. So far this assumption is commonly believed to have worked well, but future and more precise observations will not be properly analysed unless inhomogeneities are taken into account. This paper reviews recent developments in the field and shows the importance of an inhomogeneous framework in the analysis of cosmological observations.

Structures in the universe by exact methods : formation, evolution, interactions

1. The purpose of this book Part I. Theoretical Background: 2. Exact solutions of Einsteins equations that are used in cosmology 3. Light propagation Part II. Applications of the Models in Cosmology: 4. Structure formation 5. The cosmological constant and coincidence problems 6. The horizon problem 7. CMB temperature fluctuations 8. Conclusions References Index.

A (giant) void is not mandatory to explain away dark energy with a Lemaître-Tolman model

Context. Lemaitre-Tolman (L-T) toy models with a central observer have been used to study the effect of large scale inhomogeneities on the SN Ia dimming. Claims that a giant void is mandatory to explain away dark energy in this framework are currently dominating. Aims. Our aim is to show that L-T models exist that reproduce a few features of the ΛCDM model, but do not contain the giant cosmic void. Methods. We propose to use two sets of data – the angular diameter distance together with the redshift-space mass-density and the angular diameter distance together with the expansion rate – both defined on the past null cone as functions of the redshift. We assume that these functions are of the same form as in the ΛCDM model. Using the Mustapha–Hellaby–Ellis algorithm, we numerically transform these initial data into the usual two L-T arbitrary functions and solve the evolution equation to calculate the mass distribution in spacetime. Results. For both models, we find that the current density profile does not exhibit a giant void, but rather a giant hump. However, this hump is not directly observable, since it is in a spacelike relation to a present observer. Conclusions. The alleged existence of the giant void was a consequence of the L-T models used earlier because their generality was limited a priori by needless simplifying assumptions, like, for example, the bang-time function being constant. Instead, one can feed any mass distribution or expansion rate history on the past light cone as initial data to the L-T evolution equation. When a fully general L-T metric is used, the giant void is not implied.

Testing the copernican principle via cosmological observations

Observations of distances to Type-Ia supernovae can be explained by cosmological models that include either a gigaparsec-scale void, or a cosmic flow, without the need for Dark Energy. Instead of invoking dark energy, these inhomogeneous models instead violate the Copernican Principle. we show that current cosmological observations (Supernovae, Baryon Acoustic Oscillations and estimates of the Hubble parameters based on the age of the oldest stars) are not able to rule out inhomogeneous anti-Copernican models. The next generation of surveys for baryonic acoustic oscillations will be sufficiently precise to either validate the Copernican Principle or determine the existence of a local Gpc scale inhomogeneity.

Szekeres Swiss-cheese model and supernova observations

We use different particular classes of axially symmetric Szekeres Swiss-cheese models for the study of the apparent dimming of the supernovae of type Ia. We compare the results with those obtained in the corresponding Lemaitre-Tolman Swiss-cheese models. Although the quantitative picture is different the qualitative results are comparable, i.e., one cannot fully explain the dimming of the supernovae using small-scale (∼ 50 Mpc) inhomogeneities. To fit successfully the data we need structures of order of 500 Mpc size or larger. However, this result might be an artifact due to the use of axial light rays in axially symmetric models. Anyhow, this work is a first step in trying to use Szekeres Swiss-cheese models in cosmology and it will be followed by the study of more physical models with still less symmetry.

Apparent and average accelerations of the Universe

In this paper we consider the relation between the volume deceleration parameter obtained within the Buchert averaging scheme and the deceleration parameter derived from supernova observation. This work was motivated by recent findings that showed that there are models which despite having Λ = 0 have volume deceleration parameter qvol 0, while those models which we have been able to find which exhibit qvol<0 turn out to be unrealistic. This indicates that care must be exercised in relating the deceleration parameter to observations.

Anti-lensing: the bright side of voids

More than half of the volume of our Universe is occupied by cosmic voids. The lensing magnification effect from those underdense regions is generally thought to give a small dimming contribution: objects on the far side of a void are supposed to be observed as slightly smaller than if the void were not there, which together with conservation of surface brightness implies net reduction in photons received. This is predicted by the usual weak lensing integral of the density contrast along the line of sight. We show that this standard effect is swamped at low redshifts by a relativistic Doppler term that is typically neglected. Contrary to the usual expectation, objects on the far side of a void are brighter than they would be otherwise. Thus the local dynamics of matter in and near the void is crucial and is only captured by the full relativistic lensing convergence. There are also significant nonlinear corrections to the relativistic linear theory, which we show actually underpredicts the effect. We use exact solutions to estimate that these can be more than 20% for deep voids. This remains an important source of systematic errors for weak lensing density reconstruction in galaxy surveys and for supernovae observations, and may be the cause of the reported extra scatter of field supernovae located on the edge of voids compared to those in clusters.

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 explore are 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.

Formation of voids in the Universe within the Lemaître–Tolman model

We develop models of void formation starting from a small initial fluctuation at recombination and growing to a realistic present-day density profile in agreement with observations of voids. The model construction is an extension of previously developed algorithms for finding a Lemaitre–Tolman metric that evolves between two profiles of either density or velocity specified at two times. Of the four profiles of concern (those of density and velocity at recombination and at the present day), two can be specified and the other two follow from the derived model. We find that, in order to reproduce the present-day void density profiles, the initial velocity profile is more important than the initial density profile. Extrapolation of current cosmic microwave background (CMB) observations to the scales relevant to protovoids is very uncertain. Even so, we find that it is very difficult to make both the initial density and velocity fluctuation amplitudes small enough and still obtain a realistic void by today.

Structure formation in the quasispherical Szekeres model

Structure formation in the Szekeres model is investigated. Since the Szekeres model is an inhomogeneous model with no symmetries, it is possible to examine the interaction of neighboring structures and its impact on the growth of a density contrast. It has been found that the mass flow from voids to clusters enhances the growth of the density contrast. In the model presented here, the growth of the density contrast is almost 8 times faster than in the linear approach.