arXiv subjects

Krzysztof Bolejko

Publications and source records attributed to Krzysztof Bolejko.

At least 55 records · Page 3Linked to original sources

arXiv2011

The Metric of the Cosmos from Luminosity and Age Data

This paper presents the algorithm for determining the Lemaitre-Tolman (LT) model that best fits given datasets for maximum stellar ages, and SNIa luminosities, both as functions of redshift. It then applies it to current cosmological data. Special attention must be given to the handling of the origin, and the region of the maximum diameter distances. As with a previous combination of datasets (galaxy number counts and luminosity distances versus redshift), there are relationships that must hold at the region of the maximum diameter distance, which are unlikely to be obeyed exactly by real data. We show how to make corrections that enable a self-consistent solution to be found. We address the questions of the best way to approximate discrete data with smooth functions, and how to estimate the uncertainties of the output - the 3 free functions that determine a specific LT metric. While current data does not permit any confidence in our results, we show that the method works well, and reasonable LT models do fit with or without a cosmological constant.

astro-ph.CO↗

arXiv2011

Redshift propagation equations in the $β' \neq 0$ Szekeres models

The set of differential equations obeyed by the redshift in the general $β' \neq 0$ Szekeres spacetimes is derived. Transversal components of the ray's momentum have to be taken into account, which leads to a set of 3 coupled differential equations. It is shown that in a general Szekeres model, and in a general Lema\^ıtre -- Tolman (L--T) model, generic light rays do not have repeatable paths (RLPs): two rays sent from the same source at different times to the same observer pass through different sequences of intermediate matter particles. The only spacetimes in the Szekeres class in which {\em all} rays are RLPs are the Friedmann models. Among the proper Szekeres models, RLPs exist only in the axially symmetric subcases, and in each one the RLPs are the null geodesics that intersect each $t =$ constant space on the symmetry axis. In the special models with a 3-dimensional symmetry group (L--T among them), the only RLPs are radial geodesics. This shows that RLPs are very special and in the real Universe should not exist. We present several numerical examples which suggest that the rate of change of positions of objects in the sky, for the studied configuration, is $10^{-6} - 10^{-7}$ arc sec per year. With the current accuracy of direction measurement, this drift would become observable after approx. 10 years of monitoring. More precise future observations will be able, in principle, to detect this effect, but there are basic problems with determining the reference direction that does not change.

gr-qc↗

arXiv2011

Cosmic spherical void via coarse-graining and averaging non-spherical structures

Inhomogeneous cosmological models are able to fit cosmological observations without dark energy under the assumption that we live close to the "center" of a very large-scale under-dense region. Most studies fitting observations by means of inhomogeneities also assume spherical symmetry, and thus being at (or very near) the center may imply being located at a very special and unlikely observation point. We argue that such spherical voids should be treated only as a gross first approximation to configurations that follow from a suitable smoothing out of the non-spherical part of the inhomogeneities on angular scales. In this Letter we present a toy construction that supports the above statement. The construction uses parts of the Szekeres model, which is inhomogeneous and anisotropic thus it also addresses the limitations of spherical inhomogeneities. By using the thin-shell approximation (which means that the Israel-Darmois continuity conditions are not fulfilled between the shells) we construct a model of evolving cosmic structures, containing several elongated supercluster-like structures with underdense regions between them, which altogether provides a reasonable coarse-grained description of cosmic structures. While this configuration is not spherically symmetric, its proper volume average yields a spherical void profile of 250 Mpc that roughly agrees with observations. Also, by considering a non-spherical inhomogeneity, the definition of a "center" location becomes more nuanced, and thus the constraints placed by fitting observations on our position with respect to this location become less restrictive.

astro-ph.CO↗

arXiv2011

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.

astro-ph.CO↗

arXiv2011

The effect of inhomogeneities on the distance to the last scattering surface and the accuracy of the CMB analysis

The standard analysis of the CMB data assumes that the distance to the last scattering surface can be calculated using the distance-redshift relation as in the Friedmann model. However, in the inhomogeneous universe, even if <δρ> =0, the distance relation is not the same as in the unperturbed universe. This can be of serious consequences as a change of distance affects the mapping of CMB temperature fluctuations into the angular power spectrum. In addition, if the change of distance is relatively uniform no new temperature fluctuations are generated. It is therefore a different effect than the lensing or ISW effects which introduce additional CMB anisotropies. This paper shows that the accuracy of the CMB analysis can be impaired by the accuracy of calculation of the distance within the cosmological models. Since this effect has not been fully explored before, to test how the inhomogeneities affect the distance-redshift relation, several methods are examined: the Dyer-Roeder relation, lensing approximation, and non-linear Swiss-Cheese model. In all cases, the distance to the last scattering surface is different than when homogeneity is assumed. The difference can be as low as 1% and as high as 80%. Excluding extreme cases, the distance changes by about 20-30%. Since the distance to the last scattering surface is set by the position of the CMB peaks, in order to have a good fit, the distance needs to be adjusted. After correcting the distance, the cosmological parameters change. Therefore, a not properly estimated distance to the last scattering surface can be a major source of systematics. This paper shows that if inhomogeneities are taken into account when calculating the distance then models with positive spatial curvature and with Ω_Λ~ 0.8-0.9 are preferred. The ΛCDM model in most cases, is at odds with the current data.

astro-ph.CO↗

arXiv2010

Weak lensing and the Dyer-Roeder approximation

The distance-redshift relation plays an important role in cosmology. In the standard approach to cosmology it is assumed that this relation is the same as in the homogeneous universe. As the real universe is not homogeneous there are several methods to calculate the correction. The weak lensing approximation and the Dyer-Roeder relation are one of them. This paper establishes a link between these two approximations. It is shown that if the universe is homogeneous with only small, vanishing after averaging, density fluctuations along the line of sight, then the distance correction is negligible. It is also shown that a vanishing 3D average of density fluctuations does not imply that the mean of density fluctuations along the line of sight is zero. In this case, even within the linear approximation, the distance correction is not negligible. The modified version of the Dyer-Roeder relation is presented and it is shown that this modified relation is consistent with the correction obtained within the weak lensing approximation. The correction to the distance for a source at z ~ 2 is of order of a few percent. Thus, with an increasing precision of cosmological observations an accurate estimation of the distance is essential. Otherwise errors due to miscalculation the distance can become a major source of systematics.

astro-ph.CO↗

arXiv2010

Conceptual problems in detecting the evolution of dark energy when using distance measurements

Dark energy is now one of the most important and topical problems in cosmology. The first step to reveal its nature is to detect the evolution of dark energy or to prove beyond doubt that the cosmological constant is indeed constant. However, in the standard approach to cosmology, the Universe is described by the homogeneous and isotropic Friedmann models. Here we show that in the perturbed universe (even if perturbations vanish if averaged over sufficiently large scales) the distance-redshift relation is not the same as in the unperturbed universe. This has a serious consequence when studying the nature of dark energy and, as shown here, can impair the analysis and studies of dark energy. The analysis is based on two methods: the linear lensing approximation and the non-linear Szekeres Swiss-Cheese model. The inhomogeneity scale is ~50 Mpc, and both models have the same density fluctuations along the line of sight. The comparison between linear and non-linear methods shows that non-linear corrections are not negligible. When inhomogeneities are present the distance changes by several percent. To show how this change influences the measurements of dark energy, ten future observations with 2% uncertainties are generated. It is shown the using the standard methods (i.e. under the assumption of homogeneity) the systematics due to inhomogeneities can distort our analysis, and may lead to a conclusion that dark energy evolves when in fact it is constant (or vice versa). Therefore, if future observations are analysed only within the homogeneous framework then the impact of inhomogeneities (such as voids and superclusters) can be mistaken for evolving dark energy. Since the robust distinction between the evolution and non-evolution of dark energy is the first step to understanding the nature of dark energy a proper handling of inhomogeneities is essential.

astro-ph.CO↗

arXiv2010

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

Lemaître - 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. Our aim is to show that L-T models exist that reproduce a few features of the $Λ$CDM model, but do not contain the giant cosmic void. 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 $Λ$CDM 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. 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. 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.

astro-ph.CO↗

arXiv2010

Conditions for spontaneous homogenization of the Universe

The present-day Universe appears to be homogeneous on very large scales. Yet when the casual structure of the early Universe is considered, it becomes apparent that the early Universe must have been highly inhomogeneous. The current paradigm attempts to answer this problem by postulating the inflation mechanism However, inflation in order to start requires a homogeneous patch of at least the horizon size. This paper examines if dynamical processes of the early Universe could lead to homogenization. In the past similar studies seem to imply that the set of initial conditions that leads to homogenization is of measure zero. This essay proves contrary: a set of initial conditions for spontaneous homogenization of cosmological models can form a set of non-zero measure.

gr-qc↗

arXiv2010

Imitating accelerated expansion of the Universe by matter inhomogeneities - corrections of some misunderstandings

A number of misunderstandings about modeling the apparent accelerated expansion of the Universe, and about the `weak singularity' are clarified: 1. Of the five definitions of the deceleration parameter given by Hirata and Seljak (HS), only $q_1$ is a correct invariant measure of acceleration/deceleration of expansion. The $q_3$ and $q_4$ are unrelated to acceleration in an inhomogeneous model. 2. The averaging over directions involved in the definition of $q_4$ does not correspond to what is done in observational astronomy. 3. HS's equation (38) connecting $q_4$ to the flow invariants gives self-contradictory results when applied at the centre of symmetry of the Lema\^ıtre-Tolman (L-T) model. The intermediate equation (31) that determines $q_{3'}$ is correct, but approximate, so it cannot be used for determining the sign of the deceleration parameter. Even so, at the centre of symmetry of the L-T model, it puts no limitation on the sign of $q_{3'}(0)$. 4. The `weak singularity' of Vanderveld {\it et al.} is a conical profile of mass density at the centre - a perfectly acceptable configuration. 5. The so-called `critical point' in the equations of the `inverse problem' for a central observer in an L-T model is a manifestation of the apparent horizon - a common property of the past light cones in zero-lambda L-T models, perfectly manageable if the equations are correctly integrated.

gr-qc↗

arXiv2010

Bayesian analysis of the backreaction models

We present the Bayesian analysis of four different types of backreation models, which are based on the Buchert equations. In this approach, one considers a solution to the Einstein equations for a general matter distribution and then an average of various observable quantities is taken. Such an approach became of considerable interest when it was shown that it could lead to agreement with observations without resorting to dark energy. In this paper we compare the LambdaCDM model and the backreation models with SNIa, BAO, and CMB data, and find that the former is favoured. However, the tested models were based on some particular assumptions about the relation between the average spatial curvature and the backreaction, as well as the relation between the curvature and curvature index. In this paper we modified the latter assumption, leaving the former unchanged. We find that, by varying the relation between the curvature and curvature index, we can obtain a better fit. Therefore, some further work is still needed -- in particular the relation between the backreaction and the curvature should be revisited in order to fully determine the feasibility of the backreaction models to mimic dark energy.

astro-ph↗

arXiv2010

The effect of pressure gradients on luminosity distance - redshift relations

Inhomogeneous cosmological models have had significant success in explaining cosmological observations without the need for dark energy. Generally, these models imply inhomogeneous matter distributions alter the observable relations that are taken for granted when assuming the Universe evolves according to the standard Friedmann equations. Moreover, it has recently been shown that both inhomogeneous matter and pressure distributions are required in both early and late stages of cosmological evolution. These associated pressure gradients are required in the early Universe to sufficiently describe void formation, whilst late-stage pressure gradients stop the appearance of anomalous singularities. In this paper we investigate the effect of pressure gradients on cosmological observations by deriving the luminosity distance - redshift relations in spherically symmetric, inhomogeneous spacetimes endowed with a perfect fluid. By applying this to a specific example for the energy density distribution and using various equations of state, we are able to explicitly show that pressure gradients may have a non-negligble effect on cosmological observations. In particular, we show that a non-zero pressure gradient can imply significantly different residual Hubble diagrams for $z\lesssim1$ compared to when the pressure is ignored. This paper therefore highlights the need to properly consider pressure gradients when interpreting cosmological observations.

astro-ph.CO↗

arXiv2009

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.

astro-ph↗

arXiv2008

The Szekeres Swiss Cheese model and the CMB observations

This paper presents the application of the Szekeres Swiss Cheese model to the analysis of observations of the cosmic microwave background (CMB) radiation. The impact of inhomogeneous matter distribution on the CMB observations is in most cases studied within the linear perturbations of the Friedmann model. However, since the density contrast and the Weyl curvature within the cosmic structures are large, this issue is worth studying using another approach. The Szekeres model is an inhomogeneous, non-symmetrical and exact solution of the Einstein equations. In this model, light propagation and matter evolution can be exactly calculated, without such approximations as small amplitude of the density contrast. This allows to examine in more realistic manner the contribution of the light propagation effect to the measured CMB temperature fluctuations. The results of such analysis show that small-scale, non-linear inhomogeneities induce, via Rees-Sciama effect, temperature fluctuations of amplitude $10^{-7} - 10^{-5}$ on angular scale $θ< 0.24^{\circ}$ ($\ell > 750$). This is still much smaller than the measured temperature fluctuations on this angular scale.However, local and uncompensated inhomogeneities can induce temperature fluctuations of amplitude as large as $10^{-3}$, and thus can be responsible the low multipoles anomalies observed in the angular CMB power spectrum.

astro-ph↗

arXiv2008

Volume averaging in the quasispherical Szekeres model

This paper considers the volume averaging in the quasispherical Szekeres model. The volume averaging became of considerable interest after it was shown that the volume acceleration calculated within the averaging framework can be positive even though the local expansion rate is always decelerating. This issue was intensively studied within spherically symmetric models. However, since our Universe is not spherically symmetric similar analysis is needed in non symmetrical models. This papers presents the averaging analysis within the quasispherical Szekeres model which is a non-symmetrical generalisation of the spherically symmetric Lemaître--Tolman family of models. Density distribution in the quasispherical Szekeres has a structure of a time-dependent mass dipole superposed on a monopole. This paper shows that when calculating the volume acceleration, $\ddot{a}$, within the Szekeres model, the dipole does not contribute to the final result, hence $\ddot{a}$ only depends on a monopole configuration. Thus, the volume averaging within the Szekeres model leads to literally the same solutions as obtained within the Lemaître--Tolman model.

astro-ph↗

arXiv2008

Apparent and average acceleration 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 the supernova observation. This work was motivated by recent findings that showed that there are models which despite $Λ=0$ have volume deceleration parameter $q^{vol} < 0$. This opens the possibility that backreaction and averaging effects may be used as an interesting alternative explanation to the dark energy phenomenon. We have calculated $q^{vol}$ in some Lemaître--Tolman models. For those models which are chosen to be realistic and which fit the supernova data, we find that $q^{vol} > 0$, while those models which we have been able to find which exhibit $q^{vol} < 0$ turn out to be unrealistic. This indicates that care must be exercised in relating the deceleration parameter to observations.

astro-ph↗

arXiv2008

Pressure gradients, shell crossing singularities and acoustic oscillations - application to inhomogeneous cosmological models

Inhomogeneous cosmological models have recently become a very interesting alternative to standard cosmology. This is because these models are able to fit cosmological observations without the need for dark energy. However, due to inhomogeneity and pressure-less matter content, these models can suffer from shell crossing singularities. These singularities occur when two shell of dust collide with each other leading to infinite values of the density. In this Letter we show that if inhomogeneous pressure is included then these singularities can be prevented from occurring over the period of structure formation. Thus, a simple incorporation of a gradient of pressure allows for more comprehensive studies of inhomogeneous cosmological models and their application to cosmology.

astro-ph↗

arXiv2008

Light propagation through large-scale inhomogeneities in the Universe and its impact on cosmological observations

This paper analyses cosmological observations within inhomogeneous and exact solutions of the Einstein equations. In some way the analyses presented here can be freed from assumptions such as small amplitude of the density contrast. The supernova observations are analysed using the Lema\itre-Tolman model and the CMB observations are analysed using the quasispherical Szekeres model. The results show that it is possible to fit the supernova data without the cosmological constant. However if inhomogeneities of sizes and amplitudes as observed in the local Universe are considered, their impact on cosmological observations is small.

astro-ph↗