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Phillip Helbig

Publications and source records attributed to Phillip Helbig.

17 recordsLinked to original sources
arXiv2019

Calculation of distances in cosmological models with small-scale inhomogeneities and their use in observational cosmology: a review

The Universe is not completely homogeneous. Even if it is sufficiently so on large scales, it is very inhomogeneous at small scales, and this has an effect on light propagation, so that the distance as a function of redshift, which in many cases is defined via light propagation, can differ from the homogeneous case. Simple models can take this into account. I review the history of this idea, its generalization to a wide variety of cosmological models, analytic solutions of simple models, comparison of such solutions with exact solutions and numerical simulations, applications, simpler analytic approximations to the distance equations, and (for all of these aspects) the related concept of a "Swiss-cheese" universe.

astro-ph.CO↗
arXiv2015

The $m$-$z$ relation for type Ia supernovae, locally inhomogeneous cosmological models, and the nature of dark matter

The $m$-$z$ relation for type Ia supernovae is one of the key pieces of evidence supporting the cosmological `concordance model' with $λ_0 \approx 0.7$ and $Ω_0 \approx 0.3$. However, it is well known that the $m$-$z$ relation depends not only on $λ_0$ and $Ω_0$ (with $H_0$ as a scale factor) but also on the density of matter along the line of sight, which is not necessarily the same as the large-scale density. I investigate to what extent the measurement of $λ_0$ and $Ω_0$ depends on this density when it is characterized by the parameter $η$ ($0 \le η\le 1$), which describes the ratio of density along the line of sight to the overall density. I also discuss what constraints can be placed on $η$, both with and without constraints on $λ_0$ and $Ω_0$ in addition to those from the $m$-$z$ relation for type~Ia supernovae.

astro-ph.CO↗
arXiv2015

The $m$-$z$ relation for Type Ia supernovae: safety in numbers or safely without worry?

The $m$-$z$ relation for Type Ia supernovae is compatible with the cosmological concordance model if one assumes that the Universe is homogeneous, at least with respect to light propagation. This could be due to the density along each line of sight being equal to the overall cosmological density, or to `safety in numbers', with variation in the density along all lines of sight averaging out if the sample is large enough. Statistical correlations (or lack thereof) between redshifts, residuals (differences between the observed distance moduli and those calculated from the best-fitting cosmological model), and observational uncertainties suggest that the former scenario is the better description, so that one can use the traditional formula for the luminosity distance safely without worry.

astro-ph.CO↗
arXiv2012

Is there a flatness problem in classical cosmology?

I briefly review the flatness problem within the context of classical cosmology and examine some of the debate in the literature with regard to its definition and even the question whether it exists. I then present some new calculations for cosmological models which will collapse in the future; together with previous work by others for models which will expand forever, this allows one to examine the flatness problem quantitatively for all cosmological models. This leads to the conclusion that the flatness problem does not exist, not only for the cosmological models corresponding to the currently popular values of lambda_0 and Omega_0 but indeed for all Friedmann-Lemaître models.

astro-ph.CO↗
arXiv2003

Can Microlensing Explain the Long-Term Optical Variability of Quasars?

Although controversial, the scenario of microlensing as the dominant mechanism for the long-term optical variability of quasars does provide a natural explanation for both the statistical symmetry, achromaticity and lack of cosmological time dilation in quasar light curves. Here, we investigate to what extent dark matter populations of compact objects allowed in the currently favored Omega_M=0.3, Omega_Lambda=0.7 cosmology really can explain the quantitative statistical features of the observed variability. We find that microlensing reasonably well reproduces the average structure function of quasars, but fails to explain both the high fraction of objects with amplitudes higher than 0.35 magnitudes and the mean amplitudes observed at redshifts below one. Even though microlensing may still contribute to the long-term optical variability at some level, another significant mechanism must also be involved. This severely complicates the task of using light-curve statistics from quasars which are not multiply imaged to isolate properties of any cosmologically significant population of compact objects which may in fact be present.

astro-ph↗
arXiv2000

The Current Status of CLASS

I give a brief overview of the current status of some aspects of the Cosmic Lens All-Sky Survey (CLASS): description of the survey, current list of lens systems, cosmological parameters from lensing statistics, H_0 from time delays, dark lenses, wide-separation lenses.

astro-ph↗
arXiv2000

The Lens-Redshift Test Revisited

Kochanek (1992) suggested that the redshifts of gravitational lens galaxies rule out a large cosmological constant. This result was questioned by Helbig & Kayser (1996), who pointed out that selection effects related to the brightness of the lens can bias the results of this test against a high lambda value; however, we did not claim that the observations favoured a high lambda value, merely that current observational data were not sufficient to say either way, using the test as proposed by Kochanek (1992) but corrected for selection effects. Kochanek (1996) pointed out that additional information (fraction of measured lens redshifts) provides additional information which restores the sensitivity of the test to the cosmological model, at least somewhat. Here, I consider three aspects. First, I examine the accuracy of the correction to the test proposed by Kochanek (1996). Second, I compare the slightly different statistical methods which have been used in connection with this test. Third, I discuss what results can be obtained today now that more and better-defined observations are available.

astro-ph↗
arXiv1999

Gravitational lensing statistics with extragalactic surveys. III. Joint constraints on lambda_0 and Omega_0 from lensing statistics and the m-z relation for type Ia supernovae

I present constraints on cosmological parameters in the lambda_0-Omega_0 plane from a joint analysis of gravitational lensing statistics (astro-ph/9904175) and the magnitude-redshift relation for Type Ia supernovae (astro-ph/9812133 and astro-ph/9805201). I discuss reasons why this particular combination of tests is important and how the constraints can be improved in the future. The lensing statistics and supernova results are not inconsistent, thus it is meaningful to determine joint constraints on lambda_0 and Omega_0 by combining the results from both tests. The quantity measured by the lens statistics and the m-z relation for type Ia supernovae discussed here is approximately lambda_0 - Omega_0. At 95% confidence, the upper limit on lambda_0 - Omega_0 from lensing statistics alone is 0.45 and from supernovae alone is in the range 0.65--0.81 (depending on the data set). For joint constraints, the upper limit on lambda_0 - Omega_0 is in the range 0.55--0.60 (again depending on the data set). For a flat universe with lambda_0 + Omega_0 = 1, this corresponds to upper limits on lambda_0, taking the top of the range from different data sets, of 0.72, 0.90 and 0.80 for lensing statistics alone, supernovae alone and the joint analysis, respectively. This is perfectly consistent with the current `standard cosmological model' with lambda_0 approximately 0.7 and Omega_0 approximately 0.3 and is consistent with a flat universe but, neglecting other cosmological tests, does not require it.

astro-ph↗
arXiv1999

Gravitational lensing statistics with extragalactic surveys. I. A lower limit on the cosmological constant

We reanalyse optical gravitational lens surveys from the literature in order to determine relative probabilities in the $λ_{0}$-$Ω_{0}$ plane, using a softened singular isothermal sphere lens model. In addition, we examine a portion of the $λ_{0}$-$Ω_{0}$ plane which includes all viable cosmological models; this is vital for comparison with other cosmological tests. The results are, within the errors, consistent with those of more specialised analyses, such as those concerning upper limits on $λ_{0}$ in a flat universe. We note that gravitational lensing statistics can provide a quite robust LOWER limit on the cosmological constant as well, which could prove important in confirming current claims of a positive cosmological constant. At 95% confidence, our lower and upper limits on $λ_{0}-Ω_{0}$, using lens statistics information alone, are respectively -3.17 and 0.3. For a flat universe, these correspond to lower and upper limits on $λ_{0}$ of respectively -1.09 and 0.65.

astro-ph↗
arXiv1998

The image separation-source redshift relation for gravitational lenses as a cosmological test

Recently, Park & Gott claimed that there is a statistically significant, strong, negative correlation between the image separation and source redshift for gravitational lenses. This is somewhat puzzling if one believes in a flat (k = 0) universe, since in this case the typical image separation is expected to be independent of the source redshift, while one expects a negative correlation in a k = -1 universe and a positive one in a k = +1 universe. Park & Gott explored several effects which could cause the observed correlation, but no combination of these can explain the observations with a realistic scenario. Here, I explore this test further in three ways. First, I show that in an inhomogeneous universe a negative correlation is expected regardless of the value of k. Second, I test whether the image separation-source redshift relation can be used as a test to determine lambda and Omega, rather than just the sign of k. Third, I compare the results of the test from the Park & Gott sample to those using other samples of gravitational lenses, which can illuminate (unknown) selection effects and probe the usefulness of the image separation-source redshift relation as a cosmological test.

astro-ph↗
arXiv1997

A general and practical method for calculating cosmological distances

The calculation of distances is of fundamental importance in extragalactic astronomy and cosmology. However, no practical implementation for the general case has previously been available. We derive a second-order differential equation for the angular size distance valid not only in all em homogeneous Friedmann-Lemaitre cosmological models, parametrised by $λ_{0}$ and $Ω_{0}$, but also in inhomogeneous `on-average' Friedmann-Lemaitre models, where the inhomogeneity is given by the (in the general case redshift-dependent) parameter $η$. Since most other cosmological distances can be obtained trivially from the angular size distance, and since the differential equation can be efficiently solved numerically, this offers for the first time a practical method for calculating distances in a large class of cosmological models. We also briefly discuss our numerical implementation, which is publicly available.

astro-ph↗
arXiv1996

Evolution in the Lyman-alpha forest

We reanalyse the spectra used by D.-E. Liebscher (no relation) et al with the same goal -- determining the cosmological parameters -- and basically the same assumptions but with a different statistical method, which does not rely on binning the data. Also, we correct for selection effects. We basically confirm their result, with somewhat larger but still very small (formal) errors. However, all world models within the 99% confidence region are ruled out because a firm lower limit on $Ω_{0}$ is significantly larger. This directly demonstrates for the first time the existence of intrinsic evolution in the Lyman-$α$ forest.

astro-ph↗
arXiv1995

Cosmological parameters and the redshift distribution of gravitational lenses

For known gravitational lens systems the redshift distribution of the lenses is compared with theoretical expectations for $10^{4}$~Friedmann-Lema\^ıtre~cosmological models, which more than cover the range of possible cases. The comparison is used for assigning a relative probability to each of the models. The entire procedure is repeated for different values of the inhomogeneity parameter~$η$ and the limiting spectroscopic magnitude~$m_{\rm lim}$, which is important for selection effects. The dependence on these two parameters is examined in more detail for the special cases~$λ_{0}=0$ and $k=0$. Previous results that this method is a better probe for~$λ_{0}$ than $Ω_{0}$ are confirmed, but it appears that the low probability of models with large~$λ_{0}$~values found using similar methods is due to a selection effect. The power of this method to discriminate between cosmological models can of course be improved if more gravitational lens systems are found. However, our numerical simulations indicate that a reasonable number of observed systems cannot deliver interesting constraints on the cosmological parameters.

astro-ph↗
arXiv1995

Predicted Lens Redshifts and Magnitudes for Gravitational Lenses

For suitable gravitational lens systems with unknown lens redshifts, the redshifts and brightnesses (in different colours) of the lenses are predicted for a variety of cosmological models, for both elliptical and spiral galaxy lenses. Besides providing hints as to which systems should be observed with a realistic chance of measuring the lens redshifts, which are needed for detailed lensing statistics and for modelling the lenses, these calculations give a visual impression of the influence of the cosmological model in gravitational lensing.

astro-ph↗
arXiv1995

COSMOLOGICAL PARAMETERS AND GRAVITATIONAL LENSING STATISTICS

The general idea of determining cosmological parameters with gravitational lensing statistics is outlined, and then recent work---with an emphasis on applicability to all cosmological models, observational bias, better statistics and robustness testing through numerical simulations---is discussed with relevance to a scheme originally introduced by Kochanek to avoid some of the uncertainties which plague other methods. The main result is that the observations at present---and probably in the future as well---are more indicative of intrinsic scatter than a hint of the correct cosmological model.

astro-ph↗