Cosmological parameters and cosmic topology

Geometry constrains but does not dictate the topology of the three-dimensional space. In a locally spatially homogeneous and isotropic universe, however, the topology of its spatial section dictates its geometry. We show that, besides determining the geometry, the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of setting constraints on the density parameters associated with dark matter (Ω_m) and dark energy  (Ω_Λ)  . By assuming the Poincaré dodecahedral space as the circles-in-the-sky detectable topology of the spatial sections of the Universe, we re-analyse the constraints on the density parametric plane  Ω_m–Ω_Λ  from the current Type Ia supernova plus X-ray gas mass fraction data, and show that a circles-in-the sky detection of the dodecahedral space topology gives rise to strong and complementary constraints on the region of the density parameter plane currently allowed by these observational data sets.     

Spiral galaxy distance indicators based on near-infrared photometry

We compare two methods of distance determination to spiral galaxies using optical/near-infrared (NIR) observations, the ( I − K ) versus M _K colour–absolute magnitude (CM) relation and the I - and K -band Tully–Fisher relation (TFR).
Dust-free colours and NIR absolute magnitudes greatly enhance the usefulness of the NIR CM relation as a distance indicator for moderately to highly inclined spiral galaxies in the field (inclinations between ∼80° and 90°); by avoiding contamination by dust the scatter in the CM relation is significantly reduced, compared with similar galaxy samples published previously. The CM relation can be used to determine distances to field spiral galaxies with M _K >−25.5, to at least M _K ≈−20.
Our results, supplemented with previously published observations for which we can – to some degree – control the effects of extinction, are consistent with a universal nature of the CM relation for field spiral galaxies.
High-resolution observations made with the Hubble Space Telescope can provide a powerful tool to calibrate the relation and extend the useful distance range by more than a factor of 2 compared with ground-based observations.
The intrinsic scatter in the NIR CM relation in the absolute K -band magnitudes is ∼0.5 mag, yielding a lower limit to the accuracy of distance determinations of the order of 25 per cent.
Although we find an unusually low scatter in the TFR (probably a statistical accident), a typical scatter in the TFR would yield distances to our sample galaxies with uncertainties of only ∼15 per cent. However, one of the main advantages of the use of the NIR CM relation is that we need only photometric data to obtain distance estimates; use of the TFR requires additional kinematic data, although it can be used to significantly greater distances.     

The continuous limit of the multiple lens effect and the optical scalar equation

We study the continuous limit of the multiple gravitational lensing theory based on the thin lens approximation. We define a new, light-path dependent angular diameter distance     and show that it satisfies the optical scalar equation. The distance provides relations between quantities used in gravitational lensing theory (the convergence, the shear and the twist terms) and those used in scalar optics theory (the rates of expansion, shear and rotation).     

Constraining the cosmic equation of state from old galaxies at high redshift

New limits on the cosmic equation of state are derived from age measurements of three recently reported old high-redshift galaxies (OHRG). The results are based on a flat Friedmann–Robertson–Walker (FRW) type cosmological model driven by non-relativistic matter plus a smooth component parametrized by its equation of state p _x ωρ _x ( ω −1). The range of ω is strongly dependent on the matter density parameter. For Ω_M∼0.3, as indicated from dynamical measurements, the age estimates of the OHRG restrict the cosmic parameter to ω −0.27. However, if Ω_M is the one suggested by some studies of field galaxies, i.e., Ω_M≃0.5, only a cosmological constant ( ω =−1) may be compatible with these data.     

On the comoving distance as an arc-length in four dimensions

The inner product provides a conceptually and algorithmically simple method for calculating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The key to this is that just as a distance between two points 'on' the surface of the ordinary 2-sphere ² is simply an arc-length (angle multiplied by radius) in ordinary Euclidean 3-space ℰ³, the distance between two points 'on' a 3-sphere ³ (a 3-hyperboloid ℋ³) is simply an 'arc-length' in Euclidean 4-space ℰ⁴ (Minkowski 4-space ℳ⁴), i.e. an 'hyper-angle' multiplied by the curvature radius of the 3-sphere (3-hyperboloid).     

Does time dilation tell us the distance to gamma-ray bursts?

Since the discovery that dim gamma-ray bursts last longer on average than bright ones (time dilation) the cosmological origin of this effect has been contested by various researchers. I discuss the current status of this issue and conclude that current models for a non-cosmological time dilation only explain part of the observed phenomenon, and even then betray themselves by distinct signatures in the data. As those signatures have not been seen, the cosmological origin remains the favoured explanation of the time dilation.     

Peculiar velocities and the mean density parameter

We study the peculiar velocity field inferred from the Mark III spirals using a new method of analysis. We estimate optimal values of Tully–Fisher scatter and zero-point offset, and we derive the three-dimensional rms peculiar velocity ( σ _v ) of the galaxies in the samples analysed. We check our statistical analysis using mock catalogues derived from numerical simulations of cold dark matter (CDM) models considering measurement uncertainties and sampling variations. Our best determination for the observations is σ _v =(660±50) km s⁻¹. We use the linear theory relation between σ _v , the density parameter Ω, and the galaxy correlation function ξ ( r ) to infer the quantity     , where b is the linear bias parameter of optical galaxies and the uncertainties correspond to bootstrap resampling and an estimated cosmic variance added in quadrature. Our findings are consistent with the results of cluster abundances and redshift-space distortion of the two-point correlation function. These statistical measurements suggest a low value of the density parameter Ω∼0.4 if optical galaxies are not strongly biased tracers of mass.     

Constraining Dark Energy and Cosmological Transition Redshift with Type Ia Supernovae

The property of dark energy and the physical reason for the acceleration of the present universe are two of the most difficult problems in modern cosmology. The dark energy contributes about two-thirds of the critical density of the present universe from the observations of type-la supemovae (SNe Ia) and anisotropy of cosmic microwave background (CMB). The SN Ia observations also suggest that the universe expanded from a deceleration to an acceleration phase at some redshift, implying the existence of a nearly uniform component of dark energy with negative pressure. We use the "Gold" sample containing 157 SNe Ia and two recent well-measured additions, SNe Ia 1994ae and 1998aq to explore the properties of dark energy and the transition redshift. For a flat universe with the cosmological constant, we measureΩM = 0.28-0.05 0.04, which is consistent with Riess et al. The transition redshift is ZT = 0.60-0.08 0.06. We also discuss several dark energy models that define w(z) of the parameterized equation of state of dark energy including one parameter and two parameters (w(z) being the ratio of the pressure to energy density). Our calculations show that the accurately calculated transition redshift varies from ZT = 0.29-0.06 0.07 to zT = 0.60-0.08 0.06 across these models. We also calculate the minimum redshift zc at which the current observations need the universe to accelerate.     

Non-standard structure formation scenarios

Observations on galactic scales seem to be in contradiction with recent high resolution N-body simulations. This so-called cold dark matter (CDM) crisis has been addressed in several ways, ranging from a change in fundamental physics by introducing self-interacting cold dark matter particles to a tuning of complex astrophysical processes such as global and/or local feedback. All these efforts attempt to soften density profiles and reduce the abundance of satellites in simulated galaxy halos. In this contribution we are exploring the differences between a Warm Dark Matter model and a CDM model where the power on a certain scale is reduced by introducing a narrow negative feature (`dip'). This dip is placed in a way so as to mimic the loss of power in the WDM model: both models have the same integrated power out to the scale where the power of the Dip model rises to the level of the unperturbed CDM spectrum again. Using N-body simulations we show that that the new Dip model appears to be a viable alternative to WDM while being based on different physics: where WDM requires the introduction of a new particle species the Dip stems from anon-standard inflationary period. If we are looking for an alternative to the currently challenged standard ΛCDM structure formation scenario, neither the ΛWDM nor the new Dip model can be ruled out with respect to the analysis presented in this contribution. They both make very similar predictions and the degeneracy between them can only be broken with observations yet to come. This revised version was published online in August 2006 with corrections to the Cover Date.     

Numerical action reconstruction of the dynamical history of dark matter haloes in N-body simulations

We test the ability of the numerical action method (NAM) to recover the individual orbit histories of mass tracers in an expanding universe, given the masses and redshift-space coordinates at the present epoch. The mass tracers are represented by dark matter (DM) haloes identified in a region of radius  26  h ⁻¹ Mpc  of a high-resolution N -body simulation of the standard Λ cold dark matter (CDM) cosmology. Since previous tests of NAM at this scale have traced the underlying distribution of DM particles rather than extended haloes, our study offers an assessment of the accuracy of NAM in a scenario which more closely approximates the complex dynamics of actual galaxy haloes. We show that NAM can recover the present-day halo distances with typical distance errors of less than 3 per cent and radial peculiar velocities with a dispersion of  ∼130 km s⁻¹  . The accuracy of individual orbit reconstructions was limited by the inability of NAM, in some instances, to correctly model the positions of haloes at early times solely on the basis of the redshifts, angular positions and masses of the haloes at the present epoch. Improvements in the quality of NAM reconstructions may be possible using the present-day three-dimensional halo velocities and distances to further constrain the dynamics. This velocity data is expected to become available for nearby galaxies in the coming generations of observations by Space Interferometry Mission ( SIM ) and Global Astrometric Interferometer for Astrophysics ( GAIA ).     

Bulk flow and shear moments of the SFI++ survey

We find the nine bulk flow and shear moments from the SFI++ survey, as well as for subsamples of group and field galaxies. We constrain the velocity power spectrum shape parameter Γ in linear theory using these moments. A likelihood function for Γ was found after marginalizing over the power spectrum amplitude  σ₈Ω^0.6_m  using constraints obtained from comparisons between redshift surveys and peculiar velocity data. We have estimated the velocity noise  σ_*  from the data since without it our results may be biased. We also performed a statistical analysis of the difference between the field and group catalogues and found that the results from each reflect the same underlying large-scale flows. We found that we can constrain the power spectrum shape parameter to be  Γ= 0.15^+0.18_−0.08  for the groups catalogue and  Γ= 0.09^+0.04_−0.04  for the field galaxy catalogue in fair agreement with the value from Wilkinson Microwave Anisotropy Probe .     

The Δθ–zs relation for gravitational lenses as a cosmological test

Recently, Park &38; Gott claimed that there is a statistically significant, strong, negative correlation between the image separation Δθ and source redshift z _s 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 &38; Gott explored several effects that 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 . Secondly, I test whether the Δθ– z _s relation can be used as a test to determine λ₀ and Ω₀, rather than just the sign of k . Thirdly, I compare the results of the test from the Park &38; Gott sample with those using other samples of gravitational lenses, which can illuminate (unknown) selection effects and probe the usefulness of the Δθ– z _s relation as a cosmological test.