Biswajit Pandey

Testing homogeneity on large scales in the Sloan Digital Sky Survey Data Release One

The assumption that the Universe is homogeneous and isotropic on large scales is one of the fundamental postulates of cosmology. We have tested the large-scale homogeneity of the galaxy distribution in the Sloan Digital Sky Survey Data Release One (SDSS-DR1) using volumelimited subsamples extracted from the two equatorial strips that are nearly two-dimensional. The galaxy distribution was projected on the equatorial plane and we carried out a 2D multifractal analysis by counting the number of galaxies inside circles of different radii, r ,i nthe range 5‐150 h −1 Mpc centred on galaxies. Different moments of the count-in-cells were analysed to identify a range of length-scales (60‐70 h −1 Mpc to 150 h −1 Mpc ), where the moments show ap ower-law scaling behaviour, and to determine the scaling exponent that gives the spectrum of generalized dimension Dq .I fthe galaxy distribution is homogeneous, Dq does not vary with q and is equal to the Euclidean dimension, which in our case is 2. We find that Dq varies in the range 1.7‐2.2. We also constructed mock data from random, homogeneous point distributions and from lambda cold dark matter (�CDM) N-body simulations with bias b = 1, 1.6 and 2, and analysed these in exactly the same way. The values of Dq in the random distribution and the unbiased simulations show much smaller variations and these are not consistent with the actual data. The biased simulations, however, show larger variations in Dq and these are consistent with both the random and the actual data. Interpreting the actual data as a realization of

The scale of homogeneity of the galaxy distribution in SDSS DR6

The assumption that the Universe, on sufficiently large scales, is homogeneous and isotropic is crucial to our current understanding of cosmology. In this Letter, we test if the observed galaxy distribution is actually homogeneous on large scales. We have carried out a multifractal analysis of the galaxy distribution in a volume-limited subsample from the Sloan Digital Sky Survey (SDSS) Data Release 6. This considers the scaling properties of different moments of galaxy number counts in spheres of varying radius, r, centred on galaxies. This analysis gives the spectrum of generalized dimension Dq(r), where q> 0 quantifies the scaling properties in overdense regions and q< 0 in underdense regions. We expect Dq(r) = 3 for a homogeneous, random point distribution. In our analysis, we have determined Dq(r) in the range −4 ≤ q ≤ 4 and 7 ≤ r ≤ 98 h −1 Mpc. In addition to the SDSS data, we have analysed several random samples which are homogeneous by construction. Simulated galaxy samples generated from dark matter N-body simulations and the Millennium Run were also analysed. The SDSS data is considered to be homogeneous if the measured Dq is consistent with that of the random samples. We find that the galaxy distribution becomes homogeneous at a length-scale between 60 and 70 h −1 Mpc. The galaxy distribution, we find, is homogeneous at length-scales greater than 70 h −1 Mpc. This is consistent with earlier works which find the transition to homogeneity at around 70 h −1 Mpc.

The Luminosity, Colour and Morphology dependence of galaxy filaments in the Sloan Digital Sky Survey Data Release Four

We have tested for luminosity, colour and morphology dependence of the degree of filamentarity in seven nearly two-dimensional strips from the Sloan Digital Sky Survey Data Release Four .(SDSS DR4). The analysis was carried out at various levels of coarse graining allowing us to address different length-scales. We find that the brighter galaxies have a less filamentary distribution than the fainter ones at all levels of coarse graining. The distribution of red galaxies and ellipticals shows a higher degree of filamentarity compared to blue galaxies and spirals, respectively, at low levels of coarse graining. The behaviour is reversed at higher levels of coarse graining. We propose a picture where the ellipticals are densely distributed in the vicinity of the nodes where the filaments intersect while the spirals are sparsely distributed along the entire extent of the filaments. Our findings indicate that the regions with an excess of ellipticals are larger than galaxy clusters, protruding into the filaments. We have also compared the predictions of a semi-analytic model of galaxy formation (the Millennium Run galaxy catalogue) against our results for the SDSS. We find the two to be in agreement for the M* galaxies and for the red galaxies, while the model fails to correctly predict the filamentarity of the brighter galaxies and the blue galaxies.

What will anisotropies in the clustering pattern in redshifted 21 cm maps tell us

The clustering pattern in high-redshift H I maps is expected to be anisotropic for two distinct reasons: the Alcock-Paczynski effect and the peculiar velocities, both of which are sensitive to the cosmological parameters. The signal is also expected to be sensitive to the details of the H I distribution at the epoch when the radiation originated. We use simple models for the H i distribution at the epoch of reionization and the post-reionization era to investigate exactly what we hope to learn from future observations of the anisotropy pattern in H I maps. We find that such observations will probably tell us more about the H I distribution than about the background cosmological model. Assuming that reionization can be described by spherical, ionized bubbles all of the same size with their centres possibly being biased with respect to the dark matter, we find that the anisotropy pattern at small angles is expected to have a bump at the characteristic angular size of the individual bubbles whereas the large-scale anisotropy pattern will reflect the size and the bias of the bubbles. The anisotropy also depends on the background cosmological parameters, but the dependence is much weaker. Under the assumption that the H i in the post-reionization era traces the dark matter with a possible bias, we find that changing the bias and changing the background cosmology have similar effects on the anisotropy pattern. Combining observations of the anisotropy with independent estimates of the bias, possibly from the bi-spectrum, may allow these observations to constrain cosmological parameters.

Using the Filaments in the Las Campanas Redshift Survey to Test the ΛCDM Model

It has recently been established that the filaments seen in the Las Campanas Redshift Survey (LCRS) are statistically significant at scales as large as 70-80 h-1 Mpc in the δ = -3° slice and 50-70 h-1 Mpc in the five other LCRS slices. The ability to produce such filamentary features is an important test of any model for structure formation. We have tested the ΛCDM model with a featureless, scale-invariant primordial power spectrum by quantitatively comparing the filamentarity in simulated LCRS slices with the actual data. The filamentarity in an unbiased ΛCDM model, we find, is less than the LCRS. Introducing a bias b = 1.15, the model is in rough consistency with the data, although in two of the slices the filamentarity falls below the data at a low level of statistical significance. The filamentarity is very sensitive to the bias parameter, and a high value (b = 1.5), which enhances filamentarity at small scales and suppresses it at large scales, is ruled out. A bump in the power spectrum at k ~ 0.05 h Mpc-1 is found to have no noticeable effect on the filamentarity.It has recently been established that the filaments seen in the Las Campanas Redshift Survey (LCRS) are statistically significant at scales as large as 70 to 80 Mpc/h in the

Exploring star formation using the filaments in the Sloan Digital Sky Survey Data Release Five

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Testing homogeneity in the Sloan Digital Sky Survey Data Release Twelve with Shannon entropy

slice, and 50 to 70 Mpc/h in the five other LCRS slices. The ability to produce such filamentary features is an important test of any model for structure formation. We have tested the LCDM model with a featureless, scale invariant primordial power spectrum by quantitatively comparing the filamentarity in simulated LCRS slices with the actual data. The filamentarity in an unbiased LCDM model, we find, is less than the LCRS. Introducing a bias b=1.15, the model is in rough consistency with the data, though in two of the slices the filamentarity falls below the data at a low level of statistical significance. The filamentarity is very sensitive to the bias parameter and a high value b=1.5, which enhances filamentarity at small scales and suppresses it at large scales, is ruled out. A bump in the power spectrum at k~0.05 Mpc/h is found to have no noticeable effect on the filamentarity.

The size of the longest filament in the luminous red galaxy distribution

We have quantified the average filamentarity of the galaxy distribution in seven nearly two-dimensional strips from the Sloan Digital Sky Survey Data Release Five (SDSS DR5) using a volume-limited sample in the absolute magnitude range -21 ≤M r ≤ -20. The average filamentarity of star-forming (SF) galaxies, which are predominantly blue, is found to be more than that of other galaxies which are predominantly red. This difference is possibly an outcome of the fact that blue galaxies have a more filamentary distribution. Comparing the SF galaxies with only the other blue galaxies, we find that the two show nearly equal filamentarity. Separately analyzing the galaxies with high star formation rates (SFR) and low SFR, we find that the latter has a more filamentary distribution. We interpret this in terms of two effects. (i) A correlation between the SFR and individual galaxy properties like luminosity with the high-SFR galaxies being more luminous. (ii) A relation between the SFR and environmental effects like the density with the high-SFR galaxies preferentially occurring in high-density regions. These two effects are possibly not independent and are operating simultaneously. We do not find any difference in the filamentarity of SF galaxies and active galactic nuclei.

The luminosity–bias relation from filaments in the Sloan Digital Sky Survey Data Release Four

We analyze a set of volume limited samples from SDSS DR12 to quantify the degree of inhomogeneity at different length scales using Shannon entropy. We find that the galaxy distributions exhibit a higher degree of inhomogeneity as compared to a Poisson point process at all length scales. Our analysis indicates that signatures of inhomogeneities in the galaxy distributions persist at least upto a length scale of

Probing large scale homogeneity and periodicity in the LRG distribution using Shannon entropy

120 , h^{-1}, {rm Mpc}