Professor T. Padmanabhan
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Item Transfer of power in nonlinear gravitational clustering(Wiley-Blackwell, 1996-12-15) Bagla, J. S.; Padmanabhan, T.We investigate the transfer of power between different scales and the coupling of modes during the non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is exponentially damped outside a narrow range of scales, and use numerical simulations to study the evolution of this power spectrum. Non-linear effects generate power at other scales, with most power flowing from larger to smaller scales. The ‘cascade’ of power leads to equipartition of energy at smaller scales, implying a power spectrum with index n ~ - 1. We find that such a spectrum is produced in the range 1 < ð < 200 for density contrast ð. This result continues to hold even when small-scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index Nc ~-1. We find that such a spectrum is produced in the range 1< ð<200 for density contrast ð. This result continues to hold even when small-scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index Nc ~-1 in this range. For n< Nc , power in this range grows faster than linear rate, while if n> Nc , it grows at a slower rate- thereby changing the index closer to Nc. At scales larger than the narrow range of scales with initial power, a k⁴ tail is produced. We demonstrate that non-linear small scales do not affect the growth of perturbations at larger scales.Item Gravitational collapse in an expanding universe: scaling relations for two-dimensional collapse revisited(Wiley-Blackwell, 2005-03-21) Ray, Suryadeep; Bagla, J. S.; Padmanabhan, T.We investigate non-linear scaling relations for two-dimensional (2D) gravitational collapse in an expanding background using a 2D TreePM code, and study the strongly non-linear regime ( ¯ξ 200) for power-law models. Evolution of these models is found to be scale invariant in all our simulations. We find that the stable clustering limit is not reached, but there is a model independent non-linear scaling relation in the asymptotic regime. This confirms results from an earlier study that only probed the mildly non-linear regime( ¯ξ 40). The correlation function in the extremely non-linear regime is a less steep function of scale than reported in earlier studies. We show that this is due to coherent transverse motions in massive haloes. We also study density profiles, and find that the scatter in the inner and outer slopes is large and that there is no single universal profile that fits all cases. We find that the difference in typical density profiles for different models is smaller than expected from similarity solutions for halo profiles, and transverse motions induced by substructure are a likely reason for this difference being small.Item Observational constraints on low redshift evolution of dark energy: How consistent are different observations?(American Physical Society, 2005-11-04) Jassal, H. K.; Bagla, J. S.; Padmanabhan, T.The dark energy component of the Universe is often interpreted either in terms of a cosmological constant or as a scalar field. A generic feature of the scalar field models is that the equation of state parameter w P= for the dark energy need not satisfy w 1 and, in general, it can be a function of time. Using the Markov chain Monte Carlo method we perform a critical analysis of the cosmological parameter space, allowing for a varying w. We use constraints on w z from the observations of high redshift supernovae (SN), the Wilkinson Microwave Anisotropy Probe (WMAP) observations of cosmic microwave background (CMB) anisotropies, and abundance of rich clusters of galaxies. For models with a constant w, the CDM(cold dark matter) model is allowed with a probability of about 6% by the SN observations while it is allowed with a probability of 98.9% by WMAP observations. The CDM model is allowed even within the context of models with variable w: WMAP observations allow it with a probability of 99.1% whereas SN data allows it with 23% probability. The SN data, on its own, favors phantom-like equation of state (w< 1) and high values for NR. It does not distinguish between constant w (with w< 1) models and those with varying w z in a statistically significant manner. The SN data allows a very wide range for variation of dark energy density, e.g., a variation by factor ten in the dark energy density between z 0 and z 1 is allowed at 95% confidence level. WMAP observations provide a better constraint and the corresponding allowed variation is less than a factor of 3. Allowing for variation in w has an impact on the values for other cosmological parameters in that the allowed range often becomes larger. There is significant tension between SN and WMAP observations; the best fit model for one is often ruled out by the other at a very high confidence limit. Hence results based on only one of these can lead to unreliable conclusions. Given the divergence in models favored by individual observations, and the fact that the best fit models are ruled out in the combined analysis, there is a distinct possibility of the existence of systematic errors which are not understood.Item New statistical indicator to study nonlinear gravitational clustering and structure formation(American Astronomical Society, 1996-04-22) Bagla, J. S.; Padmanabhan, T.In an = 1 universe dominated by nonrelativistic matter, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality is unity and velocity and force field are equal. The Zeldovich approximation extends this feature beyond the linear regime, until formation of pancakes. Nonlinear clustering which takes place after the breakdown of Zeldovich approximation, breaks this relation and the mismatch between these two vectors increases as the evolution proceeds. We suggest that the difference of these two vectors could form the basis for a powerful, new, statistical indicator of nonlinear clustering. We define an indicator called velocity contrast, study its behaviour using N-Body simulations and show that it can be used effectively to delineate the regions where nonlinear clustering has taken place.We discuss several features of this statistical indicator and provide simple analytic models to understand its behaviour. Particles with velocity contrast higher than a threshold have a correlation function which is biased with respect to the original sample. This bias factor is scale dependent and tends to unity at large scales.