Research Publications
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Item Constraints on the shape of the density spectrum from COBE and galaxy surveys(Wiley-Blackwell, 1992-10-28) Padmanabhan, T.; Narasimha, D.Item Modelling the nonlinear gravitational clustering in the expanding universe(Wiley-Blackwell, 1995-11-02) Padmanabhan, T.The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in heirarchical models. This analysis leads to results which are in good agreement with numerical simulations thereby providing an explanation for numerical results. The ideas presented here will also serve as a powerful anlytical tool to investigate nonlinear clustering in different models. Several implications of the result are discussed.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 Effects of anticorrelation on gravitational clustering(Wiley-Blackwell, 2001-01-28) Kanekar, Nissim; Padmanabhan, T.We use non-linear scaling relations (NSRs) to investigate the effects arising from the existence of negative correlations on the evolution of gravitational clustering in an expanding universe. It turns out that such anti-correlated regions have important dynamical effects on ıt all scales. In particular, the mere existence of negative values for the linear two-point correlation function ξbL over some range of scales starting from l = Lo, implies that the non-linear correlation function is bounded from above at ıt all scales x < Lo. This also results in the relation ξb ∝ x-3, at these scales, at late times, independent of the original form of the correlation function. Current observations do not rule out the existence of negative ξb for 200 h-1 Mpc ła ξb ła 1000 h-1 Mpc; the present work may thus have relevance for the real Universe. The only assumption made in the analysis is the ıt existence of the NSR; the results are independent of the form of the NSR as well as of the stable clustering hypothesis.Item Gravitational perturbation of homogeneous collisionless dark matter(Indian Academy of Sciences, 1985-08-12) Padmanabhan, T.; Vasanthi, M. M.The effect of a perturbing mass on a homogeneous collisionless cloud of dark matter is considered in the linear approximation. It is shown by that gravitational potential can have turning points, in sharp contrast with gravitating system of finite extent. The model offers a reasonable explanation for the observed secondary maxima in the destiny distribution of rich clusters . The relevance of the model to the flatness of the rotation curves of galaxies is also discussed.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 Can the clustered dark matter and the smooth dark energy arise from the same scalar field?(American Physical Society, 2002-10-29) Padmanabhan, T.; Choudhury, T. RoyCosmological observations suggest the existence of two different kinds of energy densities dominating at small ( ≲ 500 Mpc) and large (≳ 1000 Mpc) scales. The dark matter component, which dominates at small scales, contributes Ωm ≈ 0.35 and has an equation of state p=0 while the dark energy component, which dominates at large scales, contributes ΩV ≈ 0.65 and has an equation of state p≃ -ρ. It is usual to postulate wimps for the first component and some form of scalar field or cosmological constant for the second component. We explore the possibility of a scalar field with a Lagrangian L =- V(φ) √1 - deli φ deli φ acting as ıt both clustered dark matter and smoother dark energy and having a scale dependent equation of state. This model predicts a relation between the ratio r = ρV/ρDM of the energy densities of the two dark components and expansion rate n of the universe (with a(t) ∝ tn) in the form n = (2/3) (1+r) . For r ≈ 2, we get n ≈ 2 which is consistent with observations.Item Power transfer in non-linear gravitational clustering and asymptotic universality(Wiley-Blackwell, 2006-06-13) Padmanabhan, T.; Ray, SuryadeepWe study the non-linear gravitational clustering of collisionless particles in an expanding background using an integro-differential equation for the gravitational potential. In particular, we address the question of how the non-linear mode–mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale. We show that the dynamical equation allows self-similar evolution for the gravitational potential φk(t ) in Fourier space of the form φk(t ) = F (t )D(k) where the function F(t) satisfies a second-order non-linear differential equation. We analyse the relevant solutions of this equation, thereby determining the asymptotic time evolution of the gravitational potential and density contrast. The analysis suggests that both F(t) and D(k) have well-defined asymptotic forms indicating that the power transfer leads to a universal power spectrum at late times. The analytic results are compared with numerical simulations, showing good agreement over the range at which we could test them.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 Non-linear density evolution from an improved spherical collapse model(Wiley-Blackwell, 1999-11-30) Engineer, Sunu; Kanekar, Nissim; Padmanabhan, T.We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we introduce a physically motivated closure condition which specifies the dependence of the additional terms on the density contrast, δ. The modified equation can be used to model the behaviour of an overdense region over a sufficiently large range of δ. The key new idea is a Taylor series expansion in (1/δ) to model the non-linear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behaviour of individual overdense regions with the non-linear scaling relations satisfied by the two point correlation function. Comment: 11 pages, 6 figures. Final version, contains added discussion and modified figures to match the accepted version.