Research Papers (TP)

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Cosmological N-Body Simulations
(Indian Academy of Sciences, 1997-08-12) Bagla, J. S.; Padmanabhan, T.
In this review we discuss Cosmological N-Body codes with a special emphasis on Particle Mesh codes. We present the mathematical model for each component of N-Body codes. We compare alternative methods for computing each quantity by calculating errors for each of the components. We suggest an optimum set of components that can be combined reduce overall errors in N-Body codes.
Cosmology with tachyon field as dark energy
(American Physical Society, 2003-03-14) Bagla, J. S.; Jassal, H. K.; Padmanabhan, T.
We present a detailed study of cosmological effects of homogeneous tachyon matter coexisting with nonrelativistic matter and radiation, concentrating on the inverse square potential and the exponential potential for the tachyonic scalar field. A distinguishing feature of these models ~compared to other cosmological models! is that the matter density parameter and the density parameter for tachyons remain comparable even in the matter dominated phase. For the exponential potential, the solutions have an accelerating phase, followed by a phase with a(t)}t2/3 as t!`. This eliminates the future event horizon present in cold dark matter models with a cosmological constant (LCDM) and is an attractive feature from the string theory perspective. A comparison with supernova type Ia data shows that for both the potentials there exists a range of models in which the universe undergoes an accelerated expansion at low redshifts which are also consistent with the requirements of structure formation. They do require fine-tuning of parameters but not any more than in the case of L CDM models or quintessence models.
Crisis in cosmology: Observational constraints on Omega and H
(Overseas Publishers Association, 1996-03-18) Bagla, J. S.; Padmanabhan, T.; Narlikar, J. V.
This review of recent observations of cosmological interest seeks to take stock of how they constrain the standard hot big bang models with or without inflation. We look at two specific series indicative of this class of models. In one series the flatness condition of inflation requires that the density parameter shall be unity. Of late this statement has been relaxed somewhat to include the cosmological constant also as a contributor to the density parameter. Hence we ha»e used this "generalised" flatness condition. The other series of models does not need (be cosmological constant but assumes that the curvature parameter k = -1. Both these models are currently being pushed as "the" models of the universe. The observational constraints used by us are the measurements of the Hubble constant and the deceleration parameter, the ages of globular clusters, the abundance of primordial deuterium, the abundance of rich clusters, the baryon content of galaxy clusters and the abundance of high rsdshift objects. These constraints essentially limit the allowed values of the cosmological parameters. Our findings are that with measurements within their quoted error bars, the available parameter space has shrunk to negligible proportions. For survival of the standard models, therefore, one needs to take recourse to two normally unpalatable steps: (i) to doubt the existing error bars and hope to expand them and (ii) to fine-tone the theoretical parameters so that they fall within the available space. This is the essence of our perception of the crisis in cosmology.
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.
Metal enrichment and reionization constraints on early star formation
(Wiley-Blackwell, 2009-04-29) Bagla, J. S.; Kulkarni, Girish; Padmanabhan, T.
The epoch of reionization and formation of first stars are interlinked topics that are of considerable interest. We use a simplified approach for studying the formation of stars in collapsed haloes and the resulting ionization of the intergalactic medium (IGM). We consider a set of Λ cold dark matter models allowed by observations of cosmic microwave background temperature and polarization anisotropies for this study. We constrain parameters related to star formation with the help of observations. We constrain subsets of these parameters independently by using the observed metallicity of the IGM at z∼ 5 and the requirement that the Thomson scattering optical depth due to an ionized IGM as determined for the model from CMB observations be reproduced. We consider a range of initial metallicities for star-forming gas, and some variations of the initial mass function (IMF) of stars. We find that a ‘normal’ IMF may satisfy these two constraints with a raised efficiency of star formation as compared to that seen in the local universe. Observations require a significant fraction of metals to escape from haloes to the IGM. We can also place constraints on the ratio of escape fraction for metals and ionizing photons, and find that this ratio is of order unity for most models. This highlights the importance of using the constraints arising from enrichment of the IGM. Ultrahigh mass stars or active galactic nuclei may not simplify models of reionization in that these may produce more ionizing photons but these do not contribute to the production of metals and hence help in reducing only the escape fraction for ionizing photons. However, suppression of very low mass stars is helpful in that it increases the production of metals as well as ionizing photons, and hence leads to a reduction in both escape fractions. Such a change is also warranted by observations of metal poor halo stars in the Galaxy. We also discuss correlations in parameters like the efficiency of star formation and the two escape fractions with cosmological parameters.
Neutral hydrogen at high redshifts as a probe of structure formation – III. Radio maps from N-body simulations.
(Wiley-Blackwell, 1997-04-04) Bagla, J. S.; Nath, B. B.; Padmanabhan, T.
Large inhomogeneities in neutral hydrogen in the universe can be detected at redshifts z 10 using the redshifted 21cm line emission. We use cosmological N-Body simulations for dark matter and a simple model for baryonic collapse to estimate the signal expected from structures like proto-clusters of galaxies at high redshifts.We study : (i) the standard CDM model, (ii) a modified CDM model with less power at small scales, and (iii) a +CDM model in a universe with 0 + = 1. We show that it should be possible for the next generation radio telescopes to detect such structures at the redshift 3.34 with an integration of about 100 hours. We also discuss possible schemes for enhancing signal to noise ratio to detect proto-condensates at high redshifts.
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.
Nonlinear evolution of density perturbations
(Indian Academy of Sciences, 1995-02-28) Bagla, J. S.; Padmanabhan, T.
From the epoch of recombination (z~10³) till today, the typical density contrasts have grown by a factor of about 10⁶ in a Friedmann universe with Ω= 1. However, during the same epoch the typical gravitational potential has grown only by a factor of order unity. This fact can be exploited to provide a new, powerful, approximation scheme to study the formation of nonlinear structures in the universe by evolving the initial distribution of matter using a gravitational potential frozen in time. We carry out this scheme for several standard models and discuss the results.
Nonlinear evolution of density perturbations using approximate constancy of gravitational potential
(Royal Astronomical Society, 1993-07-28) Bagla, J. S.; Padmanabhan, T.
During the evolution of density inhomogeneties in an Ω=1, matter dominated universe, the typical density contrast changes from δ≃ 10-4 to δ≃ 102. However, during the same time, the typical value of the gravitational potential generated by the perturbations changes only by a factor of order unity. This significant fact can be exploited to provide a new, powerful, approximation scheme for studying the formation of nonlinear structures in the universe. This scheme, discussed in this paper, evolves the initial perturbation using a Newtonian gravitational potential frozen in time. We carry out this procedure for different intial spectra and compare the results with the Zeldovich approximation and the frozen flow approximation (proposed by Mattarrese et al. recently). Our results are in far better agreement with the N-body simulations than the Zeldovich approximation. It also provides a dynamical explanation for the fact that pancakes remain thin during the evolution. While there is some superficial similarity between the frozen flow results and ours, they differ considerably in the velocity information. Actual shell crossing does occur in our approximation; also there is motion of particles along the pancakes leading to further clumping. These features are quite different from those in frozen flow model. We also discuss the evolution of the two-point correlation function in various approximations.
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.
Scaling Relations for Gravitational Clustering in two Dimensions
(American Astronomical Society, 1997-10-10) Bagla, J. S.; Engineer, Sunu; Padmanabhan, T.
It is known that radial collapse around density peaks can explain the key features of the evolution of a correlation function in gravitational clustering in three dimensions. The same model also makes spe-ciÐc predictions for two dimensions. In this paper we test these predictions in two dimensions with the help of N-body simulations. We Ðnd that there is no stable clustering in the extremely nonlinear regime, but a nonlinear scaling relation does exist and can be used to relate the linear and the nonlinear corre-lation function. In the intermediate regime, the simulations agree with the model.
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.
Understanding the origin of CMB constraints on dark energy
(Wiley-Blackwell, 2010-03-08) Jassal, H. K.; Bagla, J. S.; Padmanabhan, T.
We study the observational constraints of cosmic microwave background (CMB) temperature and polarization anisotropies on models of dark energy, with special focus on models with variation in properties of dark energy with time. We demonstrate that the key constraint from CMB observations arises from the location of acoustic peaks. An additional constraint arises from the limits on ΩNR from the relative amplitudes of acoustic peaks. Further, we show that the distance to the last scattering surface is not how the CMB observations constrain the combination of parameters for models of dark energy. We also use constraints from supernova observations and show that unlike the gold and silver samples, the Supernova Legacy Survey (SNLS) sample prefers a region of parameter space that has a significant overlap with the region preferred by the CMB observations. This is a verification of a conjecture made by us in an earlier work. We discuss combined constraints from Wilkinson Microwave Anisotropy Probe 5-yr and SNLS observations. We find that models with w ~−1 are preferred for models with a constant equation-of-state parameters. In case of models with a time-varying dark energy, we show that constraints on evolution of dark energy density are almost independent of the type of variation assumed for the equation-of-state parameter. This makes it easy to get approximate constraints from CMB observations on arbitrary models of dark energy. Constraints on models with a time-varying dark energy are predominantly due to CMB observations, with supernova constraints playing only a marginal role.
WMAP constraints on low redshift evolution of dark energy
(Wiley-Blackwell, 2004-10-29) Jassal, H. K.; Bagla, J. S.; Padmanabhan, T.
The conceptual difﬁculties associated with a cosmological constant have led to the investigation of alternative models in which the equation of state parameter, w = p/ρ,of the dark energy evolves with time. We show that combining the supernova type Ia observations with the constraints from WMAP observations restricts large variation of ρ(z)atlow redshifts. The combination of these two observational constraints is stronger than either one. The results are completely consistent with the cosmological constant as the source of dark energy.