J. S. Bagla

Cosmology with tachyon field as dark energy

We present a detailed study of cosmological effects of homogeneous tachyon matter coexisting with non-relativistic 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) ~ t^{2/3} as t goes to infinity. This eliminates the future event horizon present in LCDM models and is an attractive feature from the string theory perspective. A comparison with supernova 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 and are also consistent with requirements of structure formation. They do require fine tuning of parameters but not any more than in the case of LCDM or quintessence models.

WMAP constraints on low redshift evolution of dark energy

The conceptual difficulties associated with a cosmological constant have led to the investigation of alternative models in which the equation of state parameter,

Observational constraints on low redshift evolution of dark energy: How consistent are different observations?

w=p/\rho

Understanding the origin of CMB constraints on Dark Energy

, of the dark energy evolves with time. We show that combining the supernova type Ia observations {\it with the constraints from WMAP observations} restricts large variation of

Fractal dimension as a measure of the scale of homogeneity

\rho(z)

H i as a probe of the large-scale structure in the post-reionization universe

at low 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.

TreePM: A code for cosmological N-body simulations

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/rho 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 WMAP observations of CMB anisotropies and abundance of rich clusters of galaxies. For models with a constant w, the LCDM 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 LCDM 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 Omega_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 three. Allowing for variation in w has an impact on the values for other cosmological parameters in that the allowed range often becomes larger. (Abridged)

Comments on the size of the simulation box in cosmological N-body simulations

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 onNR 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 fromWilkinsonMicrowaveAnisotropyProbe 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.

Effects of the size of cosmological N-body simulations on physical quantities – I. Mass function

In the multifractal analysis of the large-scale matter distribution, the scale of the transition to homogeneity is defined as the scale above which the fractal dimension (Dq) of the underlying point distribution is equal to the ambient dimension (D) of the space in which points are distributed. With the finite sized weakly clustered distribution of tracers obtained from galaxy redshift surveys it is difficult to achieve this equality. Recently Bagla et al. have defined the scale of homogeneity to be the scale above which the deviation (� Dq) of the fractal dimension from the ambient dimension becomes smaller than the statistical dispersion ofDq, i.e. σ�D q . In this paper we use the relation between the fractal dimensions and the correlation function to compute σ�D q for any given model in the limit of weak clustering amplitude. We compare � Dq and σ�D q for thecold dark matter (� CDM) model and discuss the implication of this comparison for the expected scale of homogeneity in the concordant model of cosmology. We estimate the upper limit to the scale of homogeneity to be close to 260h −1 Mpc for theCDM model. Actual estimates of the scale of homogeneity should be smaller than this as we have considered only the statistical contribution to σ�D q and we have ignored cosmic variance and contributions due to survey geometry and the selection function. Errors arising due to these factors enhance σ�D q and asDq decreases with increasing scale, we expect to measure a smaller scale of homogeneity. We find that as long as non-linear corrections to the computation ofDq are insignificant, the scale of homogeneity does not change with epoch. The scale of homogeneity depends very weakly on the choice of tracer of the density field. Thus the suggested definition of the scale of homogeneity is fairly robust.

Nonlinear evolution of density perturbations using approximate constancy of gravitational potential

Simulated maps of the HI distribution in the post-reionization era are used to study the prospects for detection with existing and upcoming radio telescopes. We consider detection in the redshifted radiation from the hyperfine transition with a rest frame frequency of 1420 MHz. Possibility of a statistical detection using visibility correlations is discussed. We show that the MWA (Murchison Widefield Array) and the GMRT (Giant Meterwave Radio Telescope) can potentially detect signal from the HI distribution at high redshifts. MWA can detect visibility correlations at large angular scales at all redshifts accessible to it in the post-reionization era. The GMRT can detect visibility correlations at lower redshifts, specifically there is a strong case for a survey at z = 1.3. We also discuss prospects for direct detection of rare peaks in the HI distribution using the GMRT. We show that direct detection should be possible with integration time that is comparable to, or even less than, the time required for a statistical detection. Specifically, it is possible to make a statistical detection of the HI distribution by measuring the visibility correlation, and, direct detection of rare peaks in the HI distribution using the GMRT in less than 1000 hours of observations.