This paper gives a full nonlinear version of Newtonian gravity in which the gravitational energy acts as a source of the gravitational field. The generalized field equation for the scalar gravitational potential is solved for a spherically symmetric localized distribution of matter. It is shown that the perihelia of orbits of test particles in such a field precess steadily. The effect is, however, too small to account for the observed shift in the perihelion of planet Mercury. Further, the bending of light in this theory is zero. It is suggested that these inadequacies of the quasi-Newtonian framework call for more sophisticated approaches to gravity.

We consider the effect of quantizing the homogeneous mode of a scalar field on inflation. It is shown that any semiclassical description of the scalar field is bound to lead to density inhomogeneities which are unacceptably large.

The effect of a perturbing mass on a homogeneous collisionless cloud of dark matter is considered in the linear approximation. It is shown that gravitational potential can have turning points, in sharp contrast with gravitating systems of finite extent. The model offers a reasonable explanation for the observed secondary maxima in the density distribution of rich clusters. The relevance of the model to the flatness of the rotation curves of galaxies is also discussed.

We argue that observations on Milky Way and dwarf spheroidals imply existence of individual haloes around dwarf spheroidals. If neutrinos (or any other ‘hot’ particle) provide the dark matter then we show that: (i) Embedding of visible matter inside large (∼ few Mpc) dark matter islands is observationally untenable. (ii) Dwarf spheroidals possess dark matter haloes of about 10 kpc radius around them, and have an (M/L) ratio of about 10⁴. (iii) The haloes of spiral galaxies (e.g. Milky Way) extend to about 100 kpc in radius. If ‘cold’ dark matter makes up the haloes, then no significant constraints are obtained. We discuss briefly the effect of these constraints on larger scales.

Cosmological scenarios with massive unstable neutrinos are discussed. Restrictions on the mass and the lifetime of the unstable neutrino are derived from (a) age and mass density of the universe and (b) the growth of primordial fluctuations. It will not be possible to accommodate unstable neutrinos with masses above ∼ 1 ke V in standard cosmology unless they have exceedingly small lifetime: Τ <5 × 10⁸ s.

We show that, the part of the universe that is observable today (in principle), could not have evolved out of a domain which was causally connected in the past. This and other issues related to horizon problem in inflationary models are discussed.

The evolution of Gaussian quantum states in the de Sitter phase of the early universe is investigated. The potential is approximated by that of an inverted oscillator. We study the origin and magnitude of the density perturbations with special emphasis on the nature of the semiclassical limits

In the computation of density perturbation in inflation it is conventional to assume the inflation field to be in the vacuum state. There are, however, some advantages in relaxing this assumption. In an earlier paper we have estimated the density perturbations in a Gaussian coherent state using a toy-model. Here we extend this work by doing an exact analysis of this problem. The advantages of this method is discussed and the results are compared with earlier results

We study the mass-radius relationship for aggregates of galaxies, viz. binaries, small groups and clusters. The data are subjected to a simple best-fit analysis similar to the one carried out earlier for individual field galaxies. The analysis shows that: (i) The data on binary galaxies are consistent with the assumption that binaries are just two galaxies, each with an individual isothermal (M ∫R) dark matter halo, moving under the mutual gravitational attraction, (ii) The data on the groups of galaxies are too scattered to obey a single power-law relation of the formM = kRⁿ with any degree of reliability, (iii) The data on groups and clusters fit better with a law of the formM = AR³ +BR. This form suggests the existence of two components in dark matter—one which is clustered around the galaxies (M ∫R) and another which is distributed smoothly (M ∫R³). The smooth distributions becomes significant only at scales ≥ 1 Mpc and hence does not affect binaries significantly. We briefly discuss the theoretical implications of this analysis

The inverse Compton scattering of high energy electrons by photons is discussed and a simple derivation of the total power radiated is presented. The derivation is completely classical and exhibits clearly why similar formulas are applicable in the case of inverse compton scattering and synchroton radiation.

I review the constraints on standard big bang model arising from considerations related to structure formation. I will focus on two specific series of models though similar analysis can be performed for a wider class of models. The first one is a Ω = 1 model with non-zero cosmological constant and the second one is a Ω < 1 model with zero cosmological constant. The observational constraints which I shall discuss include the measurement of the Hubble’s constant, the ages of globular clusters, the abundance of rich clusters, the baryon content of galaxy clusters and the abundance of high redshift objects. These constraints limit the allowed range of the cosmological parameters and allow. for only a small region to survive. In particular, the aesthetically pleasing model with Ω = 1 and zero cosmological constant is ruled out by the observations. It seems necessary to fine-tune the theoretical parameters if they have to fall within the available space. This talk is based on the work in Baglaet al. (1996).