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Item Cosmology Today: Models and constraints(Indian Academy of Sciences, 1995-03-12) Padmanabhan, T.Cosmological models for structure formation are severely constrained by several of the recent observational results. we now have observations which probe the power spectrum of fluctuations from about 0.5h-1 Mpc. these probes and the constraints they imply on models for structure formation are reviewed.Item Attempt to explain the smallness of the cosmological constant(World Scientific Publication Company, 1987-11-09) Singh, T. P.; Padmanabhan, T.Fields which couple directly to the cosmological constant (Λ) may provide a scenario for explaining the smallness of Λ at the present epoch. In this paper we postulate the existence of a scalar field which couples universally to the trace of energy—momentum tensor of matter. Various possibilities for the explicit form of the coupling function are considered. The field equations in such a theory are derived, and the cosmological models with such a scalar field are analyzed. The proposed coupling makes the effective cosmological constant a dynamically evolving quantity, which can be driven to zero by allowing the scalar field to grow to sufficiently large values. For the case of linear coupling, however, it does not seem to be possible to attain sufficient growth during the age of the universe (~1017 s). A quadratic coupling to the trace can evolve Λ to a value consistent with today’s observations, but the universe is dominated by the scalar field, rather than by radiation, at late times. The evolution is singular for couplings through a higher power law, in that the scalar field blows up at a finite time. The model is not very sensitive to initial conditions and the problems encountered can be avoided only by a severe fine-tuning of the parameters in the basic theory.Item Approach to quantum gravity(American Physical Society, 1983-08-15) Padmanabhan, T.A model for quantum gravity is presented by treating the light-cone structure of space time as classical and the conformal factor as a quantum degree of freedom. The motivation and the details of the formalism are discussed. The approach is used to discuss the question of singularities in the cosmological models. It is shown that one can introduce the concept of stationary states for the quantum geometry, in analogy with the stationary states of simple quantum systems. The quantum stationary geometries QSG's)avoid the classical singularities. The light-cone structure is determined by a set of equations involving the expectations values in the QSG concerned. The cosmological implication of the formalism, especially to matter creation, flatness, etc. are discussed. The theory is conformally invariant in the quantum level.