Research Papers (TP)
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Item Horizon problem and inflation(Indian Academy of Sciences, 1987-06-24) Padmanabhan, T.; Seshadri, T. R.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.Item Making inflation work : Damping of density perturbations due to Planck energy cut-off(American Physical Society, 1989-04-15) Padmanabhan, T.; Seshadri, T. R.; Singh, T. P.In this paper we propose an alternative method for the computation of classical density perturbations from a quantum field in an inflationary scenario. We compute the power spectrum of density perturbations directly from vacuum Auctuations of the "time-time" component of the energy momentum tensor. We compute the inhornogeneous part of~ the correlation function (0~ T o(x, t)T 0(y, t) ~0) for a massless minimally coupled scalar field in de Sitter space. The Fourier transform of this two-point function leads to the scale-invariant spectrum of perturbations, but is ultraviolet divergent. This expression can be made finite by introducing an (ad hot.") small-distance cutoff' in the proper length. We argue that this cutoff'should be of the order of the Planck length, and show that, in such a case, the density Auctuations have the acceptable magnitude (-10 ) for the case of primordial inflation. Thus the inflationary scenario can be made to work without anyItem Uncertainty principle and the quantum fluctuations of the schwarzschild light cones(World Scientific Publishing Company, 1985-10-12) Padmanabhan, T.; Seshadri, T. R.; Singh, T. P.We consider the gravitational field of a point mass and show that the application of the uncertainty principle leads to (i) an uncertainty relation for the metric and its conjugate momentum and (ii) finite fluctuations of the light-cone at the event horizon.Item Uncertainty principle and the horizon size of our universe(Springer, 1986-07-21) Padmanabhan, T.; Seshadri, T. R.Item Does inflation solve the horizon problem?(IOP Publishing, 1987-08-27) Padmanabhan, T.; Seshadri, T. R.We stress the distinction between ‘observed region of the universe’ and ‘observable region of the universe’. We show that (i) the observable region of the universe could not have evolved out of a causally connected domain in the past, even in inflationary models, and (ii) the homogeneity of CMBR is due to the fact that the universe is still young.Item Quantum uncertainty in the horizon size in an inflationary universe(World Scientific Publication Company, 1987-12-16) Padmanabhan, T.; Seshadri, T. R.It is shown that uncertainty principle prevents simultaneous, exact measurement of the expansion factor S(t) and its time derivative Ṡ(t) in a FRW universe. We compute the uncertainties in these parameters in the semiclassical limit. It is shown that (i) there is a minimum uncertainty ΔlH in the Hubble distance lH(t)=(Ṡ/S)−1 in a semiclassical universe. (ii) this uncertainty is amplified to an unacceptably large value if there was an inflationary phase in the early universe.Item Gaussian states in the De-Sitter spacetime and the evolution of semiclassical density perturbations: 1. Homogeneous mode(Indian Academy of Sciences, 1989-08-08) Seshadri, T. R.; Padmanabhan, T.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.Item Gaussian States in de Sitter Spacetime and the Evolution of Semiclassical density perturbations. 2. Inhomogeneous Modes(Indian Academy of Sciences, 1989-08-08) Seshadri, T. R.; Padmanabhan, T.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.Item Probing the origin of large inhomogeneities in inflation using a toy quantum mechanical model(American Physical Society, 1986-08-15) Padmanabhan, T.; Seshadri, T. R.We study the quantum evolution of the homogeneous mode of a scalar field with simple potentials in Robertson-Walker spacetime. The simplicity of the model allows one to work out the exact quantum evolution of a wave packet. The model mimics the inflationary scenario quite well and is used to study the nature and origin of various constraints. We conclude that any model in which (i) the potential has only a single energy scale (10¹⁴ –10¹⁵ GeV) and dimensionless parameters of order unity and (ii) the inflationary phase is endowed with a minimum temperature of (H/2π) will produce density inhomogeneity which is too large.