Browsing by Author "Singh, T. P."

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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.
Comparison between semiclassical gravity and semiclassical electrodynamics
(IOP Publishing, 1991-05-14) Kiefer, C.; Padmanabhan, T.; Singh, T. P.
It is known how the equation of motion for a quantum tieid in a classical CUM spacetime can be derived as an approximation lo the Wheeler-DeWLtt equation. In order 10 obtain a better understanding of ths derivation, we develop an analogous approximation for quanrum electrodynamics. We show lhat quantum field lheory in an erternal, classical electromagnetic field can be oblained as a limiting case of quantum electrodynamics, by expanding the full wavefunctional in a power series in the coupling constant e2. The important difference in the yo derivalions is that unlike the metric, Lhe electromagnetic potential has to be scaled wilh respect to the coupling constant before the semiclassical limit can be obtained.
Comparison of various approaches to the back reaction problem
(Elsevier Science Publishers, 1992-05-15) Padmanabhan, T.; Singh, T. P.
We compare three possible prescriptions for the back-reaction of a quantum mechanical source on the classical gravitational field to which it is coupled. These prescriptions are (i) the transition element 〈out| Tik |in〉 of the energy-momentum operator between asymptotic vacuum states, (ii) the expectation value 〈Ψ| Tik |Ψ〉, and (iii) the Born-Oppenheimer type approximation for back-reaction as used in molecular physics. It is shown that the three approaches match only when the gravitational field is varying adiabatically, and of the three, the use of expectation value provides the most accurate description of the validity of semiclassical Einstein equations. The analysis is carried Out by studying the model of a quantized time-dependent oscillator coupled to a classical particle.
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 any
Note on the thermodynamics of gravitational radiation
(IOP Science, 2003-09-12) Padmanabhan, T.; Singh, T. P.
It is shown that linearized gravitational radiation conﬁned in a cavity can achieve thermal equilibrium if the mean density of the radiation and the size of the cavity satisfy certain constraints.
Notes on Semiclassical Gravity
(Elsevier Science Publishers, 1989-07-06) Singh, T. P.; Padmanabhan, T.
In this paper we investigate the different possible ways of defining the semiclassical limit of quantum general relativity. We discuss the conditions under which the expectation value of the energy-momentum tensor can act as the source for a semiclassical, c-number, gravitational field. The basic issues can be understood from the study of the semiclassical limit of a toy model, consisting of two interacting particles, which mimics the essential properties of quantum general relativity. We define and study the WKB semiclassical approximation and the gaussian semiclassical approximation for this model. We develop rules for finding the back-reaction of the quantum mode 4 on the classical mode Q. We argue that the back-reaction can be found using the phase of the wave-function which describes the dynamics of 4. We find that this back-reaction is obtainable from the expectation value of the hamiltonian if the dispersion in this phase can be neglected. These results on the back-reaction are generalised to the semiclassical limit of the Wheeler-Dewitt equation. We conclude that the back reaction in semiclassical gravity is ( Tlk) only when the dispersion in the phase of the matter wave functional can be neglected. This conclusion is highlighted with a minisuperspace example of a massless scalar field in a Robertson-Walker universe. We use the semiclassical theory to show that the minisuperspace approximation in quantum cosmology is valid only if the production of gravitons is negligible.
On Feynman's formula for the electromagnetic field of an arbitrarily moving charge
(American Association of Physics Teachers, 1988-01-15) Janah, A. R.; Padmanabhan, T.; Singh, T. P.
A simple derivation of Feynman's formula for the electromagnetic field of an arbitrarily moving charge, starting Maxwell's equation, is presented. Feynman's formula is also related to the standard expression for the fields of a moving charge.
On the relation between causality and topology in the semiclassical universe
(2015-01-13) Seriu, Masafumi; Singh, T. P.
We systematically derive a series of validity conditions for semiclassical gravity and deduce a strong restriction on the possible topology of the semiclassical universe founded on the path-integral formalism. We begin with the investigation of the fundamental setting of quantum gravity. We show that, in order to obtain the causal semiclassical Einstein equation at the later stage of the universe, we have to regard the in-in path-integral formalism as fundamental in quantum gravity. We then perform the stationary phase approximation for the gravity mode. From the first variation of the phase , we obtain a series of validity conditions of semiclassical gravity in a completely general manner.
On the semiclassical limit of the Wheeler-DeWitt equation
(IOP Publishing, 1989-07-20) Padmanabhan, T.; Singh, T. P.
We continue our investigation of approximation schemes for obtaining semi-classical Einstein equations with a backreaction, starting from the Wheeler-DeWitt equation. The analysis is carried out using a toy model with two degrees of freedom, which represents a matter field interacting with gravity. We argue that the backreaction is to be found using the phase of the matter part of the wavefunction. Using a semiclassical Wigner function we find the general condition for the validity of a semiclassical theory: the dispersion in the metric derivative of the phase of the matter wavefunction should be negligible. We then consider a special case of the toy Lagrangian, that of a time-dependent harmonic oscillator, and show that the backreaction is equal to the expectation value of the matter Hamiltonian only if the background 'metric' varies slowly with time. The Wigner function, when applied to a semiclassical cosmological model, shows that the semiclassical approximation is valid only when the quantum contribution to the energy-momentum tensor is small compared to the classical contribution.
Response of accelerated detectors in coherent states and the semi-classical limit
(American Physical Society, 1988-10-15) Padmanabhan, T.; Singh, T. P.
It is known that a uniformly accelerating detector gets excited in the inertial vacuum of a field, as if it were immersed in a thermal bath. We study the effect that the choice of the quantum state has on the response of the detector. The ‘‘correlation function’’ 〈Ψ‖φ(x)φ(x’)‖Ψ〉 is computed in a Fock state, in the coherent state, and in the thermal state. It is then shown that the response function is a sum of two terms—the first being the same as the response in the vacuum state and a second term which is state dependent. The limit of the response function as ħ→0 is discussed and the response of the inertial and accelerated detectors compared in this limit. The response in the large-nk limit of the Fock state is compared with the response in the coherent state. We conclude that the thermal response of an accelerated detector in the inertial vacuum has interesting similarities to its response in other states.
Response of an accelerated detector coupled to the stress-energy tensor
(IOP Science, 1987-04-09) Padmanabhan, T.; Singh, T. P.
Semiclassical cosmology with a scalar field
(American Physical Society, 1987-05-15) Singh, T. P.; Padmanabhan, T.
A self consistent scheme for studying the semiclassical limit of a quantized scalar field in a classical Robertson-Walker metric is developed. The scalar field is chosen to be in a Gaussian state. The classical and semiclassical geometries are contrasted; and it is shown that nontrivial solutions exist for the space-time geometry which are driven by the vacuum fluctuations of the scalar field. We also discuss the stability of de Sitter space to quantum fluctuations, if the cosmological constant is larger than a critical value.
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.