2,929 research outputs found
Vacuum Fluctuations of Energy Density can lead to the observed Cosmological Constant
The energy density associated with Planck length is while the energy density associated with the Hubble length is
where . The observed value of the dark
energy density is quite different from {\it either} of these and is close to
the geometric mean of the two: .
It is argued that classical gravity is actually a probe of the vacuum {\it
fluctuations} of energy density, rather than the energy density itself. While
the globally defined ground state, being an eigenstate of Hamiltonian, will not
have any fluctuations, the ground state energy in the finite region of space
bounded by the cosmic horizon will exhibit fluctuations . When used as a source of gravity, this should
lead to a spacetime with a horizon size . This bootstrapping condition
leads naturally to an effective dark energy density which is precisely the observed value. The model
requires, either (i) a stochastic fluctuations of vacuum energy which is
correlated over about a Hubble time or (ii) a semi- anthropic interpretation.
The implications are discussed.Comment: r pages; revtex; comments welcom
Hypothesis of path integral duality: Applications to QED
We use the modified propagator for quantum field based on a ``principle of
path integral duality" proposed earlier in a paper by Padmanabhan to
investigate several results in QED. This procedure modifies the Feynman
propagator by the introduction of a fundamental length scale. We use this
modified propagator for the Dirac particles to evaluate the first order
radiative corrections in QED. We find that the extra factor of the modified
propagator acts like a regulator at the Planck scales thereby removing the
divergences that otherwise appear in the conventional radiative correction
calculations of QED. We find that:(i) all the three renormalisation factors
, , and pick up finite corrections and (ii) the modified
propagator breaks the gauge invariance at a very small level of
. The implications of this result to generation of the
primordial seed magnetic fields are discussed.Comment: 15 pages, LaTeX2e (uses ijmpd.sty); To appear in IJMP-D; References
adde
The hypothesis of path integral duality II: corrections to quantum field theoretic results
In the path integral expression for a Feynman propagator of a spinless
particle of mass , the path integral amplitude for a path of proper length
connecting events and in a spacetime
described by the metric tensor is . In a recent paper, assuming the path integral amplitude to be
invariant under the duality transformation ,
Padmanabhan has evaluated the modified Feynman propagator in an arbitrary
curved spacetime. He finds that the essential feature of this `principle of
path integral duality' is that the Euclidean proper distance
between two infinitesimally separated spacetime events is replaced by . In other words, under the duality principle the spacetime
behaves as though it has a `zero-point length' , a feature that is
expected to arise in a quantum theory of gravity. In the Schwinger's proper
time description of the Feynman propagator, the weightage factor for a path
with a proper time is . Invoking Padmanabhan's `principle of
path integral duality' corresponds to modifying the weightage factor
to . In this paper, we use this modified
weightage factor in Schwinger's proper time formalism to evaluate the quantum
gravitational corrections to some of the standard quantum field theoretic
results in flat and curved spacetimes. We find that the extra factor
acts as a regulator at the Planck scale thereby `removing' the
divergences that otherwise appear in the theory. Finally, we discuss the wider
implications of our analysis.Comment: 26 pages, Revte
Response of finite-time particle detectors in non-inertial frames and curved spacetime
The response of the Unruh-DeWitt type monopole detectors which were coupled
to the quantum field only for a finite proper time interval is studied for
inertial and accelerated trajectories, in the Minkowski vacuum in (3+1)
dimensions. Such a detector will respond even while on an inertial trajctory
due to the transient effects. Further the response will also depend on the
manner in which the detector is switched on and off. We consider the response
in the case of smooth as well as abrupt switching of the detector. The former
case is achieved with the aid of smooth window functions whose width, ,
determines the effective time scale for which the detector is coupled to the
field. We obtain a general formula for the response of the detector when a
window function is specified, and work out the response in detail for the case
of gaussian and exponential window functions. A detailed discussion of both and limits are given and several
subtlities in the limiting procedure are clarified. The analysis is extended
for detector responses in Schwarzschild and de-Sitter spacetimes in (1+1)
dimensions.Comment: 29 pages, normal TeX, figures appended as postscript file, IUCAA
Preprint # 23/9
Scalar Field Dark Energy Perturbations and their Scale Dependence
We estimate the amplitude of perturbation in dark energy at different length
scales for a quintessence model with an exponential potential. It is shown that
on length scales much smaller than hubble radius, perturbation in dark energy
is negligible in comparison to that in in dark matter. However, on scales
comparable to the hubble radius () the
perturbation in dark energy in general cannot be neglected. As compared to the
CDM model, large scale matter power spectrum is suppressed in a
generic quintessence dark energy model. We show that on scales , this suppression is primarily due to different background
evolution compared to CDM model. However, on much larger scales
perturbation in dark energy can effect matter power spectrum significantly.
Hence this analysis can act as a discriminator between CDM model and
other generic dark energy models with .Comment: 12 pages, 13 figures, added new section, accepted for publication in
Phys. Rev.
Why Does Gravity Ignore the Vacuum Energy?
The equations of motion for matter fields are invariant under the shift of
the matter lagrangian by a constant. Such a shift changes the energy momentum
tensor of matter by T^a_b --> T^a_b +\rho \delta^a_b. In the conventional
approach, gravity breaks this symmetry and the gravitational field equations
are not invariant under such a shift of the energy momentum tensor. I argue
that until this symmetry is restored, one cannot obtain a satisfactory solution
to the cosmological constant problem. I describe an alternative perspective to
gravity in which the gravitational field equations are [G_{ab} -\kappa T_{ab}]
n^an^b =0 for all null vectors n^a. This is obviously invariant under the
change T^a_b --> T^a_b +\rho \delta^a_b and restores the symmetry under
shifting the matter lagrangian by a constant. These equations are equivalent to
G_{ab} = \kappa T_{ab} + Cg_{ab} where C is now an integration constant so that
the role of the cosmological constant is very different in this approach. The
cosmological constant now arises as an integration constant, somewhat like the
mass M in the Schwarzschild metric, the value of which can be chosen depending
on the physical context. These equations can be obtained from a variational
principle which uses the null surfaces of spacetime as local Rindler horizons
and can be given a thermodynamic interpretation. This approach turns out to be
quite general and can encompass even the higher order corrections to Einstein's
gravity and suggests a principle to determine the form of these corrections in
a systematic manner.Comment: Invited Contribution to the IJMPD Special Issue on Dark Matter and
Dark Energy edited by D.Ahluwalia and D. Grumiller. Appendix clarifies
several conceptual and pedgogical aspects of surface term in Hilbert action;
ver.2: references and some clarifications adde
Hawking radiation in different coordinate settings: Complex paths approach
We apply the technique of complex paths to obtain Hawking radiation in
different coordinate representations of the Schwarzschild space-time. The
coordinate representations we consider do not possess a singularity at the
horizon unlike the standard Schwarzschild coordinate. However, the event
horizon manifests itself as a singularity in the expression for the
semiclassical action. This singularity is regularized by using the method of
complex paths and we find that Hawking radiation is recovered in these
coordinates indicating the covariance of Hawking radiation as far as these
coordinates are concerned.Comment: 18 pages, 2 figures, Uses IOP style file; final version; accepted in
Class. Quant. Gra
Ultrafine grained materials through mechanical processing: An assessment
In this paper severe plastic deformation (SPD) and friction stir processing/ welding are examined. The structural changes due to SPD are reflected in improved mechanical properties. Advantages of SPD are pointed out. Within the SPD technique, a number of approaches are possible, e.g., equi-channel angular pressing/extrusion, high pressure torsion, accumulative roll bonding/fold - roll process, reciprocating extrusion – compression, cyclic close die forging, repetitive corrugation and straightening. Analyses available are elementary and often assume uniform stress and strain distribution. These processes are easily adapted to suit standard metal working equipment fitted with inexpensive devices and tools. However, scaling up the processes to handle large billets and achieve large tonnage production is difficult. In the near future, medium and small-scale industrial production only is likely.
Friction stir process, a solid state technique for joining similar or dissimilar materials of equal or different thickness, has some key metallurgical, environmental and energy benefits. It is already being considered for applications in aerospace and automotive industries. Significant improvements in surface properties and superplastic flow have been established in friction stir processed materials. Velocity of tool movement and power input needed for fast rotation of the tool are the major variables. Since significant temperature rise is there during processing, in a proper analysis, the boundary conditions arising from thermal and mechanical constraints have to be satisfied simultaneously, which is an extremely difficult. A few key issues have to be addressed before large-scale production can be attempted. An integral approach that takes into account the total system of material, design, mechanics and component forming is likely to lead to industrially relevant solutions
Ultrafine grained materials through mechanical processing: an assessment
In this paper severe plastic deformation (SPD) and friction stir processing/ welding are examined. The structural changes due to SPD are reflected in improved mechanical properties. Advantages of SPD are pointed out. Within the SPD technique, a number of approaches are possible, e.g., equi-channel angular pressing/extrusion, high pressure torsion, accumulative roll bonding/fold - roll process, reciprocating extrusion - compression, cyclic close die forging, repetitive corrugation and straightening. Analyses available are elementary and often assume uniform stress and strain distribution. These processes are easily adapted to suit standard metal working equipment fitted with inexpensive devices and tools. However, scaling up the processes to handle large billets and achieve large tonnage production is difficult. In the near future, medium and small-scale industrial production only is likely. Friction stir process, a solid state technique for joining similar or dissimilar materials of equal or different thickness, has some key metallurgical, environmental and energy benefits. It is already being considered for applications in aerospace and automotive industries. Significant improvements in surface properties and superplastic flow have been established in friction stir processed materials. Velocity of tool movement and power input needed for fast rotation of the tool are the major variables. Since significant temperature rise is there during processing, in a proper analysis, the boundary conditions arising from thermal and mechanical constraints have to be satisfied simultaneously, which is an extremely difficult. A few key issues have to be addressed before large-scale production can be attempted. An integral approach that takes into account the total system of material, design, mechanics and component forming is likely to lead to industrially relevant solutions
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