1,483 research outputs found
Singularity Free Rainbow Universe
Isotropic quantum cosmological perfect fluid model is studied in the
formalism of Rainbow gravity. It is found that the only surviving matter degree
of freedom played the role of cosmic time. It is possible to find the wave
packet naturally with a suitable choice of the Rainbow functions which resulted
from the superposition of the wave functions of the
Schrdinger-Wheeler-deWitt equation. The many-worlds interpretation of
quantum mechanics is applied to investigate the behavior of the scale factor
and the behaviour is found to depend on the operator ordering. It is shown that
the model in the Rainbow framework naturally avoids singularity and a bouncing
non-singular universe is found.Comment: This essay received an honorable mention in the 2013 Essay
Competition of the Gravity Research Foundatio
Quantum Rainbow Cosmological Model With Perfect Fluid
Isotropic quantum cosmological perfect fluid model is studied in the
formalism of Rainbow gravity. It is found that the only surviving matter degree
of freedom played the role of cosmic time. With the suitable choice of the
Rainbow functions it is possible to find the wave packet naturally from the
superposition of the wave functions of the Schrdinger-Wheeler-deWitt
equation. The many-worlds interpretation of quantum mechanics is applied to
investigate the behavior of the scale factor and the behavior is found to
depend on the operator ordering. It is shown that the model in the Rainbow
framework may avoid singularity yielding a bouncing non-singular universe.Comment: To appear in Int. J. Mod. Phys. D. arXiv admin note: substantial text
overlap with arXiv:1305.370
f(R) in Holographic and Agegraphic Dark Energy Models and the Generalized Uncertainty Principle
We studied a unified approach with the holographic, new agegraphic and the
dark energy model to construct the form of which in general
responsible for the curvature driven explanation of the very early inflation
along with presently observed late time acceleration. We considered the
generalized uncertainty principle in our approach which incorporated the
corrections in the entropy area relation and thereby modified the energy
densities for the cosmological dark energy models considered. We found that
holographic and new agegraphic gravity models can behave like phantom or
quintessence models in the spatially flat FRW universe. We also found a
distinct term in the form of which goes as due to the
consideration of the GUP modified energy densities. Although the presence of
this term in the action can have its importance in explaining the early
inflationary scenario but Capozziello {\it et.al.} recently showed that leads to an accelerated expansion, {\it i.e.}, a negative
value for the deceleration parameter which fit well with SNeIa and WMAP
data.Comment: To appear in Advances in High Energy Physic
Mutated hilltop inflation revisited
In this work we re-investigate pros and cons of mutated hilltop inflation.
Applying Hamilton-Jacobi formalism we solve inflationary dynamics and find that
inflation goes on along the branch of the Lambert function.
Depending on the model parameter mutated hilltop model renders two types of
inflationary solutions: one corresponds to small inflaton excursion during
observable inflation and the other describes large field inflation. The
inflationary observables from curvature perturbation are in tune with the
current data for a wide range of the model parameter. The small field branch
predicts negligible amount of tensor to scalar ratio , while the large field sector is capable of generating
high amplitude for tensor perturbations, . Also,
the spectral index is almost independent of the model parameter along with a
very small negative amount of scalar running. Finally we find that the mutated
hilltop inflation closely resembles the -attractor class of
inflationary models in the limit of .Comment: 17 pages, 13 figures. Accepted for publication in EPJ
Deterministic Graph Exploration with Advice
We consider the task of graph exploration. An -node graph has unlabeled
nodes, and all ports at any node of degree are arbitrarily numbered
. A mobile agent has to visit all nodes and stop. The exploration
time is the number of edge traversals. We consider the problem of how much
knowledge the agent has to have a priori, in order to explore the graph in a
given time, using a deterministic algorithm. This a priori information (advice)
is provided to the agent by an oracle, in the form of a binary string, whose
length is called the size of advice. We consider two types of oracles. The
instance oracle knows the entire instance of the exploration problem, i.e., the
port-numbered map of the graph and the starting node of the agent in this map.
The map oracle knows the port-numbered map of the graph but does not know the
starting node of the agent.
We first consider exploration in polynomial time, and determine the exact
minimum size of advice to achieve it. This size is ,
for both types of oracles.
When advice is large, there are two natural time thresholds:
for a map oracle, and for an instance oracle, that can be achieved
with sufficiently large advice. We show that, with a map oracle, time
cannot be improved in general, regardless of the size of advice.
We also show that the smallest size of advice to achieve this time is larger
than , for any .
For an instance oracle, advice of size is enough to achieve time
. We show that, with any advice of size , the time of
exploration must be at least , for any , and with any
advice of size , the time must be .
We also investigate minimum advice sufficient for fast exploration of
hamiltonian graphs
Parametric family of SDEs driven by L\'evy noise
In this article we study the existence and uniqueness of strong solutions of
a class of parameterized family of SDEs driven by L\'evy noise. These SDEs
occurs in connection with a class of stochastic PDEs, which take values in the
space of tempered distributions . This correspondence for
diffusion processes was proved in [Rajeev, Translation invariant diffusion in
the space of tempered distributions, Indian J. Pure Appl. Math. 44 (2013),
no.~2, 231--258]
Electric Charges and Magnetic Monopoles in Gravity's Rainbow
In this work, we explore the possibility that quantum fluctuations induce an
electric or magnetic charge or both, in the context of Gravity's Rainbow. A
semi-classical approach is adopted, where the graviton one-loop contribution to
a classical energy in a background spacetime is computed through a variational
approach with Gaussian trial wave functionals. The energy density of the
graviton one-loop contribution, in this context, acts as a source for the
electric/magnetic charge. The ultraviolet (UV) divergences, which arise
analyzing this procedure, are kept under control with the help of an
appropriate choice of the Rainbow's functions. In this way we avoid the
introduction of any regularization/renormalization scheme. A comparison with
the observed data lead us to determine the size of the electron and of the
magnetic monopole which appear to be of Planckian size. Both results seem to be
of the same order for a Schwarzschild and a de Sitter background, respectively.
Estimates on the magnetic monopole size have been done with the help of the
Dirac quantization procedure. We find that the monopole radius is larger than
the electron radius. Even in this case the ratio between the electric and
magnetic monopole radius appears to be of the same order for both geometries.Comment: Updated to match with published version. RevTeX 4, 12 page
- …