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 Schr$\ddot{o}$dinger-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

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 Schr$\ddot{o}$dinger-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

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 $f(R)$ dark energy model to construct the form of $f(R)$ 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 $f(R)$ 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 $f(R)$ which goes as $R^{\frac{3}{2}}$ 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 $f(R) \sim R^{\frac{3}{2}}$ leads to an accelerated expansion, {\it i.e.}, a negative value for the deceleration parameter $q$ 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 ${\cal W}_{-1}$ 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 $r\sim \mathcal{O}(10^{-4})$, while the large field sector is capable of generating high amplitude for tensor perturbations, $r\sim \mathcal{O}(10^{-1})$. 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 $\alpha$-attractor class of inflationary models in the limit of $\alpha\phi\gg 1$.Comment: 17 pages, 13 figures. Accepted for publication in EPJ

Deterministic Graph Exploration with Advice

We consider the task of graph exploration. An $n$-node graph has unlabeled nodes, and all ports at any node of degree $d$ are arbitrarily numbered $0,\dots, d-1$. 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 $\log\log\log n -\Theta(1)$, for both types of oracles. When advice is large, there are two natural time thresholds: $\Theta(n^2)$ for a map oracle, and $\Theta(n)$ for an instance oracle, that can be achieved with sufficiently large advice. We show that, with a map oracle, time $\Theta(n^2)$ 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 $n^\delta$, for any $\delta <1/3$. For an instance oracle, advice of size $O(n\log n)$ is enough to achieve time $O(n)$. We show that, with any advice of size $o(n\log n)$, the time of exploration must be at least $n^\epsilon$, for any $\epsilon <2$, and with any advice of size $O(n)$, the time must be $\Omega(n^2)$. We also investigate minimum advice sufficient for fast exploration of hamiltonian graphs

The Generalized Uncertainty Principle and the Friedmann equations

The Generalized Uncertainty Principle (or GUP) affects the dynamics in Plank scale. So the known equations of physics are expected to get modified at that very high energy regime. Very recently authors in (Ali et al. 2009) proposed a new Generalized Uncertainty Principle (or GUP) with a linear term in Plank length. In this article, the proposed GUP is expressed in a more general form and the effect is studied for the modification of the Friedmann equations of the FRW universe. In the midway the known entropy-area relation get some new correction terms, the leading order term being proportional to square root of area.Comment: 6 pages, accepted for publication in Astrophysics and Space Scienc

Productivity and technical change in Indian economy

This paper makes a modest attempt to apply input-output methodology to understand the structural changes in Indian economy in recent years. Our observations cover the period 1998-99 to 2006-07, the latest year for which India’s input-output table is published. Our analysis indicates that most of the manufacturing as well as services sectors exhibit large intermediate input factor productivity growth during the years under observations. Notable among them are electrical machinery, coke, refined petroleum etc, radio, television and communication equipments, machinery and equipments, construction, and hotels and restaurants. Furthermore barring few sectors, most of these sectors registered capital productivity gain during this period.Surprisingly, India has not been able to register significant capital productivity gains in the labour intensive sectors like food products, textile products etc, even though India has comparative advantage in these sectors being a labour rich economy. We find that there is falling labour productivity in many of the labour intensive sectors like agriculture and allied, mining and quarrying, food products, wood products, pulp and paper. On the other hand, our analysis of technical coefficient of India’s input-output table suggests that input cost on agriculture allied activities in food products, beverages sector has progressively fallen over the years. Moreover, we find that input costs on machinery related items in many of our sector are increasing which suggest that economy is on a path of modernisation. This has also helped in reducing energy cost on production.Input-putput; India; total factor productivity growth; technical change