Friedmann model with viscous cosmology in modified f(R,T)f(R,T) gravity theory

In this paper, we introduce bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function $f(R,T)$, where $R$ and $T$ denote the curvature scalar and the trace of the energy-momentum tensor, respectively within the framework of a flat Friedmann-Robertson-Walker model. As an equation of state for prefect fluid, we take $p=(\gamma-1)\rho$, where $0 \leq \gamma \leq 2$ and viscous term as a bulk viscosity due to isotropic model, of the form $\zeta =\zeta_{0}+\zeta_{1}H$, where $\zeta_{0}$ and $\zeta_{1}$ are constants, and $H$ is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non- viscous and viscous fluids, respectively by assuming a simplest particular model of the form of $f(R,T) = R+2f(T)$, where $f(T)=\alpha T$ ( $\alpha$ is a constant). A big-rip singularity is also observed for $\gamma<0$ at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of $\alpha$ to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits transition from decelerated phase to accelerated phase under certain constraints of $\zeta_0$ and $\zeta_1$. We compare the viscous models with the non-viscous one through the graph plotted between scale factor and cosmic time and find that bulk viscosity plays the major role in the expansion of the universe. A similar graph is plotted for deceleration parameter with non-viscous and viscous fluids and find a transition from decelerated to accelerated phase with some form of bulk viscosity.Comment: 19 pages, 3 figures, the whole paper has been revised to improve the quality of paper. Some references added. arXiv admin note: text overlap with arXiv:1307.4262 by other author

High Energy Emission Processes in OJ 287 during 2009 Flare

The broadband spectrum of a BL Lac object, OJ 287, from radio to $\gamma$-rays obtained during a major $\gamma$-ray flare detected by \emph{Fermi} in 2009 are studied to understand the high energy emission mechanism during this episode. Using a simple one-zone leptonic model, incorporating synchrotron and inverse Compton emission processes, we show that the explanation of high energy emission from X-rays to $\gamma$-rays, by considering a single emission mechanism, namely, synchrotron self-Compton (SSC) or external Compton (EC) requires unlikely physical conditions. However, a combination of both SSC and EC mechanisms can reproduce the observed high energy spectrum satisfactorily. Using these emission mechanisms we extract the physical parameters governing the source and its environment. Our study suggests that the emission region of OJ 287 is surrounded by a warm infrared (IR) emitting region of $\sim 250 \, K$. Assuming this region as a spherical cloud illuminated by an accretion disk, we obtain the location of the emission region to be $\sim 9 pc$. This supports the claim that the $\gamma$-ray emission from OJ 287 during the 2009 flare arises from a location far away from the central engine as deduced from millimeter-gamma ray correlation study and very long baseline array images.Comment: 22 pages, 7 figures, 1 table, accepted for publication in MNRA

Brightest Fermi-LAT Flares of PKS 1222+216: Implications on Emission and Acceleration Processes

We present a high time resolution study of the two brightest $\gamma$-ray outbursts from a blazar PKS 1222+216 observed by the \textit{Fermi} Large Area Telescope (LAT) in 2010. The $\gamma$-ray light-curves obtained in four different energy bands: 0.1--3, 0.1--0.3, 0.3--1 and 1--3 GeV, with time bin of 6 hr, show asymmetric profiles with a similar rise time in all the bands but a rapid decline during the April flare and a gradual one during the June. The light-curves during the April flare show $\sim 2$ days long plateau in 0.1--0.3 GeV emission, erratic variations in 0.3--1 GeV emission, and a daily recurring feature in 1--3 GeV emission until the rapid rise and decline within a day. The June flare shows a monotonic rise until the peak, followed by a gradual decline powered mainly by the multi-peak 0.1--0.3 GeV emission. The peak fluxes during both the flares are similar except in the 1--3 GeV band in April which is twice the corresponding flux during the June flare. Hardness ratios during the April flare indicate spectral hardening in the rising phase followed by softening during the decay. We attribute this behavior to the development of a shock associated with an increase in acceleration efficiency followed by its decay leading to spectral softening. The June flare suggests hardening during the rise followed by a complicated energy dependent behavior during the decay. Observed features during the June flare favor multiple emission regions while the overall flaring episode can be related to jet dynamics.Comment: 17 pages, 9 figures, 4 tables, accepted for publication in Ap

Ratio Estimators in Simple Random Sampling Using Information on Auxiliary Attribute

Some ratio estimators for estimating the population mean of the variable under study, which make use of information regarding the population proportion possessing certain attribute, are proposed. Under simple random sampling without replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to the first order of approximation are derived. The results obtained have been illustrated numerically by taking some empirical population considered in the literature.Comment: 7 page

Evaluation of riskiness of Indian Banks and probability of book value insolvency

Recently, a lot of questions were raised about the financial health of commercial banks in India. This paper analyzes the Indian banks' riskiness and the probability of book-value insolvency under the framework developed by Hannan and Hanweck (1988). A risk index, known as Z score, for Global Trust Bank that became insolvent in 2004 suggests that the framework developed by Hannan and Hanweck (1988) is also relevant in the Indian context. For a random sample of 15 Indian Banks (public & private sector), we determine the riskiness/probability of book value insolvency over the years and also carry out a relative comparison between public and private sector banks in India. Results obtained in the study show that the probability of book value insolvency of Indian Banks has reduced over years and the probability of book value insolvency is lower in case of public sector banks in comparison to private sector banks.Riskiness, insolvency, Z-statistic