Contrasting features of anisotropic loop quantum cosmologies: the role of spatial curvature

A characteristic feature of loop quantization of the isotropic and Bianchi-I spacetimes is the existence of universal bounds on the energy density and the expansion and shear scalars, independent of the matter content. We investigate the properties of these physical quantities in Bianchi-II and Bianchi-IX spacetimes, which have been recently loop quantized using the connection operator approach. Using the effective Hamiltonian approach, we show that for Bianchi-II spacetime, energy density and the expansion and shear scalars turn out to be bounded, albeit not by universal values. In Bianchi-IX spacetime, when the approach to the classical singularity is isotropic, above physical quantities are bounded. In addition, for all other cases, where the approach to singularities is not isotropic and effective dynamics can be trusted, these quantities turn out to be finite. These results stand in sharp distinction to general relativity, where above physical quantities are generically unbounded, leading to the break down of geodesic equations. In contrast to the isotropic and Bianchi-I models, we find the role of energy conditions for Bianchi-II model and the inverse triad modifications for Bianchi-IX to be significant to obtain above bounds. These results bring out subtle physical distinctions between the quantization using holonomies over closed loops performed for isotropic and Bianchi-I models, and the connection operator approach. We find that qualitative differences in physics exist for these quantization methods even for the isotropic models in the presence of spatial curvature. We highlight these important differences in the behavior of the expansion scalar in the holonomy based quantization and connection operator approach for isotropic spatially closed and open models.Comment: Minor clarifications added. To match published version in PR

Non-singular AdS-dS transitions in a landscape scenario

Understanding transitions between different vacua of a multiverse allowing eternal inflation is an open problem whose resolution is important to gain insights on the global structure of the spacetime as well as the problem of measure. In the classical theory, transitions from the anti-deSitter to deSitter vacua are forbidden due to the big crunch singularity. In this article, we consider toy landscape potentials: a double well and a triple well potential allowing anti-deSitter and de-Sitter vacua, in the effective dynamics of loop quantum cosmology for the $k=-1$ FRW model. We show that due to the non-perturbative quantum gravity effects as understood in loop quantum cosmology, non-singular anti-deSitter to de-Sitter transitions are possible. In the future evolution, an anti-deSitter bubble universe does not encounter a big crunch singularity but undergoes a big bounce occurring at a scale determined by the underlying quantum geometry. These non-singular transitions provide a mechanism through which a probe or a `watcher', used to define a local measure, can safely evolve through the bounce and geodesics can be smoothly extended from anti-deSitter to de-Sitter vacua.Comment: Revised version. Appendix on results in k=0 model added. To appear in PR

Chimera: A hybrid approach to numerical loop quantum cosmology

The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.Comment: Minor revision to match published version. To appear in CQ

Price and Volatility Spillovers across North American, European and Asian Stock Markets: With Special Focus on Indian Stock Market

<div align=justify>This paper investigates interdependence of fifteen world indices including an Indian market index in terms of return and volatility spillover effect. Interdependence of Indian stock market with other fourteen world markets in terms of long run integration, short run dependence (return spillover) and volatility spillover are investigated. These markets are that of are Canada, China, France, Germany, Hong-Kong, Indonesia, Japan, Korea, Malaysia, Pakistan, Singapore, Taiwan, United Kingdom and United States. Long run and short run integration is examined through Johansen cointegration techniques and Granger causality test respectively. Vector autoregressive model (VAR 15) is used to estimate the conditional return spillover among these indices in which all fifteen indices are considered together. The effect of same day return in explaining the return spillover is also modeled using univariate models. Volatility spillover is estimated through AR-GARCH in which residuals from the index return is used as explanatory variable in GARCH equation. Return and volatility spillover between Indian and other markets are modeled through bivariate VAR and multivariate GARCH (BEKK) model respectively. It is found that there is greater regional influence among Asian markets in return and volatility than with European and US. Japanese market, which is first to open, is affected by US and European markets only and affects most of the Asian Markets. Also, high degree of correlation among European indices namely FTSE, CAC and DAX is observed. US market is influenced by both Asian and European markets. Specific to Indian context, it is found that Indian market is not cointegrated with rest of the world except Indonesia. This may provide diversification benefits for potential investors. However, strong short run interdependence is found between Indian markets and most of the other markets. Indian and other markets like US, Japan, Korea, and Canada positively affect each others conditional returns significantly. Indian market also has significant effect on Malaysia, Pakistan, and Singapore return. This study found that there is significant positive volatility spillover from other markets to Indian market, mainly from Hong Kong, Korea, Japan, and Singapore and US market. Indian market affects negatively the volatility of US and Pakistan. It is interesting to note that Chinese and Pakistan markets are less integrated with other Asian, European and US markets.</div>

The Dynamic Relationship between Price and Trading Volume:Evidence from Indian Stock Market

This study investigates the nature of relationship between price and trading volume for 50 Indian stocks. Firstly the contemporaneous and asymmetric relation between price and volume are examined. Then we examine the dynamic relation between returns and volume using VAR, Granger causality, variance decomposition (VD) and impulse response function (IRF). Mixture of Distributions Hypothesis (MDH), which tests the GARCH vs. Volume effect, is also studied between the conditional volatility and volume. The results show that there is positive and asymmetric relation between volume and price changes. Further the results of VAR and Granger causality show that there is a bi-directional relation between volume and returns. However, the results of VD imply weak dynamic relation between returns and volume which becomes more evident from the plots of IRF. On MDH, our results are mixed, neither entirely rejecting the MDH nor giving it an unconditional support.

Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology

In recent years, numerical simulations with Gaussian initial states have demonstrated the existence of a quantum bounce in loop quantum cosmology in various models. A key issue pertaining to the robustness of the bounce and the associated physics is to understand the quantum evolution for more general initial states which may depart significantly from Gaussianity and may have no well defined peakedness properties. The analysis of such states, including squeezed and highly non-Gaussian states, has been computationally challenging until now. In this manuscript, we overcome these challenges by using the Chimera scheme for the spatially flat, homogeneous and isotropic model sourced with a massless scalar field. We demonstrate that the quantum bounce in this model occurs even for states which are highly squeezed or are non-Gaussian with multiple peaks and with little resemblance to semi-classical states. The existence of the bounce is found to be robust, being independent of the properties of the states. The evolution of squeezed and non-Gaussian states turns out to be qualitatively similar to that of Gaussian states, and satisfies strong constraints on the growth of the relative fluctuations across the bounce. We also compare the results from the effective dynamics and find that, although it captures the qualitative aspects of the evolution for squeezed and highly non-Gaussian states, it always underestimates the bounce volume. We show that various properties of the evolution, such as the energy density at the bounce, are in excellent agreement with the predictions from an exactly solvable loop quantum cosmological model for arbitrary states.Comment: 26 pages, 16 figures. v2: Discussion of the main results expande

Numerical simulations of a loop quantum cosmos: robustness of the quantum bounce and the validity of effective dynamics

A key result of isotropic loop quantum cosmology is the existence of a quantum bounce which occurs when the energy density of the matter field approaches a universal maximum close to the Planck density. Though the bounce has been exhibited in various matter models, due to severe computational challenges some important questions have so far remained unaddressed. These include the demonstration of the bounce for widely spread states, its detailed properties for the states when matter field probes regions close to the Planck volume and the reliability of the continuum effective spacetime description in general. In this manuscript we rigorously answer these questions using the Chimera numerical scheme for the isotropic spatially flat model sourced with a massless scalar field. We show that as expected from an exactly solvable model, the quantum bounce is a generic feature of states even with a very wide spread, and for those which bounce much closer to the Planck volume. We perform a detailed analysis of the departures from the effective description and find some expected, and some surprising results. At a coarse level of description, the effective dynamics can be regarded as a good approximation to the underlying quantum dynamics unless the states correspond to small scalar field momenta, in which case they bounce closer to the Planck volume, or are very widely spread. Quantifying the amount of discrepancy between the quantum and the effective dynamics, we find that the departure between them depends in a subtle and non-monotonic way on the field momentum and different fluctuations. Interestingly, the departures are generically found to be such that the effective dynamics overestimates the spacetime curvature, and underestimates the volume at the bounce.Comment: 47 pages, 26 figures; References updated. Minor changes to match the version published in CQ

ASASSN-14dq: A fast-declining type II-P Supernova in a low-luminosity host galaxy

Optical broadband (UBVRI) photometric and low-resolution spectroscopic observations of the type II-P supernova (SN) ASASSN-14dq are presented. ASASSN-14dq exploded in a low-luminosity/metallicity host galaxy UGC 11860, the signatures of which are present as weak iron lines in the photospheric phase spectra. The SN has a plateau duration of $\sim\,$90 d, with a plateau decline rate of 1.38 $\rm mag\ (100 d)^{-1}$ in V-band which is higher than most type II-P SNe. ASASSN-14dq is a luminous type II-P SN with a peak $V$-band absolute magnitude of -17.7$\,\pm\,$0.2 mag. The light curve of ASASSN-14dq indicates it to be a fast-declining type II-P SN, making it a transitional event between the type II-P and II-L SNe. The empirical relation between the steepness parameter and $\rm ^{56}Ni$ mass for type II SNe was rebuilt with the help of well-sampled light curves from the literature. A $\rm ^{56}Ni$ mass of $\sim\,$0.029 M$_{\odot}$ was estimated for ASASSN-14dq, which is slightly lower than the expected $\rm ^{56}Ni$ mass for a luminous type II-P SN. Using analytical light curve modelling, a progenitor radius of $\rm \sim3.6\times10^{13}$ cm, an ejecta mass of $\rm \sim10\ M_{\odot}$ and a total energy of $\rm \sim\,1.8\times 10^{51}$ ergs was estimated for this event. The photospheric velocity evolution of ASASSN-14dq resembles a type II-P SN, but the Balmer features (H$\alpha$ and H$\beta$) show relatively slow velocity evolution. The high-velocity H$\alpha$ feature in the plateau phase, the asymmetric H$\alpha$ emission line profile in the nebular phase and the inferred outburst parameters indicate an interaction of the SN ejecta with the circumstellar material (CSM).Comment: 28 pages, 29 figures, Accepted in MNRA

Role of MgO impurity on the superconducting properties of MgB2

We address the effect of MgO impurity on the superconducting properties of MgB2. The synthesis of MgB2 is very crucial because of sensitivity of Mg to oxidation which may lead to MgO as a secondary phase. Rietveld refinement was performed to determine the quantitative volume fraction of MgO in the samples synthesized by two different techniques. Both the samples were subjected to magnetization measurements under dc and ac applied magnetic fields and the observed results were compared as a function of temperature. Paramagnetic Meissner effect has been observed in a sample of MgB2 having more amount of MgO (with Tc = 37.1K) whereas the pure sample MgB2 having minor quantity of MgO shows diamagnetic Meissner effect with Tc = 38.8K. M-H measurements at 10K reveal a slight difference in irreversibility field which is due to MgO impurity along with wide transition observed from ac magnetic susceptibility measurements. The magnetotransport measurements R(T)H using RN = 90%, 50% and 10% criterion on pure sample of MgB2 has been used to determine the upper critical field whereas the sample having large quantity of MgO does not allow these measurements due to its high resistance.Comment: 15 pages text + Fig