We present optical photometric and spectroscopic observations of supernova 2013ej. It is one of the brightest type II supernovae exploded in a nearby (∼ 10 Mpc) galaxy NGC 628. The light curve characteristics are similar to type II SNe, but with a relatively shorter (∼ 85 day) and steeper (∼ 1.7 mag (100 d) −1 in V ) plateau phase. The SN shows a large drop of 2.4 mag in V band brightness during plateau to nebular transition. The absolute ultraviolet (UV) light curves are identical to SN 2012aw, showing a similar UV plateau trend extending up to 85 days. The radioactive 56 Ni mass estimated from the tail luminosity is 0.02M ⊙ which is significantly lower than typical type IIP SNe. The characteristics of spectral features and evolution of line velocities indicate that SN 2013ej is a type II event. However, light curve characteristics and some spectroscopic features provide strong support in classifying it as a type IIL event. A detailed synow modelling of spectra indicates the presence of some high velocity components in Hα and Hβ profiles, implying possible ejecta-CSM interaction. The nebular phase spectrum shows an unusual notch in the Hα emission which may indicate bipolar distribution of 56 Ni. Modelling of the bolometric light curve yields a progenitor mass of ∼ 14M ⊙ and a radius of ∼ 450R ⊙ , with a total explosion energy of ∼ 2.3 × 10 51 erg.

We provide an in depth study of the theoretical peculiarities that arise in effective negative mass lensing, both for the case of a point mass lens and source, and for extended source situations. We describe novel observational signatures arising in the case of a source lensed by a negative mass. We show that a negative mass lens produces total or partial eclipse of the source in the umbra region and also show that the usual Shapiro time delay is replaced with an equivalent time gain. We describe these features both theoretically, as well as through numerical simulations. We provide negative mass microlensing simulations for various intensity profiles and discuss the differences between them. The light curves for microlensing events are presented and contrasted with those due to lensing produced by normal matter. Presence or absence of these features in the observed microlensing events can shed light on the existence of natural wormholes in the Universe.PACS numbers: 95.30. Sf, 98.90.+s, 04.20.Gz

The search for life on the planets outside the Solar System can be broadly classified into the following: looking for Earth-like conditions or the planets similar to the Earth (Earth similarity), and looking for the possibility of life in a form known or unknown to us (habitability). The two frequently used indices, Earth Similarity Index (ESI) and Planetary Habitability Index (PHI), describe heuristic methods to score similarity/habitability in the efforts to categorize different exoplanets or exomoons. ESI, in particular, considers Earth as the reference frame for habitability and is a quick screening tool to categorize and measure physical similarity of any planetary body with the Earth. The PHI assesses the probability that life in some form may exist on any given world, and is based on the essential requirements of known life: a stable and protected substrate, energy, appropriate chemistry and a liquid medium. We propose here a different metric, a Cobb-Douglas Habitability Score (CDHS), based on Cobb-Douglas habitability production function (CD-HPF), which computes the habitability score by using measured and calculated planetary input parameters. As an initial set, we used radius, density, escape velocity and surface temperature of a planet. The values of the input parameters are normalized to the Earth Units (EU). The proposed metric, with exponents accounting for metric elasticity, is endowed with verifiable analytical properties that ensure global optima, and is scalable to accommodate finitely many input parameters. The model is elastic, does not suffer from curvature violations and, as we discovered, the standard PHI is a special case of CDHS. Computed CDHS scores are fed to K-NN (K-Nearest Neighbour) classification algorithm with probabilistic herding that facilitates the assignment of exoplanets to appropriate classes via supervised feature learning methods, producing granular clusters of habitability. The proposed work describes a decision-theoretical model using the power of convex optimization and algorithmic machine learning.

A strictly linear evolution of the scale factor is a characteristic feature in several classes of alternative gravity theories. In this article we investigate the overall viability of an open linear coasting cosmological model. We report that this model is consistent with gravitational lensing statistics (within 1σ) and accomodates old high-redshift galaxies. We finally conclude that such a linear coasting, α(t) = t, is not ruled out on basis of these observational tests. *

Seven Earth-sized planets, known as the TRAPPIST-1 system was discovered with great fanfare in the last week of February 2017. Three of these planets are in the habitable zone of their star, making them potentially habitable planets a mere 40 light years away. Discovery of the closest potentially habitable planet to us just a year before -Proxima b and a realization that Earth-type planets in circumstellar habitable zones are a common occurrence provides the impetus to the existing pursuit for life outside the Solar System. The search for life has two goals essentially: Earth similarity and habitability. An index was recently proposed, Cobb-Douglas Habitability Score (CDHS), based on Cobb-Douglas habitability production function, which computes the habitability score by using measured and estimated planetary parameters like radius, density, escape velocity and surface temperature of a planet. The proposed metric, with exponents accounting for metric elasticity, is endowed with analytical properties that ensure global optima and can be scaled to accommodate a finite number of input parameters. We show here that the model is elastic, and the conditions on elasticity to ensure global maxima can scale as the number of predictor parameters increase. K-Nearest Neighbor classification algorithm, embellished with probabilistic herding and thresholding restriction, utilizes CDHS scores and labels exoplanets to appropriate classes via feature-learning methods. The algorithm works on top of a decision-theoretical model using the power of convex optimization and machine learning. The goal is to classify the recently discovered exoplanets into the "Earth League" and other classes. A second approach, based on a novel feature-learning and tree-building method classifies the same planets without computing the CDHS of the planets and produces a similar outcome. The convergence of the two different approaches indicates the strength of the proposed scheme and the likelihood of the potential habitability of the recent discoveries. 2016). This planet generated a lot of stir in the news (Witze, 2016) because it is located in the habitable zone and its mass is in the Earth's mass range: 1.27 − 3 M ⊕ , making it a potentially habitable planet (PHP) and an immediate destination for the Breakthrough Starshot initiative (Starshot, 2016). A few months after the announcement of Proxima b, another family of terrestrial-size exoplanets -the TRAPPIST-1 systemwas discovered (Gillon, 2016).This work is motivated by testing the efficacy of the suggested model, CDHS, in determining the habitability score, the proximity to the "Earth-League", of the recently discovered Proxima b. The habitability score model has been found to work well in classifying previously known exoplanets in terms of potential habitability. Therefore it was natural to test whether the model can also classify it as potentially habitable by computing its habitability score. This could indicate whether the model may be extended for a quick check of the potential habitability of n...