A study of generalized second law of thermodynamics in modified f(R) Horava–Lifshitz gravity

This work investigates the validity of the generalized second law of thermodynamics in modified f(R) Horava–Lifshitz gravity proposed by Chaichian et al. (Class. Quantum Grav. 27: 185021, 2010), which is invariant under foliation-preserving diffeomorphisms. It has been observed that the equation of state parameter behaves like quintessence (w>−1). We study the thermodynamics of the apparent, event and particle horizons in this modified gravity. We observe that under this gravity, the time derivative of total entropy stays at positive level and hence the generalized second law is validated.     

Measurement of Hubble constant: were differences in secondary distance indicators apparent as early as the HST Key Project?

Different measurements of the Hubble constant(H₀)are not consistent,and a tension between the CMB based methods and cosmic distance ladder based methods has been observed.Measurements from various distance based methods are also inconsistent.To aggravate the problem,the same cosmological probe(TypeⅠa SNe for instance)calibrated through different methods also provides different values of H₀.We compare various distance ladder based methods through the already available unique data obtained from the Hubble Space Telescope(HST).Our analysis is based on parametric(t-test)as well as non-parametric statistical methods such as the Mann-Whitney U test and Kolmogorov-Smirnov test.Our results show that different methods provide different values of H₀ and the differences are statistically significant.The biases in the calibration would not account for these differences as the data have been taken from a single telescope with a common calibration scheme.The unknown physical effects or issues with the empirical relations of distance measurement from different probes could give rise to these differences.     

Geochemistry and petrogenesis of radioactive Palaeoproterozoic granitoids of Kinwat crystalline inlier,Nanded and Yeotmal districts,Maharashtra

Kinwat crystalline inlier exposes Palaeoproterozoic granitoids belonging to the northern extensions of younger phase of Peninsular gneissic complex (PGC) within Deccan Trap country in Eastern Dharwar Craton (EDC) and bounded in south by a major NW-SE trending lineament (Kaddam fault). Geochemically, the Kinwat granitoids are similar to high-K, calc-alkaline to shoshonite magnesian granitoids and subdivided into two major groups, i.e. felsic group (pink and grey granites) and intermediate to felsic group (hybrid granitoids). The felsic group (∼67–74% SiO₂) shares many features with Neoarchaean to Palaeoproterozoic high potassic granites of PGC such as higher LILE and LREE content and marked depletion in Eu, P and HFSE, especially Nb, Ti, relative to LILE and LREE. The hybrid granitoids (∼58–67% SiO₂) have comparatively higher Ca, Mg and Na contents and slightly lower REE content than the granitoids of felsic group. Both, felsic and hybrid granitoids are metaluminous to weakly peraluminous and belong to highly fractionated I-type suite as evidenced by negative correlation of SiO₂ with MgO, FeO^t, CaO, Na₂O, Al₂O₃, whereas K₂O, Rb and Ba show sympathetic relationship with SiO₂. Moderate to strong fractionated REE patterns (Ce/Yb_N: ∼54–387) and strong negative Eu anomalies (Eu/Eu*: 0.13–0.41) are quite apparent in these granitoids. The geochemical characteristics together with mineralogical features such as presence of biotite±hornblende as the dominant ferromagnesian mineral phases point towards intracrustal magma source, i.e. derivation of magma by partial melting of probably tonalitic igneous protolith at moderate crustal levels for felsic granites, whereas hybrid granitoids appear to be products of juvenile mantle-crust interaction, in an active continental margin setting.