An emergent gravity metric incorporating k−essence scalar fields φ having a Born-Infeld type lagrangian is mapped into a metric whose structure is similar to that of a blackhole of large mass M that has swallowed a global monopole. However, here the field is not that of a monopole but rather that of a k−essence scalar field. If φemergent be solutions of the emergent gravity equations of motion under cosmological boundary conditions at ∞, then for r → ∞ the rescaled field φemergent 2GM −1 has exact correspondence with φ with φ(r, t) = φ1(r)+φ2(t). The Hawking temperature of this metric is Temergent =h c 3 8πGM k B (1 − K) 2 ≡h 8πGM k B (1 − K) 2 , taking the speed of light c = 1. Here K =φ 2 2 is the kinetic energy of the k−essence field φ and K is always less than unity, kB is the Boltzmann constant. This is phenomenologically interesting in the context of Belgiorno et al's gravitational analogue experiment.

The Leggett-Garg inequality (LGI) as a temporal analog of Bell's inequality, derived using the notion of realism, is studied in a hitherto unexplored context involving weak-interaction-induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of the LGI obtained from the relevant quantum mechanical results is significantly higher for oscillating neutrinos compared to that for kaons. Interestingly, the effect of CP noninvariance for the kaon oscillation is to enhance this violation, while, for neutrinos, the violation is sensitive to the value of mixing parameter.

For emergent gravity metrics, the presence of dark energy modifies the Hawking temperature. We show that for the spherically symmetric Reissner-Nordstrom background metric, the emergent metric can be mapped into a Robinson-Trautman black hole. Allowed values of the dark energy density follow from rather general conditions. For some allowed values of the dark energy density this black hole can have zero Hawking temperature, i.e. the black hole does not radiate. For a Kerr background along θ = 0, the emergent black hole metric satisfies Einstein's equations for large r and always radiates. Our analysis is done in the context of emergent gravity metrics having k-essence scalar fields φ with a Born-Infeld type lagrangian. In both cases the scalar field φ(r, t) = φ 1 (r )+φ 2 (t) also satisfies the emergent gravity equations of motion for r → ∞ and θ = 0.

Three flavoured neutrino oscillations are investigated in the light of the Leggett-Garg inequality. The outline of an experimental proposal is suggested whereby the findings of this investigation may be verified. The results obtained are: (a) The maximum violation of the Leggett Garg Inequality (LGI) is 2.17036 for neutrino path length L1 = 140.15 Km and ∆L = 1255.7 Km.(b) Presence of the mixing angle θ13 enhances the maximum violation of LGI by 4.6%.(c) The currently known mass hierarchy parameter α = 0.0305 increases the the maximum violation of LGI by 3.7%. (d)Presence of CP violating phase parameter enhances the maximum violation of LGI by 0.24%, thus providing an alternative indicator of CP violation in 3-flavoured neutrino oscillations.

We consider the evolution of primordial black holes in a generalized Jordan-Brans-Dicke cosmological model where both the Brans-Dicke scalar field and its coupling to gravity are dynamical functions determined from the evolution equations. The evaporation rate for the black holes is different from the case in standard cosmology. We show that the accretion of radiation can proceed effectively in the radiation-dominated era. It follows that the black hole lifetime shortens for low initial mass, but increases considerably for larger initial mass, thus providing a mechanism for the survival of primordial black holes as candidates of dark matter. We derive a cut-off value for the initial black hole mass, below which primordial black holes evaporate out in the radiation-dominated era, and above which they survive beyond the present era.