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The onset of thermal instability with hybrid nanoparticles Al₂O₃–Cu in nanofluid is investigated with the combined effects of variable gravity, variable heat source and Lorentz force in a porous medium. Its applications are in many areas like chemical engineering, geophysics, astrophysics, etc. Based on literature, many gravity variations are assumed in the present analysis, along with a space-dependent heat source/sink parameter that varies along the width of the channel. The finite difference-based Lobatto IIIa method has been applied to solve the system under no nanoparticle flux and rough boundary conditions, and approximate analytical results are generated for some special cases. The roughness parameters (${\lambda }_1,{\lambda }_2$), Darcy number (Da), gravity variation function ($G(z)$), and Chandrasekhar number (Q) delay the onset of convection and thus stabilize the system. It is also observed that an increase in the Lewis number Le, power index in variable heat source, and the nanoparticle Rayleigh concentration number Rn decreases the critical Rayleigh number $R_{\theta ,c}$ which destabilizes the system, and increases the critical wave number, which enlarges the convection cell size. In the case of exponential variation ($1-e^z$) in the gravity variation parameter, the system becomes stabilized due to a delay in the onset of convection. In addition, we have considered multilayer perceptron-artificial neural network (MLP-ANN) computation to predict the critical Rayleigh number as per function of important controlling parameters. The data set of 625 observations is chosen keeping 70% for testing, 15% for training and 15% for validation using efficient Levenberg−Marquardt back propagation algorithm with optimal accuracy measures i.e., root mean square deviation (RMSE), root mean relative error (RMRE) and $R^2$ (coefficient of determination). Finally, the regression plots are drawn that correlate, target and output data.

Solar models suggest that four billion years ago the young Sun was ~25% fainter than it is today, rendering Earth's oceans frozen and lifeless. However, there is ample geophysical evidence that Earth had a liquid ocean teeming with life 4 Gyr ago. Since , the Sun's luminosity is exceedingly sensitive to small changes in the gravitational constant G. We show that a percent-level increase in G in the past would have prevented Earth's oceans from freezing, resolving the faint young Sun paradox. Such small changes in G are consistent with observational bounds on ΔG/G. Since , an increase in G leads to fainter supernovae, creating tension between standard candle and standard ruler probes of dark energy. Precisely such a tension has recently been reported by the Planck team.

This pedagogical review is devoted to quintessential inflation, which refers to unification of inflation and dark energy using a single scalar field. We present a brief but concise description of the concepts needed to join the two ends, which include discussion on scalar field dynamic, conformal coupling, instant preheating and relic gravitational waves. Models of quintessential inflation broadly fall into two classes, depending upon the early and late time behavior of the field potential. In the first type we include models in which the field potential is steep for most of the history of the universe but turn shallow at late times, whereas in the second type the potential is shallow at early times followed by a steep behavior thereafter. In models of the first category inflation can be realized by invoking high-energy brane-induced damping, which is needed to facilitate slow roll along a steep potential. In models of second type one may invoke a nonminimal coupling of the scalar field with massive neutrino matter, which might induce a minimum in the potential at late times as neutrinos turn nonrelativistic. In this category we review a class of models with noncanonical kinetic term in the Lagrangian, which can comply with recent B mode polarization measurements. The scenario under consideration is distinguished by the presence of a kinetic phase, which precedes the radiative regime, giving rise to blue spectrum of gravity waves generated during inflation. We highlight the generic features of quintessential inflation and also discuss on issues related to Lyth bound.