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amine the physical validity of the solutions, we per- form tests of energy conditions, stability against the equilibrium of forces, adiabatic index, etc., and find that the proposed f ( R, T ) model sur- vives from all these critical tests, and hence, not only can explain the non-singular charged strange stars but also viability of the supermassive com- pact stellar objects having their masses beyond the maximum mass limit for the compact stars in the standard scenario. Therefore, the present f ( R, T ) gravity model seems promising regarding existence of several exotic astrophysical objects, like super- Chandrasekhar white dwarfs, massive pulsars, and even magnetars, which remain unexplained in the framework of general relativity (GR). This work has been studied in collaboration with Debabrata Deb, Sergei V. Ketov, and Maxim Khlopove. Inflation in anisotropic brane universe using tachyon field Cosmological solution to the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I ge- ometry and perfect fluid as matter sources has been considered. The matter on the brane is described by a tachyonic field. The solution admits inflation- ary era, and at a later epoch the anisotropy of the universe washes out. We obtain two classes of cos- mological scenario, in the first case universe evolves from singularity, and in the second case universe expands without singularity. This work has been done in collaboration with Rikpratik Sengupta. Prabir Rudra Dynamical system analysis of generalized energy- momentum-squared gravity In this work, we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model f ( R, T 2 ), where R represents the scalar cur- vature and T 2 the square of the energy-momentum tensor. By using dynamical system analysis for various types of gravity functions, we have stud- ied the structure of the phase space and the physi- cal implications of the energy–momentum squared coupling. In the first case of functional where f ( R, T 2 ) = f 0 R n ( T 2 ) m , with f 0 constant, we have shown that the phase space structure has a reduced complexity, with a high sensitivity to the values of m and n parameters. Depending on the values of m and n parameters, the model exhibits various cosmological epochs, corresponding to matter eras, solutions associated to an accelerated expansion, or decelerated periods. The second model stud- ied corresponds to the f ( R, T 2 ) = αR n + β ( T 2 ) m form with α, β constant parameters. In this case, a richer phase space structure is obtained, which can recover different cosmological scenarios, associated to matter eras, deSitter solutions, and dark energy epochs. Hence, this model represents an interest- ing cosmological model which can explain the cur- rent evolution of the universe and the emergence of the accelerated expansion as a geometrical conse- quence. This work has been done in collaboration with Sebastian Bahamonde, and Mihai Marciu. Gravitational baryogenesis in Horava-Lifshitz grav- ity In this work, we intend to address the matter- antimatter asymmetry via the gravitational baryo- genesis mechanism in the background of a quan- tum theory of gravity. We investigate this mecha- nism under the framework of Horava-Lifshitz grav- ity. We compute the baryon-to-entropy ratio in the chosen framework and investigate its physical viability against the observational bounds. We also conduct the above study for various sources of mat- ter like scalar field and Chaplygin gas as specific examples. We infer that quantum corrections from the background geometry will lead to interesting results. This work has been done in collaboration with Sayani Maity. Sanjay K. Sahay An overview of deep learning architecture of deep neural networks and autoencoders Recently, deep learning has shown great progress in multiple fields, but to perform optimally, it re- quires the adjustment of various architectural fea- tures and hyper-parameters. Moreover, deep learn- ing could be used with multiple varieties of ar- chitecture aimed at different objectives, e.g., au- toencoders are popular for un-supervised learning applications for reducing the dimensionality of the dataset. Similarly, deep neural networks are pop- ular for supervised learning applications viz., clas- sification, regression, etc. Besides the type of deep learning architecture, some other decision criteria and parameter selection decisions are required for determining the number of layers, size of each layer,