Hislop College

In the present study, we explore the cosmological implications of Rényi holographic dark energy within the framework of f(R,T) gravity by considering an anisotropic Kantowski–Sachs space time. To obtain exact solutions, we employ Berman’s law corresponding to a constant deceleration parameter and assume a proportional relationship between the shear scalar and the expansion scalar. The derived model exhibits a gradual decrease in the RHDE density as the Universe evolves, eventually tending toward a finite positive value at late times. At the same time, the pressure remains negative throughout the evolution and approaches a nearly constant value in the asymptotic regime. The behaviour of the equation of state parameter indicates a transition from values near zero to more negative values, supporting the onset of accelerated expansion. Our analysis shows that the Null Energy Condition (NEC) and the Dominant Energy Condition (DEC) remain satisfied; however, the Strong Energy Condition (SEC) is violated, consistent with late-time acceleration. Statefinder diagnostics reveal that the model evolves toward the ΛCDM fixed point. Although the squared sound speed is negative, reflecting non-canonical perturbative behaviour common in modified gravity, the background evolution remains well behaved. Overall, RHDE in f(R,T) gravity provides a viable description of late-time cosmic acceleration.

Lanthanum (La3+)-doped nickel-cobalt-iron spinel nanoferrites (Ni0.6Co0.4Fe2-xLaxO4) using a cost-effective solgel autocombustion method. This technique helps to improve the materials for use in electromagnetic interference (EMI) shielding and high-frequency applications. X-ray diffraction with Lorentz Fit showed a clear cubic spinel structure with La addition leading to a smaller lattice size (from 8.3150 f 0.0001 & Aring; to 8.2954 f 0.0002 & Aring;) and smaller crystal sizes (from 49.71 f 0.41 nm to 28.37 f 0.25 nm). Rietveld analysis confirmed these findings with a goodness-of-fit value (chi 2) of 1.2-1.3. Fourier transform infrared (FTIR) and Raman spectroscopy confirmed the presence of strong M-O bonds. The addition of La3+ decreased the strength of these bonds (Kt decreased by 4 %, Ko decreased by 3 %) and increased the Debye temperature (theta D increased by 5 %). The best mechanical properties were at x = 0.04, with bulk modulus (B) of 2.15 x 1012 Pa and Young's modulus (Y) of 2.78 x 1012 Pa. This resulted in sound velocities of 7.2 km/s for longitudinal waves and 4.6 km/s for transverse waves. Field-emission scanning electron microscopy (FESEM) showed spherical grains measuring 94-61 nm and an aspect ratio of 1.05-1.15. The surface area measured using the BET method ranged from 15 to 22 m2/g, and Xray photoelectron spectroscopy (XPS) showed a mix of Fe2+ and Fe3+ ions (in a 1:4 ratio) creating vacancies. Magnetic measurements showed that the materials became softer when La was added, with saturation magnetization (Ms) decreasing from 59.81 to 39.81 emu/g, coercivity (Hc) dropping from 855 to 766 Oe, and magnetic energy density (K) declining from 933 to 822 erg/g. The squareness ratio was around 0.5, with resonance frequencies ranging from 13.20 to 8.79 GHz, making them suitable for X-band applications. Cole-Cole plots indicated that the materials did not show typical relaxation patterns. The dielectric constant (epsilon ') varied from 253,723 (at 878 K and low frequencies) to about 150 at 1 MHz, with a loss tangent (tan delta) of 1.15 for x = 0.04. These changes in properties exceeded those of undoped ferrites by 30-50 %. This study presents the first modulus spectroscopy of La-NiCo ferrites, highlighting how rare-earth vacancy control can optimize electrical and magnetic properties. These advances could support sustainable spintronics by making materials suitable for 5G antennas and supercapacitors while reducing the need for rare-earth elements.

In this paper, we investigate a non-minimally coupled cosmological model in f(Q,Lm) gravity within the framework of the FLRW metric in the presence of a perfect fluid. We consider the functional form f(Q,L_m)=-Q+α L_m+β QL_m, where Q is the non-metricity scalar, Lm is the matter Lagrangian and α , β are the model parameters. The coupling between geometry and matter leads to a density-dependent gravitational interaction and modifies the cosmological dynamics in the presence of a perfect fluid. We derive the modified Friedmann equations, constrain the model parameters H0, ω and λ =6β H_0^2/α using the observational datasets H(z), Pantheon+SH0ES and DESI BAO, and discuss their physical implications for the cosmological evolution. The values of equation of state (EoS) parameter ω is obtained in the range -1< ω < -1/3 , represent the quintessence type dark energy behaviour of a perfect fluid. From all the datasets, the negative values of deceleration parameter q(z) at z=0, confirms the late-time accelerated expansion of the universe, whereas the transition redshift zt indicates the transition of the universe from an earlier decelerating phase to the present accelerating phase. This shows that our f(Q,Lm) gravity model is capable of reproducing the late-time accelerated expansion through the non-minimal coupling between geometry and matter, without introducing an explicit cosmological constant term in the model under consideration.