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This paper rigorously examines the potential of the $f(T, \mathcal{T})$ theory as a promising framework for understanding the dark sector of the universe, particularly in relation to cosmic acceleration. The $f(T, \mathcal{T})$ theory extends gravitational dynamics by incorporating both the torsion scalar $T$ and the trace of the energy-momentum tensor $\mathcal{T}$. Further, we explore the functional form $f(T, \mathcal{T}) = T + \beta \mathcal{T}$, where $\beta$ is a free parameter that modulates the matter's influence on spacetime evolution. To evaluate this model, we employ an effective EoS parameter dependent on redshift $z$, to solve the field equations and analyze the evolution of the Hubble parameter $H(z)$. Using a joint dataset ($H(z)+Pantheon^+$) and the Markov Chain Monte Carlo (MCMC) method with Bayesian analysis, we obtain the best-fit parameter values: $H_0 = 68.04 \pm 0.64$, $\beta = 0.14 \pm 0.17$, and $\gamma = 0.96^{+0.38}_{-0.69}$, which align well with current observational data. Our findings indicate a deceleration parameter of $q_0 = -0.51$, supporting a present-day accelerated expansion phase, with a transition redshift $z_t = 0.57$ marking the universe's shift from deceleration to acceleration. Moreover, we confirm a positive cosmic fluid energy density, reinforcing stability, and find an EoS parameter value of $\omega_0 = -0.76$, consistent with quintessence-driven acceleration. These results underscore the viability of $f(T, \mathcal{T})$ as a robust framework for addressing the accelerating universe and dark energy dynamics, paving the way for future investigations into its cosmological implications., Comment: International Journal of Geometric Methods in Modern Physics accepted version

In the generalized matter-geometry coupling theory, we investigate the physical characteristics and causality of some new cosmological models for a flat, homogeneous, and isotropic spacetime filled with stiff, radiation, dust, and curvature fluid sources. We obtain a particular cosmological model corresponding to each source fluid, called Models I, II, III, and IV, respectively. We make observational constraints on each model using the joint analysis of $31$ Cosmic Chronometer (CC) Hubble dataset and $1048$ Pantheon datasets to estimate the current values of model parameters. Using these statistical results, we have analyzed the information criteria, effective EoS parameter, causality of the models, and viability of this generalized gravity theory. Subsequently, we investigate the effective equation of state and deceleration parameter for each model. We found that all models in the late-time universe exhibit transit-phase acceleration, and Models I and II show both the early as well as late-time accelerating phase of the expanding universe. We found the current values of the deceleration parameter in the range $-0.886\le q_{0}\le-0.54$ with transition redshift $0.5137\le z_{t}\le0.6466$ and the effective EoS parameter in the range $-0.924\le\omega_{eff}\le-0.6933$. We analyzed the square sound speed condition $c_{s}^{2}\le c^{2}$ for each model., Comment: 23 pages, 8 figures

In this manuscript, we investigate the constraints on dynamical vacuum models within the framework of $\Lambda(t)$CDM cosmology by assuming a parameterization of the vacuum energy density as $\rho_{\Lambda}(t)=\rho_{\Lambda 0} \left[1 + \alpha (1 - a)\right]$, where $\rho_{\Lambda 0}$ is the present vacuum density and $\alpha$ is a free parameter. We use 31 cosmic chronometer data points and 1048 Pantheon type Ia supernova samples to constrain the model parameters. Our statistical analysis employs Markov Chain Monte Carlo (MCMC) simulations. We have found that the universe is currently undergoing accelerated expansion, transitioning from a decelerating phase. The transition redshift $z_t=0.65^{+0.03}_{-0.19}$ obtained from the combined CC+SNe dataset is consistent with recent constraints. The total EoS indicates an accelerating phase, with density parameters for matter and vacuum energy exhibiting expected behaviors. The $Om(z)$ diagnostic shows distinct behaviors for different datasets, and the present value of the jerk parameter deviates slightly from the $\Lambda$CDM model but remains consistent within uncertainties. These findings support the dynamic nature of dark energy and provide valuable constraints on the evolution of the universe., Comment: Chinese Journal of Physics accepted version

In this paper, we investigate the effects of varying bulk viscosity coefficients $\zeta(t)=\zeta_{0}+\zeta_{1}H$ on cosmic evolution within the framework of $f(T)$ teleparallel gravity. We focus on two cases: (i) $\zeta_{1} \neq0$ and (ii) $\zeta_{1} =0$, deriving the Hubble parameter $H$ as a function of redshift $z$ using a linear $f(T)$ model ($f(T) = \alpha T$ where $\alpha \neq 0$). Using the combined $H(z)+Pantheon^{+}+BAO$ dataset, we obtain observational constraints on model parameters. For Case I ($\zeta_1 \neq 0$), best-fit values are $H_0=60.0^{+2.0}_{-1.9}$ km/s/Mpc, $\alpha=1.01^{+0.10}_{-0.098}$, $\zeta_0=40.1^{+1.9}_{-2.0}$, and $\zeta_1=0.123^{+0.093}_{-0.088}$, while for Case II ($\zeta_1 = 0$), they are $H_0=67.5^{+1.3}_{-1.3}$ km/s/Mpc, $\alpha=0.94^{+0.14}_{-0.13}$, and $\zeta_0=34.7^{+2.0}_{-2.0}$. The analysis reveals a transition in the deceleration parameter, indicating a shift from deceleration to acceleration of the universe's expansion, with present-day values of $q_{0} \approx -0.49$ and $q_{0} \approx -0.32$ for the respective cases. The jerk parameter $j(z)$ and effective EoS for the cosmic viscous fluid also support the cosmic acceleration, with trajectories aligning with the quintessence scenario. These findings underscore the potential of our $f(T)$ model dominated by bulk viscous matter in explaining cosmic acceleration., Comment: Physics Letters A accepted version

We investigate the cosmological implications of a generalized total equation of state (EoS) model by constraining its parameters using observational datasets to effectively characterize the universe's expansion history and its dynamic properties. We introduce three parameters: $\alpha$, $\beta$, and $n$ to capture the EoS behavior across different evolutionary phases. Our analysis indicates that at high redshifts ($z \gg 1$), the EoS approaches a matter- or radiation-dominated regime, transitioning to a dark energy-dominated phase as $z \to -1$, where it tends towards a constant value $\alpha$. Using a Markov Chain Monte Carlo (MCMC) method, we analyze a combined dataset that includes 31 data points from $H(z)$ and 1701 data points from the Pantheon+ dataset. The results reveal a smooth transition from deceleration to acceleration in the universe's expansion, with current EoS values suggesting quintessence-like behavior. The model aligns with observations and indicates that dark energy is dynamically evolving rather than acting as a cosmological constant. Furthermore, energy conditions and stability analyses highlight the nature and future of dark energy. This parametrized EoS model thus offers a robust framework for understanding the complexities of dark energy and the evolution of the cosmos., Comment: Physics of the Dark Universe accepted version

In this paper, we investigate the freezing quintessence scenario in late-time cosmic expansion using a non-linear $f(R, L_m)$ gravity model, $f(R,L_m)=\frac{R}{2}+L_m^\alpha$, where $\alpha$ is a free parameter. We consider a solution for this model using an appropriate parametrization of the scale factor, and then the model is constrained by observational datasets, including CC, Pantheon+ (SN), and CC+SN+BAO. Our analysis yields results aligning closely with observational data. The Hubble parameter, deceleration parameter, matter-energy density, and EoS parameter of our model exhibit expected trends over cosmic time, supporting its physical validity. Furthermore, the model demonstrates consistency with the $\Lambda$CDM model in late times, displaying freezing behavior in the $\omega - \omega'$ plane and stability against density perturbations. Our findings suggest that the modified $f(R, L_m)$ gravity model is a credible approach to describing the universe's accelerating phase., Comment: IJGMMP accepted version

Motivated by anomalies in cosmic microwave background observations, we investigate the implications of $f(Q, T)$ gravity in Bianchi type-I spacetime, aiming to characterize the universe's spatially homogeneous and anisotropic properties. By using a linear combination of non-metricity $Q$ and the energy-momentum tensor trace $T$, we parametrize the deceleration parameter and derive the Hubble solution, which we then impose in the Friedmann equations of $f(Q, T)$ gravity. Bayesian analysis is employed to find the best-fit values of model parameters, with $1-\sigma$ and $2-\sigma$ contour plots illustrating the constraints from observational data, including $H(z)$ data and the Pantheon+ sample. Our analysis reveals a transition from a decelerated to an accelerated expansion phase, with the present deceleration parameter indicating an accelerating universe. The energy density gradually decreases over time, approaching zero for the present and future, indicating continuous expansion. The anisotropic pressure, initially notably negative, transitions to slightly negative values, suggesting the presence of dark energy. The evolving equation of state parameter $\omega$ exhibits behavior akin to phantom energy, influenced by spacetime anisotropy. Violations of the null energy condition and the strong energy condition imply phantom-like behavior and accelerated expansion., Comment: Journal of High Energy Astrophysics accepted version

This study explores the extension of teleparallel gravity within the framework of general relativity, introducing an algebraic function $f(T)$ dependent on the torsion scalar $T$. Motivated by the teleparallel formulation, we investigate cosmological implications, employing the simplest parametrization of the dark energy equation of state. Our chosen $f(T)$ function, $f(T)=\alpha(-T)^n$, undergoes stringent constraints using recent observational data ($H(z)$, SNeIa, BAO, and CMB). The model aligns well with cosmic dynamics, exhibiting quintessence behavior. The evolution of the deceleration parameter, the behavior of dark energy components, and the $Om(z)$ diagnostic further reveal intriguing cosmological phenomena, emphasizing the model's compatibility with quintessence scenarios., Comment: Physics of the Dark Universe accepted version

In this paper, we investigate a cosmological model based on viscous $f(R,T)$ gravity as a potential alternative to dark energy. This model incorporates bulk viscosity and is analyzed using an effective equation of state. We consider the simplest specific model, $f(R,T)=R+\lambda T$, where $\lambda$ is a constant. The exact solution of our viscous $f(R,T)$ cosmological model is derived, and then we use the combined datasets consisting of 31 $H(z)$ data points and 1701 Pantheon+ SNe data points to determine the best-fit values of the model parameters. We find good agreement with observations, particularly at higher redshifts. Our model's behavior, including energy density, pressure with viscosity, effective equation of state, and deceleration parameter, is analyzed. It indicates a shift from decelerated to accelerated phases of the universe's expansion, suggesting that bulk viscosity in the cosmic fluid could effectively generate the negative pressure necessary for cosmic expansion. Finally, we explore statefinder diagnostics to differentiate between various dark energy models, revealing that our model resides in the quintessence region., Comment: Physics of the Dark Universe published version

We investigate the influence of bulk viscosity on late-time cosmic acceleration within an extended $f(Q, L_m)$ gravity framework, where the non-metricity $Q$ is non-minimally coupled with the matter Lagrangian $L_m$. Analyzing the function $f(Q, L_m) = \alpha Q + \beta L_m$, we derive exact solutions under non-relativistic matter domination. Using observational datasets ($H(z)$, Pantheon supernovae, and their combination), we constrain the model parameters $H_0$, $\alpha$, $\beta$, and $\zeta$. The deceleration parameter transitions from positive to negative values around redshifts $z_t \approx 0.80$ to $0.99 $, indicating current accelerated expansion. Moreover, the effective equation of state parameter, $\omega_{eff}$, resembles quintessence dark energy ($-1 < \omega_{eff} < -\frac{1}{3}$), with corresponding values from respective datasets. Finally, we use the $Om(z)$ diagnostic, which confirms that our model demonstrates quintessence-like behavior. Our findings underscore the significant role of bulk viscosity in understanding accelerated expansion in the universe within alternative gravity theories., Comment: Minor revision in Physics of the Dark Universe

We introduce a vortex phase transform with a lenslet-array to accompany shallow, dense, ``small-brain'' neural networks for high-speed and low-light imaging. Our single-shot ptychographic approach exploits the coherent diffraction, compact representation, and edge enhancement of Fourier-tranformed spiral-phase gradients. With vortex spatial encoding, a small brain is trained to deconvolve images at rates 5-20 times faster than those achieved with random encoding schemes, where greater advantages are gained in the presence of noise. Once trained, the small brain reconstructs an object from intensity-only data, solving an inverse mapping without performing iterations on each image and without deep-learning schemes. With this hybrid, optical-digital, vortex Fourier encoded, small-brain scheme, we reconstruct MNIST Fashion objects illuminated with low-light flux (5 nJ/cm$^2$) at a rate of several thousand frames per second on a 15 W central processing unit, two orders of magnitude faster than convolutional neural networks.

We consider the family of $3 \times 3$ operator matrices ${\bf H}(K),$ $K \in {\Bbb T}^3:=(-\pi; \pi]^3$ associated with the lattice systems describing two identical bosons and one particle, another nature in interactions, without conservation of the number of particles. We find a finite set $\Lambda \subset {\Bbb T}^3$ to prove the existence of infinitely many eigenvalues of ${\bf H}(K)$ for all $K \in \Lambda$ when the associated Friedrichs model has a zero energy resonance. It is found that for every $K \in \Lambda,$ the number $N(K, z)$ of eigenvalues of ${\bf H}(K)$ lying on the left of $z,$ $z<0,$ satisfies the asymptotic relation $\lim\limits_{z \to -0} N(K, z) |\log|z||^{-1}={\mathcal U}_0$ with $0<{\mathcal U}_0<\infty,$ independently on the cardinality of $\Lambda.$ Moreover, we prove that for any $K \in \Lambda$ the operator ${\bf H}(K)$ has a finite number of negative eigenvalues if the associated Friedrichs model has a zero eigenvalue or a zero is the regular type point for positive definite Friedrichs model., Comment: 18 pages