Narrow Results

We have examined a $\mathrm{\Lambda }(T)$ cosmological model with mixture of two fluids by assuming a special law of variation of Hubble parameter proposed by Berman [Nuovo Cimento B74 (1983) 182–186] that yields constant deceleration parameter in LRS-Bianchi type-I space-time in $f(R,T)$ theory of gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy–momentum tensor. In this paper, one of the fluids represents the matter content of the universe and the other fluid is the cosmic microwave background. We have used the form $f(R,T)=f(R)+f(T)$ with $f(R)=\alpha R$ and $f(T)=\alpha T$, where $\alpha$ is any arbitrary coupling constant of $f(R,T)$ gravity. Such a selection of functional $f(R,T)$ leads to general relativistic field equations with trace $T$-dependent term of cosmological constant $\mathrm{\Lambda }(T)$. To obtain the exact solutions of field equations we have considered the equation of state $P=(\gamma -1)\rho$. The different anisotropic physical models such as dust, radiation, hard and Zeldovich models are explained, Statefinder and om diagnostic parameter are also discussed.

We develop two different singularity-free interior stellar models characterizing anisotropic fluid distribution in this paper in the background of $f(R,T)$ gravity. The modified Einstein field equations and the corresponding pressure anisotropy are then calculated in conjunction with a static spherical spacetime. We then address the field equations by using two different constraints that make a system easy to solve. By taking into account specific forms of pressure anisotropy, we formulate two different stellar models. The differential equations appear in both cases whose solutions incorporate integration constants and we determine them by equating the metric potentials of the interior and the Schwarzschild exterior metrics at the spherical interface. Another condition that plays a crucial role in this regard is the vanishing radial pressure at the matching surface. We subsequently discuss multiple conditions that, when met, yield physically feasible compact models. We also consider the estimated data of a pulsar LMC X-4 along with five distinct values of the model parameter to graphically assess the developed solutions. It is concluded that both our models are well-aligned with the physically existence conditions in this modified gravity framework.

The magnetized strange quark matter (MSQM) solutions are obtained for a Marder type universe using constant deceleration parameter. The exact solutions of field equations are obtained for f(R,T) = R + 2f(T) model given by [T. Harko et al., Phys. Rev. D84, 024020 (2011)] with cosmological term. Also, we have obtained General Relativity (GR) solutions for MSQM distributions. For $t\to \infty$, we get the dark energy model, i.e. $p\to -B_c$, $\rho \to B_c$ and $\omega =-1$. However, for $t\to \infty$, we find the cosmological constant $\mathrm{\Lambda }$ as negative in f(R,T) theory and GR. These results agree with [S. Aygün et al., Astrophys. Space Sci.361, 380 (2016); C. Aktaş and S. Aygün, Chinese J. Phys.55, 71 (2017); P. K. Sahoo et al., Mod. Phys. Lett. A32, 1750105 (2017)] in f(R,T) theory. The physical consequences of our obtained models are discussed at the end.

In this work, we have studied LRS Bianchi type I cosmological models in $f(R,T)$ gravity with tilted observers, where $R$ is the Ricci scalar and $T$ is the trace of the stress energy tensor. We have explored a tilted model and determined the solutions of the field equations by assuming special law of variation of Hubble’s parameter, proposed by Berman (1983) that yields constant deceleration parameter. In this scenario, we have used the equation of state $p=(\gamma -1)\rho$ and power law of velocity to describe the different anisotropic physical models such as Dust Universe, Radiation Universe, Hard Universe and Zedovich Universe. We have discussed graphical presentation of all parameters of the derived models with the help of MATLAB. Some physical and geometrical aspects of the models are also discussed.

This work deals with the two fluid Bianchi type-V cosmological models consisting of matter and radiating source in the $f(R,T)$ theory of gravity studied by Harko et al. [Phys. Rev. D 84, 024020 (2011)]. In this paper, we developed a new idea about $f(R,T)$ gravity with the help of two fluids: one fluid is matter field modeling material content of the Universe and other fluid is radiation field modeling the cosmic microwave background (CMB). We have determined the solution of the two fluid gravitational field equations with the systematic structure in $f(R,T)$ gravity. Here, we have deliberated four types of universe such as dust universe, radiation universe, hard universe and Zel’dovich universe and also extended our work to observe the big rip and big bang singularity. We have also tested the cosmological parameters.

We have presented the Big Rip singularity in $f(R,T)$ gravity with tilt congruences and creation field. We have solved the field equations by considering a conformally flat universe and the condition $B=A^n$, where $n$ is a constant. The solutions of the field equations have also been investigated by using the method of [J. V. Narlikar and T. Padmanabhan, Phys. Rev. D 32, 1928 (1985)] in which the creation field $C$ is a function of time $t$. Some geometric aspects of the model are also discussed by using MATLAB.

In this paper, generalized Friedmann–Robertson–Walker universe for Strange Quark Matter (SQM) and Normal Matter (NM) coupled with Domain Wall (DW) in form perfect fluid have been investigated in $f(R,T)$ modified theory. $f(R,T)$ function has been assumed as $f(R,T)=R+\mu T$ and Modified Field Equations (MEFEs) have been attained. The MEFEs of the constructed model do not allow solutions of open and closed FRW universe. Obtained modified field equations of higher dimensional flat FRW universe have been solved by using Linearly Varying Deceleration Parameter (LVDP) suggested by Akarsu and Dereli [Int. J. Theor. Phys. 51, 612 (2012)]. Pressure and energy density of the matter distributions for the Linearly Expansion Model (LEM) and Constant Expansion Model (CEM) have been attained as decreasing values by the cosmic time t and constant $\mu$ in $f(R,T)$ gravity. But for the Exponential Expansion Model (XEM), these quantities have been obtained as time-independent. It is found out that the domain wall behaves like invisible matter when $s_1=0$ due to negative domain wall tension (${\sigma }_w^{\mathrm{\text{LSQM}}}=-B_c$) for SQM with DW of LEM. Strange quark matters for LDW and CDW models behave like cold dark matter when $s_1=0$ and $s_3=0$, respectively. One can say that SQM with DW for LEM and CEM may cause the expansion of the universe in these special situations. Also, solutions of XEM have shown that domain wall matter behaves like stiff matter when $\mu =20\pi$. All solutions of the constructed model in $f(R,T)$ theory have been reduced to General Relativity (GR) theory solutions by assuming $\mu =0$. Finally, all solutions obtained have been discussed in detail.

In this study, we have examined the cosmological model of the locally rotationally symmetric (LRS) Bianchi Type-I universe within the framework of the $f(R,T)$ theory of gravity. The $f(R,T)$ theory incorporates the Ricci scalar (R) and the trace of the energy–momentum tensor (T) in its formulation. Our investigation focuses on the cold dark matter (CDM) and holographic dark energy (DE) cosmological models, particularly in relation to the occurrence of a big rip singularity. To solve the field equation, we have assumed a specific relationship between the parameters, $\alpha$ and $\beta$, where $\alpha$ is proportional to $m\beta$ and m is held constant. We have examined the existence of both the Big Bang and Big Rip singularities within this cosmological model. Additionally, we have analysed the state-finder parameter, which provides insights into the dynamics and evolution of the universe. Furthermore, we have discussed the physical and geometrical parameters of the universe in this context. These parameters help characterize and describe the behavior of the universe, shedding light on its underlying properties and dynamics. Through our investigation, we aim to deepen our understanding of the LRS Bianchi Type-I cosmological model within the $f(R,T)$ theory of gravity, exploring the interplay between CDM, holographic DE, singularities, and the various parameters that contribute to the understanding of the universe.

This study includes the cosmic evolution and the potential periodicity of the universe. It employs a periodic varying deceleration parameter (PVDP) within the framework of $f(R,T)$ theory of gravity, with a specific focus on the Bianchi-II model. We explore the dynamic nature of the universe, with physical and geometrical properties within this theoretical framework. We have also analyzed the cosmographic parameters, including jerk, snap, and lerk, for deeper insights into the universe’s evolution and behavior. Utilizing state finder diagrams and the Om diagnostic (which illustrates the variation of $\mathrm{\text{Om}}(z)$ with redshift) signifying a shift from matter dominance to a stronger influence of dark energy (DE), we construct a comprehensive map of the universe’s trajectory and behavior. By employing the Bianchi-II model within the $f(R,T)$ theory, our proposed model helps us in understanding the universe’s oscillatory patterns and underlying mechanisms. This research significantly contributes to our understanding of cosmic evolution and periodicity within the $f(R,T)$ theory.

This work deals with the Kaluza–Klein cosmological model with strange-quark-matter in $f(R,T)$ theory of gravity, where R is the Ricci scalar and T is the trace of the energy–momentum tensor. To determine the solution of the field equation, we have assumed that scalar expansion $\theta$ is proportional to shear scalar ${\sigma }^2$ which leads to $R=A^m$, where R and A are metric potentials and m is constant. The cosmological parameters are investigated with the help of the equation of state strange-quark-matter (SQM) is $p=\frac{\rho -4B_c}{3}$, where $B_c$ is Bag constant. We have concentrated on the distances of cosmology such as the look-back time, proper distance, luminosity distance, angular-diameter distance and distance modulus which are presented graphically by using suitable data of $H_0$. The physical and geometrical properties of models are also discussed.

In this study, Tsallis holographic dark energy (THDE) was discussed within the frame of $f(R,T)$ gravitational theory and considering the homogeneous and anisotropic Marder universe. The Hubble horizon was taken into consideration as infrared cutoff of the system. To get the field equations, solutions were used for the THDE density and the anisotropy parameter. Furthermore, a variety of physical parameters such as deceleration parameter, anisotropy parameter and volume have been examined. They have been also been visually examined with the help of graphics. Different values of deceleration parameter consistent with different observational data were mentioned. In addition to this, cosmological parameters like jerk, lerk and snap parameters were analyzed. Statefinder diagnostics which are helpful tools for the separation of dark energy models have been examined. By the calculation and representation of the overall density parameter ($\mathrm{\Omega }$) it can be concluded that the anisotropic nature of model vanishes showing a tendency to isotropy in accordance with present universe. Finally, the physical and geometrical nature of the model was studied, collating with relevant studies and observations.

In this study, we investigated quintessence and tachyon field dark energy (DE) models for the inhomogeneous and anisotropic Ruban universe in $f(R,T)$ gravitation theory. We utilized the Hubble parameter in the field equations as $\frac{\beta }{\sqrt{t+\alpha }}$ for the solutions. Since DE candidates are classified according to the $\frac{p}{\rho }$ values of the EoS parameter $\omega$, we obtained the p and $\rho$ solutions for each DE candidate and analyzed the scalar field (SF) and scalar potential solution. We also talked about the model’s physical characteristics and parameters with the help of a various of graphics for redshift z and cosmic time t. Additionally, the statefinder parameters, which are essential tools for distinguishing various dark energy models, have been explored.

In this paper, we have studied flat Friedmann–Lemaître–Robertson–Walker (FLRW) model with modified Chaplygin gas (MCG) having equation of state $p_m=A\rho -\frac{B}{{\rho }^{\gamma }}$, where $0\le A\le 1$, $0\le \gamma \le 1$ and $B$ is any positive constant in $f(R,T)$ gravity with particle creation. We have considered a simple parametrization of the Hubble parameter $H$ in order to solve the field equations and discussed the time evolution of different cosmological parameters for some obtained models showing unique behavior of scale factor. We have also discussed the statefinder diagnostic pair $\{r,s\}$ that characterizes the evolution of obtained models and explore their stability. The physical consequences of the models and their kinematic behaviors have also been scrutinized here in some detail.

A study is made of the LRS Bianchi type-I cosmological model in $f(R,T)$ modified gravity theory. Einstein’s field equations in $f(R,T)$ gravity are solved by taking $f(R,T)=R+2f(T)$ and the deceleration parameter $(q)$ to be a linear function of the Hubble parameter $(H)$. The universe begins with an initial singular state and changes with time from an early deceleration phase to a late time acceleration phase. We have found that the jerk parameter $(j)$ in the model approaches that of the $\mathrm{\Lambda }CDM$ model at late times. We also discuss the physical and geometrical properties of the model.

In this paper, we have proposed a new form for the varying deceleration parameter that is a generalization of the form of Ö. Akarsu and T. Dereli [Cosmological models with linearly varying deceleration parameter, Int. J. Theor. Phys.51(2012) 612]. LRS Bianchi type-I cosmological model filled with a perfect fluid source in $f(R,T)$ gravity theory, where $R$ is the Ricci scalar and $T$ is the trace of the stress energy–momentum tensor, has been studied in order to investigate early time deceleration and late time acceleration of the universe by using this new form of time-varying deceleration parameter. The time evolution of physical and dynamical parameters have been analyzed and shown by graphs. Moreover, the deceleration parameter has been considered in terms of redshift. It has been shown that the model starts with a big bang and ends with a big rip. It is filled by a quintessence like fluid at the early time and by a phantom like fluid at the late time.

In this study, we have investigated homogeneous and anisotropic Marder and Bianchi type I universe models filled with normal and phantom scalar field matter distributions with $\mathrm{\Lambda }$ in $f(R,T)$ gravitation theory (T. Harko et al., Phys. Rev. D84 (2011) 024020). In this model, $R$ is the Ricci scalar and $T$ is the trace of energy–momentum tensor. To obtain exact solutions of modified field equations, we have used anisotropy feature of the universe and different scalar potential models with $f(R,T)=R+2f(T)$ function. Also, we have obtained general relativity (GR) solutions for normal and phantom scalar field matter distributions in Marder and Bianchi type I universes. Additionally, we obtained the same scalar function values by using different scalar field potentials for Marder and Bianchi type I universe models with constant difference in $f(R,T)$ gravity and GR theory. From obtained solutions, we get negative cosmological term value for $V(\varphi )=V_0$ constant scalar potential model with Marder and Bianchi type I universes in GR theory. These results agree with the studies of Maeda and Ohta, Aktaş et al. also Biswas and Mazumdar. Finally, we have discussed and compared our results in gravitation theories.

In this study, Friedmann–Robertson–Walker space-time filled with a perfect fluid in $f(R,T)$ modified theory, where $R$ is the Ricci scalar and $T$ is the trace of the energy–momentum tensor of matter, has been considered. The investigation of the phase transition of the universe from the decelerating expansion phase to the accelerating one has been made by adopting a special form of the varying deceleration parameter that is inversely proportional to the Hubble parameter. The exact solution of the field equations has been derived. The kinematic and dynamical quantities of the model have been obtained and their evolutions have been discussed by means of their graphs. The statefinder diagnostic has been used and the age of the universe has been computed for testing the validity of the model. It has been shown that the dominant energy of the model is ordinary matter which behaves as the SCDM model at the beginning and it is a quintessence like fluid which behaves as the $\mathrm{\Lambda }$CDM model at late times.

This paper inspects the impact of minimal matter-geometry coupling present in $R+\alpha R^2+\gamma T$ model of $f(R,T)$ theory on the physical attributes of anisotropic quark stars. The geometry of considered stellar candidates is modeled via spherically symmetric static spacetime whose metric functions are influenced by Heintzmann solutions. The inner matter distribution of the stellar system is assumed as anisotropic with the phenomenological MIT bag model equation of state. The expressions of unknown parameters that appear in Heintzmann solution are evaluated in terms of mass and radius by the continuity of interior and exterior geometries. Further, insertion of masses and radii of some particular observed stellar models will yield their numerical values. In order to discuss the physical acceptability as well as stability of the quarks stars based on the considered solutions, we have checked the physical behavior of matter variables, mass and related quantities, energy conditions, equilibrium of forces, adiabatic index and Herrera’s cracking concept. The energy conditions are fulfilled ensuring the compatibility of assumed matter and geometry of quark stars. It is also found that all compact star candidates exhibit stable structures corresponding to the proposed values of the model parameters. Hence, the considered $f(R,T)$ model shows consistency with all the physical conditions and presents a viable study to the nature of anisotropic massive stellar system.

In this paper, an attempt is made to construct a Friedmann–Lemaitre–Robertson–Walker model in $f(R,T)$ gravity with a perfect fluid that yields acceleration at late times. We take $f(R,T)$ as $R+8\pi \mu T$. As in the $\mathrm{\Lambda }$CDM model, we take the matter to consist of two components, viz., ${\mathrm{\Omega }}_m$ and ${\mathrm{\Omega }}_{\mu }$ such that ${\mathrm{\Omega }}_m+{\mathrm{\Omega }}_{\mu }=1$. The parameter ${\mathrm{\Omega }}_m$ is the matter density (baryons $+$ dark matter), and ${\mathrm{\Omega }}_{\mu }$ is the density associated with the Ricci scalar $R$ and the trace $T$ of the energy–momentum tensor, which we shall call dominant matter. We find that at present ${\mathrm{\Omega }}_{\mu }$ is dominant over ${\mathrm{\Omega }}_m$, and that the two are in the ratio 3:1–3:2 according to the three data sets: (i) 77 Hubble OHD data set, (ii) 580 SNIa supernova distance modulus data set and (iii) 66 pantheon SNIa data which include high red shift data in the range $0\le z\le 2.36$. We have also calculated the pressures and densities associated with the two matter densities, viz., $p_{\mu }$, ${\rho }_{\mu }$, $p_m$ and ${\rho }_m$, respectively. It is also found that at present, ${\rho }_{\mu }$ is greater than ${\rho }_m$. The negative dominant matter pressure $p_{\mu }$ creates acceleration in the universe. Our deceleration and snap parameters show a change from negative to positive, whereas the jerk parameter is always positive. This means that the universe is at present accelerating and in the past it was decelerating. State finder diagnostics indicate that our model is at present a dark energy quintessence model. The various other physical and geometric properties of the model are also discussed.

In this study, we consider the Bianchi type I model in the framework of $f(R,T)$ gravity theory. We solve the field equations with the help of an anisotropy parameter that can show the anisotropic behavior of the universe in the past and its approximation to isotropy today. For two different models, we examine the phase transition in the expansion of the universe by analyzing some cosmologic parameters. We conduct our investigation by applying the Markov Chain Monte-Carlo analysis and Bayesian technique to the Cosmic Chronometer, Phanteon and BAO datasets, taking into account the observational constraints on the parameters. We show that the two different models we obtained explain the transition from the slowing phase to the accelerating phase in the expansion of the universe, that the models behave in harmony with the $\mathrm{\Lambda }$CDM model today, and that the current values of the cosmological parameters predicted by the models are compatible with the values indicated by the observations and we conclude that the Model-I is more compatible than the Model-II in this conformity.