A bouncing scenario of a flat homogeneous and isotropic universe is explored by using the reconstruction technique for the power-law parametrization of the Hubble parameter in a modified gravity theory with higher-order curvature and trace of the energy-momentum tensor terms. It is demonstrated that bouncing criteria are satisfied so that the cosmological initial singularity can be avoided. In addition, it is shown that the equation of state parameter crosses the line of the phantom divide. In the present scenario, the universe is filled with perfect fluid around the bouncing point, in which the universe becomes highly unstable and a big bounce can be realized. Furthermore, it is found that extremal acceleration occurs at the bouncing point.

We investigate the extended phase space thermodynamics of nonsingular-AdS black holes minimally coupled to clouds of strings in which we consider the cosmological constant ( $$\Lambda $$Λ ) as the pressure (P) of the black holes and its conjugate variable thermodynamical volume (V) of the black holes. Owing to the background clouds of strings parameter (a), we analyse the Hawking temperature, entropy and specific heat on horizon radius for fixed-parameter k. We find that the strings clouds background does not alter small/large black hole (SBH/LBH) phase transition but occurs at a larger horizon radius, and two second-order phase transitions occur at a smaller horizon radius. Indeed, the G–T plots exhibit a swallowtail below the critical pressure, implying that the first-order phase transition is analogous to the liquid–gas phase transition at a lower temperature and lower critical pressure. To further examine the analogy between nonsingular-AdS black holes and a liquid–gas system, we derive the exact critical points and probe the effects of a cloud of strings on $$P-V$$P - V criticality to find that the isotherms undergo liquid–gas like phase transition for $${\tilde{T}}\,<\,{\tilde{T}}_c$$T ~ < T ~ c at lower $${\tilde{T}}_c$$T ~ c . We have also calculated the critical exponents identical with Van der Walls fluid, i.e., same as those obtained before for arbitrary other AdS black holes, which implies that the background clouds of strings do not change the critical exponents.

In this paper, we study a cosmological model in the background of Friedmann–Lemaitre–Robertson–Walker (FLRW) space time by assuming an appropriate parametrization in the form of a differential equation in terms of energy density of scalar field $$\rho _{\phi } $$ρϕ , which is defined as Energy Density Scalar Field Differential equation (EDSFD) parametrization. The EDSFD parametrization leads to a required phase transition from early deceleration to present cosmic acceleration. This parametrization is used to reconstruct the equation of state parameter $$ \omega _{\phi }$$ωϕ in terms of redshift z i.e. $$ \omega _{\phi }(z) $$ωϕ(z) to examine the evolutionary history of the universe in a flat FLRW space time. Here, we constrain the model parameter using the various observational datasets of Hubble parameter H(z) , latest Union 2.1 compilation dataset SNeIa, BAO, joint dataset $$H(z)+SNeIa $$H(z)+SNeIa and $$ H(z)+SNeIa+BAO $$H(z)+SNeIa+BAO for detail analysis of the behavior of physical parameters and we find its best fit present value. Also, we discuss the dynamics of reheating phase after inflation, analyse the behaviors of the physical features using some diagnostic tools, and examine the viability of our parametric model.

We propose a novel dark-energy equation-of-state parametrization, with a single parameter $\eta$ that quantifies the deviation from $\Lambda$CDM cosmology. We first confront the scenario with various datasets, from the Hubble function (OHD), Pantheon, baryon acoustic oscillations (BAO), and their joint observations, and we show that $\eta$ has a preference for a non-zero value, namely, a deviation from $\Lambda$CDM cosmology is favored, although the zero value is marginally inside the 1$\sigma$ confidence level. However, we find that the present Hubble function value acquires a higher value, namely, $H_0=66.{624}_{-0.013}^{+0.011}$ Km s⁻¹ Mpc⁻¹, which implies that the $H_0$ tension can be partially alleviated. Additionally, we perform a cosmographic analysis, showing that the universe transits from deceleration to acceleration in the recent cosmological past; nevertheless, in the future, it will not result in a de Sitter phase since it exhibits a second transition from acceleration to deceleration. Finally, we perform the statefinder analysis. The scenario behaves similarly to the $\Lambda$CDM paradigm at high redshifts, while the deviation becomes significant at late and recent times and especially in the future.

In this paper, we investigate a scalar field cosmological model of accelerating Universe with the simplest parametrization of the equation of state parameter of the scalar field. We use $H\left(z\right)$ data, pantheon compilation of SN Ia data and BAO data to constrain the model parameters using the ${\chi }^2$ minimization technique. We obtain the present values of Hubble constant $H_0$ as $66.2_{-1.34}^{+1.42}$, $70.7_{-0.31}^{+0.32}$ and $67.{74}_{-1.04}^{+1.24}$ for $H\left(z\right)$, $H\left(z\right)$ + Pantheon and $H\left(z\right)$ + BAO respectively. In addition, we estimate the present age of the Universe in a derived model $t_0=14.{38}_{-0.64}^{+0.63}$ for joint $H\left(z\right)$ and pantheon compilation of SN Ia data which has only $0.88\sigma$ tension with its empirical value obtained in Plank collaboration. Moreover, the present values of the deceleration parameter $q_0$ come out to be $-0.{55}_{-0.038}^{+0.031}$, $-0.{61}_{-0.021}^{+0.030}$ and $-0.{627}_{-0.025}^{+0.022}$ by bounding the Universe in the derived model with $H\left(z\right)$, $H\left(z\right)$ + Pantheon compilation of SN Ia and $H\left(z\right)$ + BAO data sets, respectively. We also have performed the state-finder diagnostics to discover the nature of dark energy.