Certain results on Kenmotsu pseudo-metric manifolds

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature, and prove the structure theorem for $\xi$-conformally flat and $\varphi$-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an $\eta$-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature $-\varepsilon$.Comment: 17 page

Model-independent cosmological insights from three newly reconstructed deceleration parameters with observational data

This article introduces three novel parametrizations of the deceleration parameter (DP) to explore the cosmological scenario. The newly introduced parametric forms of the DP are physically plausible and model-independent. We constrained the model parameters using a Markov Chain Monte Carlo (MCMC) method by utilizing a combined dataset of 31 cosmic chronometers (CC) data points, 26 non-correlated baryonic acoustic oscillations (BAO) points, and recently updated 1701 Pantheon+ data points from supernovae type Ia (SNeIa). To explore the kinematic behavior of the model, we analyze various aspects such as the transition from deceleration to acceleration, as well as the energy conditions. The current analysis of the three parametric models reveals that the Universe is currently in an accelerated phase, which is supported by the present values of the EoS parameter and the negative SEC behavior within specific redshift ranges for all three models. Additionally, all three parametric models meet the WEC, DEC, and NEC conditions across the entire range of redshift values. We use the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) model selection criteria to compare the performance of the models. Overall, this study offers valuable insights into the accelerating Universe and emphasizes the significance of adopting a model-independent approach in cosmological investigations

Impact of a newly parametrized deceleration parameter on the accelerating universe and the reconstruction of f(Q) non-metric gravity models

Abstract This article presents a novel parametrization of the deceleration parameter (DP) to investigate the cosmological scenario. The newly proposed parametric form of the DP is both physically plausible and model-independent. Constrained by a combined dataset of 31 cosmic chronometers (CC) data points, 26 non-correlated baryonic acoustic oscillations (BAO) points, and 1701 Pantheon $$+$$ + data points from supernovae type Ia (SNeIa), we determine the model parameters using a Markov Chain Monte Carlo (MCMC) method. The analysis explores the kinematic behavior of the model, including the transition from deceleration to acceleration. The results indicate that the Universe is currently in an accelerated phase. Furthermore, we apply the obtained parameter values to constrain f(Q) gravity models and compare them with observations. This study provides valuable insights into the accelerating Universe and underscores the importance of employing a model-independent approach in cosmological investigations

Characterization of Ricci Almost Soliton on Lorentzian Manifolds

Ricci solitons (RS) have an extensive background in modern physics and are extensively used in cosmology and general relativity. The focus of this work is to investigate Ricci almost solitons (RAS) on Lorentzian manifolds with a special metric connection called a semi-symmetric metric u-connection (SSM-connection). First, we show that any quasi-Einstein Lorentzian manifold having a SSM-connection, whose metric is RS, is Einstein manifold. A similar conclusion also holds for a Lorentzian manifold with SSM-connection admitting RS whose soliton vector Z is parallel to the vector u. Finally, we examine the gradient Ricci almost soliton (GRAS) on Lorentzian manifold admitting SSM-connection