# Anisotropic bulk viscous string cosmological models of the Universe under a time-dependent deceleration parameter

## TL;DR

This paper develops new anisotropic string cosmological models with a time-dependent deceleration parameter, aligning with recent astronomical data, and demonstrates their transition from deceleration to acceleration.

## Contribution

It introduces a novel class of LRS Bianchi type-II models with a time-varying deceleration parameter, improving upon previous models and aligning with recent observational constraints.

## Key findings

- Models exhibit transition from decelerated to accelerated expansion.
- Results are consistent with recent SN Ia, BAO, and CMB observations.
- Models are stable and in good agreement with cosmological data.

## Abstract

We investigate a new class of LRS Bianchi type-II cosmological models by revisiting in the paper of Mishra {\it et al} (2013) by considering a new deceleration parameter (DP) depending on the time in string cosmology for the modified gravity theory suggested by S$\acute{a}$ez \& Ballester (1986). We have considered the energy-momentum tensor proposed by Leteliar (1983) for bulk viscous and perfect fluid under some assumptions. To make our models consistent with recent astronomical observations, we have used scale factor (Sharma {\it et al} 2018; Garg {\it et al} 2019) $ a(t)=\exp{[\frac{1}{\beta}\sqrt{2 \beta t + k}]}$, where $\beta $ and $k$ are positive constants and it provides a time-varying DP. By using the recent constraints ($H_{0}=73.8$, and $q_{0} = -0.54$) from SN Ia data in combination with BAO and CMB observations (Giostri {\it et al}, arXiv:1203.3213v2[astro-ph.CO]), we affirm $\beta = 0.0062$ and $k = 0.000016$. For these constraints, we have substantiated a new class of cosmological transit models for which the expansion takes place from early decelerated phase to the current accelerated phase. Also, we have studied some physical, kinematic and geometric behavior of the models, and have found them consistent with observations and well established theoretical results . We have also compared our present results with those of Mishra {\it et al} (2013) and observed that the results in this paper are much better, stable under perturbation and in good agreement with cosmological reflections.