#
Constraining the Viscous Dark Energy Equation of State in f (R, L_{m}) Gravity

^{*}

## Abstract

**:**

## 1. Introduction

## 2. $\mathit{f}(\mathit{R},{\mathit{L}}_{\mathit{m}})$ Gravity Theory

## 3. Motion Equations in $\mathit{f}(\mathit{R},{\mathit{L}}_{\mathit{m}})$ Gravity

## 4. Cosmological $\mathit{f}(\mathit{R},{\mathit{L}}_{\mathit{m}})$ Model

## 5. Data, Methodology, and Physical Interpretation

`emcee`in the Python library [65].

#### 5.1. H(z) Dataset

#### 5.2. Pantheon Dataset

## 6. Statefinder Diagnostic

## 7. Om Diagnostics

## 8. Energy Conditions

**Null energy condition (NEC):**${\rho}_{eff}+{p}_{eff}\ge 0$;**Weak energy condition (WEC):**${\rho}_{eff}\ge 0$ and ${\rho}_{eff}+{p}_{eff}\ge 0$;**Dominant energy condition (DEC):**${\rho}_{eff}\pm {p}_{eff}\ge 0$;**Strong energy condition (SEC):**${\rho}_{eff}+3{p}_{eff}\ge 0$,

## 9. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The $1\sigma $ and $2\sigma $ contours for the model parameters $\alpha $, $\gamma $, $\zeta $, and ${H}_{0}$, using the combined $H\left(z\right)$ + Pantheon + Analysis datasets.

**Figure 2.**The reconstruction of the energy density as a function of the redshift, for our model, is presented for 7500 samples, which are reproduced by re-sampling the chains through emcee. We plot all the obtained curves, alongside the curve corresponding to the best fit of the parameters (red curve).

**Figure 3.**The reconstruction of the effective pressure as a function of the redshift, for our model, is presented for 7500 samples, which are reproduced by re-sampling the chains through emcee. We plot all the obtained curves, alongside the curve corresponding to the best fit of the parameters (red curve).

**Figure 4.**The reconstruction of the effective EoS parameter as a function of the redshift, for our model, is presented for 7500 samples, which are reproduced by re-sampling the chains through emcee. We plot all the obtained curves, alongside the curve corresponding to the best fit of the parameters (red curve).

**Figure 5.**Profile of the evolution trajectory of the given model in the r–s plane, with the agreement of obtained observational constraints.

**Figure 6.**Profile of Om diagnostic parameter, with the agreement of obtained observational constraints.

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**MDPI and ACS Style**

Jaybhaye, L.V.; Solanki, R.; Mandal, S.; Sahoo, P.K. Constraining the Viscous Dark Energy Equation of State in *f* (*R*, *L*_{m}) Gravity. *Universe* **2023**, *9*, 163.
https://doi.org/10.3390/universe9040163

**AMA Style**

Jaybhaye LV, Solanki R, Mandal S, Sahoo PK. Constraining the Viscous Dark Energy Equation of State in *f* (*R*, *L*_{m}) Gravity. *Universe*. 2023; 9(4):163.
https://doi.org/10.3390/universe9040163

**Chicago/Turabian Style**

Jaybhaye, Lakhan V., Raja Solanki, Sanjay Mandal, and Pradyumn Kumar Sahoo. 2023. "Constraining the Viscous Dark Energy Equation of State in *f* (*R*, *L*_{m}) Gravity" *Universe* 9, no. 4: 163.
https://doi.org/10.3390/universe9040163