Constraining Parameters for the Accelerating Universe in $f(R,\mathcal{L}_{m})$ Gravity
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| Format: | Preprint |
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2024
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| author | Devi, Y. Kalpana Narawade, S. A. Mishra, B. |
| author_facet | Devi, Y. Kalpana Narawade, S. A. Mishra, B. |
| contents | In the paper, we present an accelerating cosmological model in $f(R,\mathcal{L}_{m})$ gravity with the parameter constrained through the cosmological data sets. At the beginning, we have employed a functional form of $f(R,\mathcal{L}_{m}) =\frac{R}{2}+αR^2+\mathcal{L}_{m}^β$, where $α$ and $β$ are model parameters. This model is well motivated from the Starobinsky model in $f(R)$ gravity and the power law form of $f(\mathcal{L}_{m})$. The Hubble parameter has been derived with some algebraic manipulation and constrained by Hubble data and Pantheon$^{+}$ data. With the constraint parameters, present value of deceleration parameter has been obtained to as $q_{0}\approx-0.63$ with the transition at $z_{t}\approx0.7$. It shows the early deceleration and late time acceleration behaviour. The present value of other geometric parameters such as the jerk and snap parameter are obtained to be $j_{0}\approx0.78$ and $s_{0}\approx 0.1$ respectively. The state finder diagnostic test gives the quintessence behaviour at present and converging to $Λ$CDM at late times. Moreover the $Om(z)$ diagnostics gives negative slope which shows that the model favours the state finder diagnostic result. Also the current age of Universe has been obtained as, $t_{0} = 13.64~~Gyrs$. The equation of state parameter also shows the quintessence behaviour. Based on the present analysis, it indicates that the $f(R,\mathcal{L}_{m})$ gravitational theory may be another alternative to study the dark energy models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_09569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constraining Parameters for the Accelerating Universe in $f(R,\mathcal{L}_{m})$ Gravity Devi, Y. Kalpana Narawade, S. A. Mishra, B. General Relativity and Quantum Cosmology High Energy Physics - Theory In the paper, we present an accelerating cosmological model in $f(R,\mathcal{L}_{m})$ gravity with the parameter constrained through the cosmological data sets. At the beginning, we have employed a functional form of $f(R,\mathcal{L}_{m}) =\frac{R}{2}+αR^2+\mathcal{L}_{m}^β$, where $α$ and $β$ are model parameters. This model is well motivated from the Starobinsky model in $f(R)$ gravity and the power law form of $f(\mathcal{L}_{m})$. The Hubble parameter has been derived with some algebraic manipulation and constrained by Hubble data and Pantheon$^{+}$ data. With the constraint parameters, present value of deceleration parameter has been obtained to as $q_{0}\approx-0.63$ with the transition at $z_{t}\approx0.7$. It shows the early deceleration and late time acceleration behaviour. The present value of other geometric parameters such as the jerk and snap parameter are obtained to be $j_{0}\approx0.78$ and $s_{0}\approx 0.1$ respectively. The state finder diagnostic test gives the quintessence behaviour at present and converging to $Λ$CDM at late times. Moreover the $Om(z)$ diagnostics gives negative slope which shows that the model favours the state finder diagnostic result. Also the current age of Universe has been obtained as, $t_{0} = 13.64~~Gyrs$. The equation of state parameter also shows the quintessence behaviour. Based on the present analysis, it indicates that the $f(R,\mathcal{L}_{m})$ gravitational theory may be another alternative to study the dark energy models. |
| title | Constraining Parameters for the Accelerating Universe in $f(R,\mathcal{L}_{m})$ Gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.09569 |