arXiv:2407.09569v1 Announce Type: new
Abstract: 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 $f(R,mathcal{L}_{m}) =frac{R}{2}+alpha R^2+mathcal{L}_{m}^beta$, where $alpha$ and $beta$ 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 $Lambda$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.
Accelerating Cosmological Model in f(R,Lm) Gravity
Introduction
In this paper, we present an accelerating cosmological model in f(R,Lm) gravity. The model is derived based on the Starobinsky model in f(R) gravity and the power law form of f(Lm). The parameter in the model is constrained using cosmological data sets.
Model Description
The functional form of the model is f(R,Lm) = R/2 + αR^2 + Lm^β, where α and β are model parameters. The Hubble parameter is derived through algebraic manipulation and constrained using Hubble data and Pantheon+ data. The model exhibits early deceleration and late-time acceleration behavior.
Geometric Parameters
The present values of various geometric parameters are obtained: deceleration parameter q0 ≈ -0.63 with the transition at zt ≈ 0.7, jerk parameter j0 ≈ 0.78, snap parameter s0 ≈ 0.1. The state finder diagnostic test shows quintessence behavior at present, converging to ΛCDM at late times.
Om(z) Diagnostics and Age of the Universe
The Om(z) diagnostics reveals a negative slope, indicating that the model favors the results of the state finder diagnostic. The current age of the Universe is calculated as t0 = 13.64 Gyrs.
Conclusion
Based on the analysis conducted, the f(R,Lm) gravitational theory presents itself as another alternative to study dark energy models. The model shows promising results in terms of reproducing observed cosmological data sets.
Future Roadmap
- Further exploration of the f(R,Lm) model and its implications for various cosmological observations
- Investigation of the model’s behavior under different parameter values
- Comparison of the f(R,Lm) model with other dark energy models to identify its unique features
- Testing the model against additional cosmological data sets to validate and refine its predictions
- Exploration of the consequences of the f(R,Lm) model for the evolution of large-scale cosmic structures
Challenges and Opportunities
Challenges:
- Understanding the physical implications of the model’s parameter choices
- Exploring potential limitations and constraints of the f(R,Lm) gravitational theory
- Addressing any inconsistencies or discrepancies between the model’s predictions and observational data
Opportunities:
- Advancing our understanding of the nature of dark energy through alternative theories
- Exploring new avenues for cosmological research and uncovering novel phenomena
- Contributing to the development of a more comprehensive picture of the evolution of the Universe
Overall, the f(R,Lm) gravitational theory holds promise as an alternative approach to studying dark energy models, and further investigation will shed light on its potential implications and limitations.