by jsendak | Jul 16, 2024 | GR & QC Articles
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.
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by jsendak | Mar 28, 2024 | GR & QC Articles
arXiv:2403.17037v1 Announce Type: new
Abstract: In the background of $f(R, L_m)$ gravity, this work investigates three distinct dark matter halo profiles to test the possibility of generalised wormhole geometry within the galactic halo regions. The current study aims to accomplish these goals by examining various dark matter profiles including Universal Rotation Curves (URC), Navarro-Frenk-White (NFW) model-I, and NFW model-II inside two distinct $f(R, L_m)$ gravity models. According to the $f(R, L_m) = frac{R}{2} + L_m^alpha$ model, the DM halo density profiles produce suitable shape functions that meet all the necessary requirements for exhibiting the wormhole geometries with appropriate choice of free parameters. In addition, to examine DM profiles under the $f(R, L_m) = frac{R}{2} + (1 + lambda R)L_m$ model, we consider a specific shape function. Further, we observed that the derived solution from both two models violates the null energy constraints, confirming that the DM supports wormholes to maintain in the galactic halo.
Examining the Possibility of Generalised Wormhole Geometry in the Galactic Halo
This study investigates the possibility of generalised wormhole geometry in the galactic halo regions within the framework of $f(R, L_m)$ gravity. The goal is to examine various dark matter profiles and determine if they can meet the necessary requirements for exhibiting wormhole geometries.
Dark Matter Profiles
Three distinct dark matter halo profiles are examined in this study:
- Universal Rotation Curves (URC)
- Navarro-Frenk-White (NFW) model-I
- Navarro-Frenk-White (NFW) model-II
The examination of these profiles will help determine if they can produce suitable shape functions for exhibiting wormhole geometries.
$f(R, L_m)$ Gravity Models
Two $f(R, L_m)$ gravity models are considered in this study:
- $f(R, L_m) = frac{R}{2} + L_m^alpha$
- $f(R, L_m) = frac{R}{2} + (1 + lambda R)L_m$
The goal is to examine the dark matter profiles under these models and determine if they can meet the necessary requirements for exhibiting wormhole geometries. For the second model, a specific shape function is considered.
Challenges and Opportunities
While the study shows promising results in terms of the dark matter halo profiles producing suitable shape functions for wormhole geometries, there are some challenges and opportunities on the horizon:
- Validation of the derived solutions: The derived solutions violate the null energy constraints, which raises questions about their validity. Further analysis and validation are required to confirm the existence of wormholes in the galactic halo.
- Exploration of other gravity models: The two $f(R, L_m)$ gravity models considered in this study are just a fraction of the possible models. Exploring other gravity models and their impact on dark matter profiles and wormhole geometries could reveal new opportunities and insights.
- Experimental verification: The study is based on theoretical analysis and mathematical models. Experimental verification through observations and measurements would provide essential evidence for the existence of wormholes in the galactic halo.
In conclusion, this study provides a preliminary exploration of the possibility of generalised wormhole geometry within the galactic halo regions. Further research and analysis are needed to address the challenges and opportunities outlined above and to provide a more complete understanding of wormholes in the context of $f(R, L_m)$ gravity.
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by jsendak | Feb 23, 2024 | GR & QC Articles
arXiv:2402.13360v1 Announce Type: new
Abstract: This study explores the behavior of compact stars within the framework of $f(R,L_m,T)$ gravity, focusing on the functional form $f(R,L_m,T) = R + alpha TL_m$. The modified Tolman-Oppenheimer-Volkoff (TOV) equations are derived and numerically solved for several values of the free parameter $alpha$ by considering both quark and hadronic matter — described by realistic equations of state (EoSs). Furthermore, the stellar structure equations are adapted for two different choices of the matter Lagrangian density (namely, $L_m= p$ and $L_m= -rho$), laying the groundwork for our numerical analysis. As expected, we recover the traditional TOV equations in General Relativity (GR) when $alpha rightarrow 0$. Remarkably, we found that the two choices for $L_m$ have appreciably different effects on the mass-radius diagrams. Results showcase the impact of $alpha$ on compact star properties, while final remarks summarize key findings and discuss implications, including compatibility with observational data from NGC 6397’s neutron star. Overall, this research enhances comprehension of $f(R,L_m,T)$ gravity’s effects on compact star internal structures, offering insights for future investigations.
This study examines the behavior of compact stars within the framework of $f(R,L_m,T)$ gravity, focusing specifically on the functional form $f(R,L_m,T) = R + alpha TL_m$. The modified Tolman-Oppenheimer-Volkoff (TOV) equations are derived and numerically solved for different values of the parameter $alpha$, considering both quark and hadronic matter with realistic equations of state. The stellar structure equations are adapted for two choices of the matter Lagrangian density, laying the foundation for the numerical analysis.
When $alpha$ approaches zero, the traditional TOV equations in General Relativity (GR) are recovered. However, it was discovered that the two choices for $L_m$ have significantly different effects on the mass-radius diagrams. This highlights the impact of $alpha$ on the properties of compact stars. The study concludes by summarizing the key findings and discussing their implications, including their compatibility with observational data from NGC 6397’s neutron star.
Overall, this research enhances our understanding of the effects of $f(R,L_m,T)$ gravity on the internal structures of compact stars. It provides insights that can contribute to future investigations in this field.
Roadmap for Future Investigations
To further explore the implications and potential applications of $f(R,L_m,T)$ gravity on compact stars, several avenues of research can be pursued:
1. Expansion to Other Functional Forms
While this study focuses on the specific functional form $f(R,L_m,T) = R + alpha TL_m$, there is potential for investigation into other functional forms. Different choices for $f(R,L_m,T)$ may yield interesting and diverse results, expanding our understanding of compact star behavior.
2. Exploration of Different Equations of State
Currently, the study considers realistic equations of state for both quark and hadronic matter. However, there is room for exploration of other equations of state. By incorporating different equations of state, we can gain a more comprehensive understanding of the behavior of compact stars under $f(R,L_m,T)$ gravity.
3. Inclusion of Additional Parameters
Expanding the analysis to include additional parameters beyond $alpha$ can provide a more nuanced understanding of the effects of $f(R,L_m,T)$ gravity on compact stars. By investigating how different parameters interact with each other and impact the properties of compact stars, we can uncover new insights into the behavior of these celestial objects.
4. Comparison with Observational Data
While this study discusses the compatibility of the findings with observational data from NGC 6397’s neutron star, it is important to expand this comparison to a wider range of observational data. By comparing the theoretical predictions with a larger dataset, we can validate the conclusions drawn and identify any discrepancies or areas for further investigation.
Challenges and Opportunities
Potential Challenges:
- Obtaining accurate and comprehensive observational data on compact stars for comparison with theoretical predictions can be challenging due to their extreme conditions and limited visibility.
- Numerically solving the modified TOV equations for various parameter values and choices of matter Lagrangian density may require significant computational resources and optimization.
- Exploring different functional forms and equations of state can lead to complex analyses, requiring careful interpretation and validation of results.
Potential Opportunities:
- The advancements in observational techniques and instruments provide opportunities for obtaining more precise data on compact stars, enabling more accurate validation of theoretical models.
- Ongoing advancements in computational power and numerical techniques allow for more efficient and faster solution of the modified TOV equations, facilitating the exploration of a broader parameter space.
- The diverse range of functional forms and equations of state available for investigation provides ample opportunities for uncovering novel insights into the behavior and properties of compact stars.
By addressing these challenges and capitalizing on the opportunities, future investigations into the effects of $f(R,L_m,T)$ gravity on compact star internal structures can continue to push the boundaries of our understanding and pave the way for further advancements in the field.
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by jsendak | Dec 30, 2023 | GR & QC Articles
We construct asymptotically flat, static spherically symmetric black holes
with regular centre in $f(R,T)$ gravity coupled to nonlinear electrodynamics
Lagrangian. We obtain generalized metric function of the Bardeen and Hayward
black holes. The null, weak and strong energy conditions of these solutions are
discussed. All the energy conditions hold outside the black hole’s outer event
horizon by appropriated choices of parameters. Quasinormal mode of massive
scalar perturbation is also investigated. Quasinormal frequencies are computed
via the sixth order Wentzel-Kramers-Brillouin (WKB) with Pad’e approximation.
All the imaginary parts of the frequencies are found to be negative. Finally,
we provide an analysis in the eikonal limit.
In this study, we have examined the construction of asymptotically flat, static spherically symmetric black holes with regular centers in the context of $f(R,T)$ gravity coupled to nonlinear electrodynamics Lagrangian. The goal was to obtain the generalized metric function for Bardeen and Hayward black holes.
We have also discussed the null, weak, and strong energy conditions of these solutions. It was found that by appropriately choosing the parameters, all the energy conditions hold outside the black hole’s outer event horizon.
In addition to analyzing the energy conditions, we have investigated the quasinormal mode of massive scalar perturbation in these black holes. The quasinormal frequencies were computed using the sixth-order Wentzel-Kramers-Brillouin (WKB) method with Padé approximation. Notably, all the imaginary parts of the frequencies were found to be negative.
Finally, we have provided an analysis in the eikonal limit. This analysis helps us understand the behavior of waves as they approach the black hole’s horizon.
Future Roadmap
Building on this research, there are several potential challenges and opportunities on the horizon:
1. Generalization to other black hole geometries
While this study focused on asymptotically flat, static spherically symmetric black holes, there is room for examining other geometries. Generalizing these findings to more complex black hole configurations could provide valuable insights into the behavior of black holes in different spacetime backgrounds.
2. Exploration of alternative gravity theories
The $f(R,T)$ gravity framework used in this study offers a fascinating approach to describing black holes. Exploring other alternative gravity theories and understanding their implications for black hole physics could lead to innovative results and potential breakthroughs in our understanding of gravity.
3. Investigation of other perturbation modes
While this study focused on the quasinormal mode of massive scalar perturbation, exploring the behavior of other perturbation modes, such as gravitational or electromagnetic perturbations, could provide a more complete understanding of the dynamics near black holes.
4. Experimental verification
One of the essential steps in validating the theoretical findings is experimental verification. Collaborating with observational astronomers and designing experiments to test the predictions made based on the constructed black hole solutions would provide further confirmation of the validity of these models.
In conclusion, this study has made significant progress in constructing and analyzing asymptotically flat, static spherically symmetric black holes in the context of $f(R,T)$ gravity coupled to nonlinear electrodynamics. The future roadmap outlined above presents exciting directions for further research and exploration in black hole physics.
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