by jsendak | Feb 11, 2025 | GR & QC Articles
arXiv:2502.05217v1 Announce Type: new
Abstract: In this paper, we consider the spherically symmetric gravitational collapse of isotropic matter undergoing dissipation in the form of heat flux, with a generalized Vaidya exterior, in the context of $f(R, T)$ gravity. Choosing $f(R, T)=R+2lambda T$, and applying the $f(R, T)$ junction conditions on the field equations for the interior and exterior regions, we have obtained matching conditions of the matter-Lagrangian and its derivatives across the boundary. The time of formation of singularity and the time of formation of apparent horizon have been determined and constraints on the integration constants are examined for which the final singularity is hidden behind the horizon.
In this paper, the authors study the gravitational collapse of isotropic matter with dissipation in the form of heat flux, using the framework of $f(R, T)$ gravity. They focus on the spherically symmetric case, with a generalized Vaidya exterior. The specific choice for the $f(R, T)$ function is $f(R, T)=R+2lambda T$, and the authors apply the $f(R, T)$ junction conditions to the field equations for the interior and exterior regions.
One of the main results of the study is the matching conditions of the matter-Lagrangian and its derivatives across the boundary. These matching conditions are important for a consistent description of the gravitational collapse process.
The authors then determine the time of formation of the singularity and the time of formation of the apparent horizon. They examine the constraints on the integration constants that lead to the singularity being hidden behind the horizon.
Roadmap for Readers
To further explore the topic of spherically symmetric gravitational collapse and its relation to $f(R, T)$ gravity, readers can follow the suggested roadmap:
1. Understand the basics of gravitational collapse
Before diving into the specific case of spherically symmetric collapse, it is important to have a solid understanding of the basics of gravitational collapse. Readers should familiarize themselves with concepts such as singularities, event horizons, and the different types of collapse scenarios.
2. Study the Vaidya metric and its application to gravitational collapse
The Vaidya metric is a useful tool for describing the gravitational collapse process. Readers should study the properties of the Vaidya metric and its application to modeling collapse scenarios. This will provide the necessary background for understanding the specific case considered in the paper.
3. Learn about $f(R, T)$ gravity
$f(R, T)$ gravity is a modified theory of gravity that includes additional terms in the gravitational action. Readers should familiarize themselves with the basic concepts of $f(R, T)$ gravity and its motivations. Understanding the field equations and the junction conditions will be crucial for comprehending the results presented in the paper.
4. Analyze the matching conditions derived in the paper
The matching conditions of the matter-Lagrangian and its derivatives across the boundary are an essential result of the study. Readers should carefully analyze these matching conditions and understand their implications for the physical description of the collapse process.
5. Explore the constraints on integration constants
The constraints on the integration constants, which determine whether the singularity is hidden behind the horizon, are an important aspect of the study. Readers should investigate the different constraints and their implications. This will provide insights into the behavior of collapsing systems in $f(R, T)$ gravity.
6. Consider other applications and extensions
Finally, readers can consider other applications and extensions of the results presented in the paper. This could include studying different matter models, exploring alternative $f(R, T)$ functions, or investigating the implications for black hole formation.
Challenges and Opportunities
While studying the spherically symmetric collapse in the context of $f(R, T)$ gravity opens up new avenues of research, several challenges and opportunities lie ahead:
- Theoretical Challenges: The theoretical analysis of gravitational collapse in modified gravity theories is a challenging task. Readers should be prepared to delve into advanced mathematical techniques and field equations.
- Experimental Verification: The predictions of $f(R, T)$ gravity for gravitational collapse need to be tested against observational data or laboratory experiments. The opportunities for experimental verification can lead to a deeper understanding of the theory.
- Extensions and Generalizations: The results obtained in this paper are specific to spherically symmetric collapse with a particular $f(R, T)$ function. Readers can explore extensions of the study to other geometries, matter models, or different choices of $f(R, T)$ functions.
- Connections to Other Fields: Gravitational collapse has connections to various fields, such as astrophysics and cosmology. Readers can explore the interdisciplinary aspects and implications of the results in this paper.
In summary, readers interested in the spherically symmetric gravitational collapse and its relation to $f(R, T)$ gravity should follow a roadmap that includes understanding the basics, studying the specific case presented in the paper, analyzing the derived matching conditions and constraints, and exploring further applications and extensions. Along the way, they will encounter theoretical challenges, opportunities for experimental verification, possibilities for generalizations, and connections to other fields.
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by jsendak | Nov 15, 2024 | GR & QC Articles
arXiv:2411.08921v1 Announce Type: new
Abstract: We construct equilibrium configurations for neutron stars using a specific $f(R,T)$ functional form, recently derived through gaussian process applied to measurements of the Hubble parameter. By construction, this functional form serves as an alternative explanation for cosmic acceleration, circumventing the cosmological constant problem. Here, we aim to examine its applicability within the stellar regime. In doing so, we seek to contribute to the modified gravity literature by applying the same functional form of a given gravity theory across highly distinct regimes. Our results demonstrate that equilibrium configurations of neutron stars can be obtained within this theory, with the energy density and maximum mass slightly exceeding those predicted by General Relativity. Additionally, we show that the value of some parameters in the $f(R,T)$ functional form must differ from those obtained in cosmological configurations, suggesting a potential scale-dependence for these parameters. We propose that further studies apply this functional form across different regimes to more thoroughly assess this possible dependence.
Summary: This article examines the applicability of a specific functional form of the $f(R,T)$ gravity theory, derived through gaussian process applied to measurements of the Hubble parameter, to equilibrium configurations of neutron stars. The results show that equilibrium configurations can be obtained within this theory, with slightly higher energy density and maximum mass compared to General Relativity. The study also suggests a potential scale-dependence for certain parameters in the functional form, indicating the need for further investigation across different regimes.
Introduction
The $f(R,T)$ functional form, derived through gaussian process applied to measurements of the Hubble parameter, provides an alternative explanation for cosmic acceleration and addresses the cosmological constant problem. This article aims to explore the applicability of this functional form within the stellar regime by studying equilibrium configurations of neutron stars.
Results
The study demonstrates that equilibrium configurations of neutron stars can be obtained within the $f(R,T)$ gravity theory. The energy density and maximum mass predicted by this theory slightly exceed those predicted by General Relativity. This suggests a potential modification to our understanding of gravity in the stellar regime.
Parameter Variation
The study also reveals that the values of certain parameters in the $f(R,T)$ functional form must differ from those obtained in cosmological configurations. This implies a potential scale-dependence of these parameters, which needs to be further investigated. Understanding the scale-dependence of these parameters is crucial for fully comprehending the implications of the $f(R,T)$ theory across different regimes.
Roadmap for Future Studies
- Further Studies: Future studies should apply the $f(R,T)$ functional form across different regimes to assess the potential scale-dependence of the theory’s parameters more thoroughly. This could involve examining other astrophysical objects, such as white dwarfs or black holes, to investigate whether the modifications observed in neutron stars are unique to this specific stellar regime.
- Parameter Exploration: Researchers should conduct extensive parameter exploration to determine the range of values that allow for consistent equilibrium configurations of neutron stars. This will help establish the validity of the $f(R,T)$ theory and refine our understanding of the scale-dependence of its parameters.
- Observational Tests: Observational tests should be designed to verify the predictions of the $f(R,T)$ theory in the stellar regime. This could involve comparing the observed properties of neutron stars with the theoretical predictions derived from the $f(R,T)$ functional form. Such observational tests will provide empirical evidence to support or refute the applicability of this theory.
Challenges and Opportunities
- Challenges: One of the main challenges is the complexity of the $f(R,T)$ theory, which requires careful parameterization and exploration. Additionally, obtaining observational data on neutron stars with sufficient accuracy and precision may pose a challenge.
- Opportunities: Successfully applying the $f(R,T)$ functional form across different regimes and validating its predictions would revolutionize our understanding of gravity. It could potentially lead to a unified theory of gravity that encompasses both cosmological and stellar phenomena. Furthermore, the potential scale-dependence of the theory’s parameters opens up avenues for new research and theoretical developments.
Conclusion
The results of this study demonstrate the viability of using the $f(R,T)$ functional form within the stellar regime to obtain equilibrium configurations of neutron stars. The slightly higher energy density and maximum mass compared to General Relativity indicate the need for further investigation into the scale-dependence of the theory’s parameters. Future studies should apply this functional form across different regimes, conduct parameter exploration, and design observational tests to fully assess the potential of the $f(R,T)$ theory and its implications for our understanding of gravity.
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by jsendak | Nov 1, 2024 | GR & QC Articles
arXiv:2410.23307v1 Announce Type: new
Abstract: Teleparallel description of gravity theories where the gravity is mediated through the tetrad field and consequent torsion provide an alternative route to explain the late time cosmic speed up issue. Generalization of the teleparallel gravity theory with different functional forms of the torsion scalar $T$ leads to $f(T)$ gravity. The role of scalar field played in addressing issues in cosmology and astrophysics has developed an interest in the inclusion of a scalar field along with an interaction potential in the action. Such a generalized gravity theory is dubbed as $f(T,phi)$ theory. We have explored such a gravity theory to reconstruct the interaction potential of the scalar field required for an extended matter bounce scenario. The cosmological implications of the reconstructed scalar field potential are studied considering two viable and well known functional forms of $f(T,phi)$. The energy conditions of these model are discussed to assess the viability of the cosmological models.
Recent research has explored the concept of teleparallel gravity theories as an alternative explanation for the late-time cosmic speed up issue. These theories involve the use of the tetrad field and consequent torsion to mediate gravity. A specific type of teleparallel gravity theory, known as $f(T)$ gravity, has been developed by generalizing the functional form of the torsion scalar $T$.
In this study, a further generalization of the teleparallel gravity theory is considered, incorporating a scalar field $phi$ and an interaction potential. This theory, known as $f(T,phi)$ theory, is explored to reconstruct the interaction potential of the scalar field that is required for an extended matter bounce scenario.
The reconstructed scalar field potentials are then analyzed in terms of their cosmological implications. Two viable and well-known functional forms of $f(T,phi)$ are considered, and the energy conditions of these models are discussed to assess their viability.
Roadmap for the future
1. Further exploration of $f(T)$ gravity
One potential future direction is to continue studying the properties and implications of $f(T)$ gravity theories. This could involve investigating different functional forms of the torsion scalar $T$ and analyzing their effects on the late-time cosmic speed up issue.
2. Investigation of additional scalar field potentials
Expanding on the current study, future research could explore alternative interaction potentials for the scalar field $phi$ in the $f(T,phi)$ theory. This could involve considering different functional forms and analyzing their impact on cosmological models.
3. Experimental confirmation
Another important step is to seek experimental confirmation or observational evidence for the predictions made by the $f(T,phi)$ theory. This could involve analyzing observational data, conducting laboratory experiments, or utilizing other experimental techniques to test the validity of the reconstructed scalar field potential.
4. Assessing the viability of cosmological models
Continued analysis of the energy conditions and other criteria for assessing the viability of cosmological models is crucial. Future research could focus on refining these assessments and applying them to a broader range of models to gain a better understanding of the viability of the $f(T,phi)$ theory.
Challenges and opportunities on the horizon
While the $f(T,phi)$ theory shows promise in addressing the late-time cosmic speed up issue and offering an alternative description of gravity, there are several challenges and opportunities to consider.
- Theoretical challenges: Developing a deeper theoretical understanding of the $f(T,phi)$ theory and its implications is essential for further progress. This may involve confronting the theory with other fundamental principles and theories in physics to ensure its consistency.
- Experimental challenges: Testing the predictions of the $f(T,phi)$ theory requires advanced experimental techniques and observational data. Experimentalists and observational astronomers will need to collaborate closely with theorists to design and carry out experiments that can confirm or refute the predictions of the theory.
- Bridging the gap between theory and observation: Establishing a clear connection between the theoretical framework of the $f(T,phi)$ theory and observational data is essential for its acceptance within the scientific community. Efforts should be made to communicate the theory’s predictions in a way that observational astronomers can test and verify.
- Interdisciplinary collaboration: The study of $f(T,phi)$ theory requires collaboration among researchers in different disciplines, including theoretical physics, cosmology, and observational astronomy. Encouraging interdisciplinary collaboration and communication is crucial for making progress in this field.
In conclusion, the $f(T,phi)$ theory offers a potential avenue for explaining the late-time cosmic speed up issue and provides an alternative description of gravity. Future research should focus on further exploring the theory, investigating alternative scalar field potentials, seeking experimental confirmation, and refining the assessments of cosmological models. However, several challenges, including theoretical and experimental hurdles, must be overcome to advance the understanding and acceptance of the $f(T,phi)$ theory.
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by jsendak | Sep 30, 2024 | GR & QC Articles
arXiv:2409.18160v1 Announce Type: new
Abstract: In this study, we present an approach $ f(R, G) $ gravity incorporating power law in $ G $. To study the cosmic evolution of the universe given by the reconstruction of the Hubble parameter given by $ E(z) = bigg( 1+frac{z(alpha+(1+z)^{beta})}{2 beta + 1} bigg)^{frac{3}{2 beta}} $. Subsequently, we use various recent observational datasets of OHD, Pantheon, and BAO to estimate the model parameters $ H_0,~alpha $, and $ beta $ applying the Markov Chain Monte Carlo (MCMC) technique in the emcee package to establish the validity of the model. In our findings, we observe that our model shows consistency with standard $ Lambda $CDM, transits from deceleration to acceleration, and enters the quintessence region in late times. The cosmological model satisfies necessary energy constraints, simultaneously violating the strong energy condition (SEC), indicating a repulsive nature and consistent with accelerated expansion. The cosmic evolution of the Hawking temperature and the total entropy for the various observational datasets also show the validity of the model. Thus, our established model demonstrates sufficient potential for explicitly describing cosmological models.
Examining the Conclusions of the Study on $f(R, G)$ Gravity
Introduction
In this study, the researchers propose an approach to $f(R, G)$ gravity by incorporating power law in $G$. They use the reconstruction of the Hubble parameter given by $E(z) = bigg( 1+frac{z(alpha+(1+z)^{beta})}{2 beta + 1} bigg)^{frac{3}{2 beta}}$ to investigate the cosmic evolution of the universe. The validity of the model is then assessed using various recent observational datasets and the Markov Chain Monte Carlo (MCMC) technique.
Key Findings
The researchers’ findings indicate that their proposed $f(R, G)$ gravity model is consistent with the standard $Lambda$CDM model. The model also exhibits a transition from deceleration to acceleration and enters the quintessence region in late times, which aligns with the accelerated expansion observed in the universe. Additionally, the model satisfies necessary energy constraints and violates the strong energy condition (SEC), suggesting a repulsive nature that supports accelerated expansion.
The cosmic evolution of the Hawking temperature and the total entropy, as derived from various observational datasets, also confirm the validity of the proposed model.
Future Roadmap: Challenges and Opportunities
1. Further Validation and Fine-Tuning
Although the proposed $f(R, G)$ gravity model demonstrates consistency with current observations and exhibits several desirable characteristics, further validation is necessary. Future studies could aim to test the model using additional observational datasets and compare its predictions with observational data from different cosmological probes. Fine-tuning of the model parameters may be required to better align with observational constraints.
2. Extending the Model
To enhance the usefulness and applicability of the model, researchers could extend its capabilities. For example, including additional components such as dark matter and dark energy could provide a more comprehensive description of the universe’s cosmic evolution. Exploring the effects of other cosmological parameters and their interactions within the model would help uncover deeper insights into the nature of the universe.
3. Exploring Alternative Gravity Models
Although the proposed $f(R, G)$ gravity model shows promising results, there are other alternative gravity models worth exploring. Researchers could investigate other modified gravity theories, such as $f(R)$ or $f(T)$ gravity, to compare their predictions and constraints with the $f(R, G)$ gravity model. This exploration would provide a broader understanding of the possibilities in describing the cosmic evolution of the universe.
4. Implications for Cosmological Models
The established $f(R, G)$ gravity model opens up avenues for explicitly describing cosmological models. Future research could focus on utilizing the model to study various cosmological phenomena, such as the formation of large-scale structures, the growth of cosmic voids, or the behavior of gravitational waves. By exploring these implications, researchers can further investigate the model’s validity and uncover new insights into the workings of the universe.
5. Technological Advancements
Advancements in observational techniques and technology will play a crucial role in refining and validating the proposed $f(R, G)$ gravity model. Future observations from upcoming telescopes and experiments, such as the James Webb Space Telescope and the Large Synoptic Survey Telescope, will provide more precise and detailed data. Leveraging these advancements will allow researchers to better constrain the model’s parameters and strengthen its predictions.
Conclusion
The study on $f(R, G)$ gravity presents a promising approach that incorporates a power law in $G$ to describe the cosmic evolution of the universe. The model has been found to be consistent with current observations, exhibiting characteristics such as a transition from deceleration to acceleration and violation of the strong energy condition. However, further validation, fine-tuning, and exploration of alternative gravity models are crucial for refining our understanding of the universe’s evolution.
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by jsendak | Sep 27, 2024 | GR & QC Articles
arXiv:2409.17193v1 Announce Type: new
Abstract: We investigate the cosmic evolution of the Universe across different cosmological epochs in exponential Weyl-type $f(Q, T)$ gravity model. The theoretical analysis involves a detailed dynamical system approach, where we define dimensionless variables and derive a system of linear differential equations to identify critical points corresponding to the radiation, matter and de Siter phase. The findings show the transition from deceleration to acceleration phase, with stable and unstable critical points characterizing different phases of the evolution. In the second approach, we validate the theoretical predictions by using observational data from Cosmic Chronometers ($CC$) and $Pantheon^+$ datasets. We constrain the Hubble parameter and subsequently analysed the other cosmological and geometrical parameters. In this approach also, the transition from deceleration to acceleration has been confirmed, with the equation of state (EoS) parameter approaching $Lambda$CDM at late times. The further validate this, we present the behaviour of state finder pair. We obtain the age of the Universe $13.81$ Gyr according to $CC$ data and $13.96$ Gyr with the $Pantheon^+$ dataset. The model behaviour in both the approaches shows strong agreement in the late-time behavior of the Universe. The evolutionary behaviour of Hubble parameter and distance modulus, reinforcing the reliability of the Weyl-type $f(Q, T)$ gravity model in describing the expansion history of Universe.
In this study, the authors investigate the cosmic evolution of the Universe using the exponential Weyl-type $f(Q, T)$ gravity model. They employ a dynamical system approach, deriving a system of linear differential equations and identifying critical points corresponding to different cosmological epochs.
By analyzing the theoretical predictions, the researchers find a transition from a deceleration phase to an acceleration phase, with stable and unstable critical points characterizing different phases of the evolution. To validate their findings, they use observational data from Cosmic Chronometers ($CC$) and $Pantheon^+$ datasets.
Using the observational data, the authors constrain the Hubble parameter and analyze other cosmological and geometrical parameters. These analyses confirm the transition from deceleration to acceleration, with the equation of state (EoS) parameter approaching $Lambda$CDM at late times.
To further validate their results, the authors present the behavior of the state finder pair. They obtain an age of the Universe of .81$ Gyr according to the $CC$ data and .96$ Gyr with the $Pantheon^+$ dataset. The model’s behavior in both approaches shows strong agreement in the late-time behavior of the Universe, reinforcing the reliability of the Weyl-type $f(Q, T)$ gravity model in describing the expansion history of the Universe.
Future Roadmap
Challenges
- One of the potential challenges that researchers may face is obtaining more precise observational data. The accuracy of the model’s predictions heavily relies on the quality and quantity of the data used for validation.
- Further investigation is needed to explore the limitations of the Weyl-type $f(Q, T)$ gravity model and its applicability beyond the current observations. This will require more advanced theoretical analyses and simulations.
- Understanding the physical interpretation of the critical points identified in the dynamical system approach is another challenge that researchers might encounter. Elucidating the implications of these critical points could provide deeper insights into the cosmic evolution.
Opportunities
- As new observational techniques and instruments are developed, researchers will have the opportunity to collect more precise and extensive data sets. This will enable more accurate validation of the Weyl-type $f(Q, T)$ gravity model and potentially uncover new phenomena in the cosmic evolution.
- Exploring alternative gravity models and comparing them with the Weyl-type $f(Q, T)$ model could provide valuable insights into the nature of the Universe’s expansion. This could open up new avenues for understanding fundamental physics and the nature of dark energy.
- Collaboration between theorists and experimentalists will be crucial in advancing our understanding of the cosmic evolution. By combining theoretical analyses with cutting-edge observations, researchers can refine and improve the models, leading to a more comprehensive understanding of the Universe.
Conclusion
This study highlights the cosmic evolution of the Universe using the exponential Weyl-type $f(Q, T)$ gravity model. The theoretical analysis and observational data validation both confirm a transition from a deceleration phase to an acceleration phase. The model’s agreement with the late-time behavior of the Universe, as well as the obtained age estimates, reinforce the reliability of the Weyl-type $f(Q, T)$ gravity model. However, further investigations, improvements in observational data, and collaboration between different branches of physics are necessary to overcome challenges and unlock new opportunities for understanding the cosmic evolution.
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