by jsendak | Jan 15, 2024 | GR & QC Articles
We investigate gravitational waves in the $f(Q)$ gravity, i.e., a geometric
theory of gravity described by a non-metric compatible connection, free from
torsion and curvature, known as symmetric-teleparallel gravity. We show that
$f(Q)$ gravity exhibits only two massless and tensor modes. Their polarizations
are transverse with helicity equal to two, exactly reproducing the plus and
cross tensor modes typical of General Relativity. In order to analyze these
gravitational waves, we first obtain the deviation equation of two trajectories
followed by nearby freely falling point-like particles and we find it to
coincide with the geodesic deviation of General Relativity. This is because the
energy-momentum tensor of matter and field equations are Levi-Civita
covariantly conserved and, therefore, free structure-less particles follow,
also in $f(Q)$ gravity, the General Relativity geodesics. Equivalently, it is
possible to show that the curves are solutions of a force equation, where an
extra force term of geometric origin, due to non-metricity, modifies the
autoparallel curves with respect to the non-metric connection. In summary,
gravitational waves produced in non-metricity-based $f(Q)$ gravity behave as
those in torsion-based $f(T)$ gravity and it is not possible to distinguish
them from those of General Relativity only by wave polarization measurements.
This shows that the situation is different with respect to the curvature-based
$f(R)$ gravity where an additional scalar mode is always present for $f(R)neq
R$.
The Future Roadmap for Gravitational Waves in $f(Q)$ Gravity
Introduction
In this article, we explore the behavior of gravitational waves in $f(Q)$ gravity, a geometric theory of gravity described by a non-metric compatible connection known as symmetric-teleparallel gravity. We analyze the properties of these waves and compare them to gravitational waves in General Relativity.
Two Massless and Tensor Modes
Our findings reveal that $f(Q)$ gravity exhibits only two massless and tensor modes. These modes have transverse polarizations with helicity equal to two, which is consistent with the plus and cross tensor modes observed in General Relativity.
Geodesic Deviation and Trajectory Analysis
To further study these gravitational waves, we examine the deviation equation of two nearby freely falling point-like particles. Surprisingly, we discover that this deviation equation coincides with the geodesic deviation observed in General Relativity. This suggests that free particles without any structure follow the geodesics of General Relativity even in $f(Q)$ gravity.
Force Equation and Geometric Origin
Alternatively, we can interpret the particle trajectories as solutions of a force equation. In this equation, an extra force term of geometric origin arises due to non-metricity. This modification to the autoparallel curves introduced by the non-metric connection showcases how non-metricity affects the behavior of gravitational waves in $f(Q)$ gravity.
Comparison with Torsion and Curvature-Based Gravity Theories
We compare the behavior of gravitational waves in $f(Q)$ gravity to torsion-based $f(T)$ gravity and curvature-based $f(R)$ gravity. Our analysis reveals that gravitational waves in $f(Q)$ gravity behave similarly to those in $f(T)$ gravity, where wave polarization measurements alone cannot distinguish them from waves in General Relativity. However, this differs from gravitational waves in $f(R)$ gravity, where an additional scalar mode is always present for $f(R)neq R$.
Conclusion and Future Challenges
This research demonstrates the similarity between gravitational waves in $f(Q)$ gravity and General Relativity. The absence of additional modes and the reproduction of the plus and cross tensor modes suggest that $f(Q)$ gravity may provide a consistent framework for describing gravitational waves. However, further investigation is needed to fully understand the implications and potential differences of gravitational wave behavior in $f(Q)$ gravity compared to General Relativity. Continued research in this area may uncover new challenges and opportunities, ultimately shaping the future of gravitational wave study.
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by jsendak | Jan 12, 2024 | GR & QC Articles
This study aims to investigate the strong gravitational lensing effects in
$f(T)$ gravity. We present the theoretical analytic expressions for the lensing
effects in $f(T)$ gravity, including deflection angle, magnification, and time
delay. On this basis, we also take the plasma lensing effect into
consideration. We compare the lensing effects between the General Relativity in
a vacuum environment and the $f(T)$ gravity in a plasma environment. From a
strongly lensed fast radio burst, the results indicate that in a plasma
environment, General Relativity and $f(T)$ gravity can generate
indistinguishable image positions, but the magnification and time delay on
these positions are significantly different, which can be distinguished by
current facilities in principle. Therefore, the discrepancies between
observational results and theoretical expectations can serve as clues for a
modified gravity theory and provide constraints on $f(T)$ gravity.
The study investigates the strong gravitational lensing effects in $f(T)$ gravity and presents theoretical analytic expressions for these effects, including deflection angle, magnification, and time delay. The plasma lensing effect is also taken into consideration. By comparing the lensing effects between General Relativity in a vacuum environment and $f(T)$ gravity in a plasma environment, the study finds that in a plasma environment, General Relativity and $f(T)$ gravity can generate indistinguishable image positions. However, the magnification and time delay on these positions are significantly different, which can be potentially distinguished by current facilities. This suggests that discrepancies between observational results and theoretical expectations can provide clues for a modified gravity theory and constraints on $f(T)$ gravity.
Future Roadmap
To further explore and validate the findings of this study, future research can focus on the following areas:
1. Experimental Verification
Experimental observations using advanced telescopes and facilities should be conducted to test the differences in magnification and time delay predicted by General Relativity and $f(T)$ gravity in a plasma environment. By comparing the observations with the theoretical expectations, researchers can gauge the validity of $f(T)$ gravity in describing strong gravitational lensing effects.
2. Improved Models
Developing more sophisticated models for $f(T)$ gravity and plasma lensing effects could enhance our understanding of the observed discrepancies. These models should consider additional factors that may influence the lensing effects, such as the density and composition of the plasma. Improvements to the theoretical analytic expressions presented in this study may also be necessary.
3. Theoretical Framework
A deeper theoretical analysis may uncover the underlying reasons for the significant differences in magnification and time delay between General Relativity and $f(T)$ gravity in a plasma environment. Exploring the theoretical framework of $f(T)$ gravity and its relation to plasma lensing could provide valuable insights into the nature of gravity and its behavior in various environments.
4. Constraints on $f(T)$ Gravity
Utilizing the discrepancies between observational results and theoretical expectations as constraints on $f(T)$ gravity can guide the development and modification of gravity theories. Further investigations should aim to establish more precise constraints and explore the range of applicability for $f(T)$ gravity as a potential alternative to General Relativity.
Challenges and Opportunities
While this research opens up new possibilities and directions for studying gravitational lensing in $f(T)$ gravity, several challenges and opportunities lie ahead:
- Data Collection: Obtaining sufficient and high-quality observational data, especially of strongly lensed fast radio bursts, will be crucial for testing the predictions of $f(T)$ gravity and comparing them with General Relativity.
- Technological Advancements: Advancements in telescope technology, data analysis algorithms, and computational power are needed to accurately measure the magnification and time delay of lensed images, as well as to differentiate between the effects of General Relativity and $f(T)$ gravity.
- Theoretical Complexity: The theoretical analysis of $f(T)$ gravity and plasma lensing is a complex task that requires advanced mathematical tools and computational methods. Overcoming these challenges will require interdisciplinary collaborations and expertise.
- Scientific Exploration: Further exploration of modified gravity theories, such as $f(T)$ gravity, can lead to breakthroughs in our understanding of the fundamental nature of gravity, expanding our knowledge of the Universe and its behavior under extreme conditions.
In conclusion, the study demonstrates that $f(T)$ gravity in a plasma environment can produce distinguishable differences in magnification and time delay compared to General Relativity. The observed discrepancies between theoretical expectations and observational results can serve as valuable clues for modified gravity theories and provide constraints on $f(T)$ gravity. To advance this field of research, future efforts should focus on experimental verification, improved models, deeper theoretical analysis, and utilizing discrepancies as constraints.
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by jsendak | Jan 7, 2024 | GR & QC Articles
The Teleparallel Theory is equivalent to General Relativity, but whereas in
the latter gravity has to do with curvature, in the former gravity is described
by torsion. As is well known, there is in the literature a host of alternative
theories of gravity, among them the so called extended theories, in which
additional terms are added to the action, such as for example in the $f(R)$ and
$f(T)$ gravities, where $R$ is the Ricci scalar and $T$ is the scalar torsion,
respectively. One of the ways to probe alternative gravity is via compact
objects. In fact, there is in the literature a series of papers on compact
objects in $f(R)$ and $f(T)$ gravity. In particular, there are several papers
that consider $f(T) = T + xi T^2$, where $xi$ is a real constant. In this
paper, we generalise such extension considering compact stars in $f (T ) = T +
xi T^beta$ gravity, where $xi$ and $beta$ are real constants and looking
out for the implications in their maximum masses and compactness in comparison
to the General Relativity. Also, we are led to constrain the $beta$ parameter
to positive integers which is a restriction not imposed by cosmology.
Exploring Compact Objects in Extended Theories of Gravity
In recent years, there has been a surge of interest in alternative theories of gravity that go beyond General Relativity. These extended theories introduce additional terms to the action, offering new ways to describe gravity. One such theory is the Teleparallel Theory, where gravity is described by torsion rather than curvature.
Among the various extended theories, $f(R)$ and $f(T)$ gravities have gained significant attention. These theories involve adding extra terms to the action, involving the Ricci scalar $R$ and scalar torsion $T$, respectively.
A promising avenue for probing alternative gravity theories is through the study of compact objects. Compact stars, in particular, have been extensively explored in the context of $f(R)$ and $f(T)$ gravity. One specific extension that has been investigated is $f(T) = T + xi T^2$, with $xi$ being a real constant.
In this paper, we aim to generalize this extension by considering compact stars in $f(T) = T + xi T^beta$ gravity. Here, $xi$ and $beta$ are real constants that allow us to explore the implications on the maximum masses and compactness of these objects in comparison to General Relativity.
An interesting aspect that arises from our investigation is the restriction imposed on the $beta$ parameter. We find that it must be constrained to positive integers, which is not a restriction enforced by cosmology.
Roadmap for Future Research:
- Further investigate and refine the generalized extension $f(T) = T + xi T^beta$ gravity theory.
- Explore the implications of different values of $beta$ on the maximum masses and compactness of compact stars in $f(T)$ gravity.
- Compare the results obtained in $f(T)$ gravity with those predicted by General Relativity to identify any deviations.
- Consider the implications of the restricted $beta$ parameter on the overall consistency and validity of the theory.
- Extend the study to other compact objects, such as neutron stars, to gain a more comprehensive understanding of the behavior of $f(T)$ gravity.
Challenges and Opportunities:
While this research presents exciting opportunities to explore alternative theories of gravity and their implications on compact objects, there are several challenges to overcome:
- The complexity of the mathematical formalism involved in $f(T)$ theories requires careful analysis and numerical calculations.
- Validating the predictions of $f(T)$ gravity through observational data from compact objects poses a significant challenge due to the limited availability of precise measurements.
- Ensuring consistency with cosmological observations and constraints while studying compact stars in $f(T)$ gravity is essential to assess the viability of the theory.
In conclusion, the investigation of compact objects in extended theories of gravity, specifically $f(T) = T + xi T^beta$ gravity, offers new avenues for understanding the nature of gravity. By exploring the implications on maximum masses and compactness, we can gain insights into deviations from General Relativity. However, addressing challenges related to mathematical complexity, observational validation, and cosmological consistency will be crucial for advancing our understanding of alternative gravity theories.
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by jsendak | Jan 4, 2024 | GR & QC Articles
Mergers of binary compact objects, accompanied with electromagnetic (EM)
counterparts, offer excellent opportunities to explore varied cosmological
models, since gravitational waves (GW) and EM counterparts always carry the
information of luminosity distance and redshift, respectively. $f(T)$ gravity,
which alters the background evolution and provides a friction term in the
propagation of GW, can be tested by comparing the modified GW luminosity
distance with the EM luminosity distance. Considering the third-generation
gravitational-wave detectors, Einstein Telescope and two Cosmic Explorers, we
simulate a series of GW events of binary neutron stars (BNS) and
neutron-star-black-hole (NSBH) binary with EM counterparts. These simulations
can be used to constrain $f(T)$ gravity (specially the Power-law model
$f(T)=T+alpha(-T)^beta$ in this work) and other cosmological parameters, such
as $beta$ and Hubble constant. In addition, combining simulations with current
observations of type Ia supernovae and baryon acoustic oscillations, we obtain
tighter limitations for $f(T)$ gravity. We find that the estimated precision
significantly improved when all three data sets are combined ($Delta beta
sim 0.03$), compared to analyzing the current observations alone ($Delta
beta sim 0.3$). Simultaneously, the uncertainty of the Hubble constant can be
reduced to approximately $1%$.
Mergers of binary compact objects, such as binary neutron stars and neutron-star-black-hole binaries, with electromagnetic counterparts provide a unique opportunity to explore cosmological models. Gravitational waves and electromagnetic counterparts carry information about the luminosity distance and redshift, respectively, allowing us to test theories such as $f(T)$ gravity.
$f(T)$ gravity modifies the background evolution and introduces a friction term in the propagation of gravitational waves. By comparing the modified gravitational wave luminosity distance with the electromagnetic luminosity distance, we can constrain $f(T)$ gravity and other cosmological parameters such as the Power-law model $f(T)=T+alpha(-T)^beta$ and the Hubble constant.
To investigate $f(T)$ gravity, we can utilize the next-generation gravitational-wave detectors: Einstein Telescope and two Cosmic Explorers. Through simulations of binary neutron stars and neutron-star-black-hole binaries with electromagnetic counterparts, we can obtain constraints on $f(T)$ gravity. Combined with current observations of type Ia supernovae and baryon acoustic oscillations, we can further refine these limitations.
By combining all three data sets (gravitational waves, type Ia supernovae, and baryon acoustic oscillations), we can significantly improve the precision of our estimations for $f(T)$ gravity. The uncertainty in $beta$ decreases from $Delta beta sim 0.3$ when analyzing only current observations, to $Delta beta sim 0.03$ when combining all data sets together. Additionally, the uncertainty in the Hubble constant can be reduced to approximately %$.
Future Roadmap
1. Gather observational data
- Continue observing binary compact object mergers and their electromagnetic counterparts
- Collect data on type Ia supernovae and baryon acoustic oscillations
2. Simulate gravitational-wave events
- Create simulations of binary neutron stars and neutron-star-black-hole binaries with electromagnetic counterparts
- Use the simulations to analyze the gravitational wave luminosity distance and compare it to the electromagnetic luminosity distance
- Constrain $f(T)$ gravity and other cosmological parameters
3. Combine data sets for tighter constraints
- Combine the simulated gravitational-wave events with the observational data from type Ia supernovae and baryon acoustic oscillations
- Analyze the combined data set to refine the limitations on $f(T)$ gravity
4. Evaluate precision improvements
- Assess the precision improvements in estimating $beta$, the Hubble constant, and other cosmological parameters
- Compare the results obtained from analyzing current observations alone to those obtained from combining all three data sets
- Determine the level of uncertainty reduction achieved in each case
5. Explore applications and implications
- Analyze the implications of tighter constraints on $f(T)$ gravity and its effects on cosmological models
- Investigate potential applications of $f(T)$ gravity in understanding the nature of dark energy and the expansion of the universe
6. Further developments and challenges
- Continued improvements in observational techniques and gravitational-wave detection technology can provide more precise data for future analyses
- Accounting for systematic uncertainties and potential biases in the data sets is crucial for accurate constraints
- Exploring alternative theories and models beyond $f(T)$ gravity that can be tested using similar methodologies
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by jsendak | Dec 31, 2023 | GR & QC Articles
We use galaxy-galaxy lensing data to test general relativity and $f(T)$
gravity at galaxies scales. We consider an exact spherically symmetric solution
of $f(T)$ theory which is obtained from an approximate quadratic correction,
and thus it is expected to hold for every realistic deviation from general
relativity. Quantifying the deviation by a single parameter $Q$, and following
the post-Newtonian approximation, we obtain the corresponding deviation in the
gravitational potential, shear component, and effective surface density (ESD)
profile. We used five stellar mass samples and divided them into blue and red
to test the model dependence on galaxy color, and we modeled ESD profiles using
Navarro-Frenk-White (NFW) profiles. Based on the group catalog from the Sloan
Digital Sky Survey Data Release 7 (SDSS DR7) we finally extract
$Q=2.138^{+0.952}_{-0.516}times 10^{-5},$Mpc$^{-2}$ at $1sigma$ confidence.
This result indicates that $f(T)$ corrections on top of general relativity are
favored. Finally, we apply information criteria, such as the AIC and BIC ones,
and although the dependence of $f(T)$ gravity on the off-center effect implies
that its optimality needs to be carefully studied, our analysis shows that
$f(T)$ gravity is more efficient in fitting the data comparing to general
relativity and $Lambda$CDM paradigm, and thus it offers a challenge to the
latter.
Based on the analysis of galaxy-galaxy lensing data, this study examines the validity of general relativity and $f(T)$ gravity at the scale of galaxies. The $f(T)$ theory is a spherically symmetric solution obtained from a quadratic correction, which is expected to hold for realistic deviations from general relativity. By quantifying the deviation using a parameter $Q$ and employing the post-Newtonian approximation, the study investigates the effects of $f(T)$ theory on the gravitational potential, shear component, and effective surface density profiles.
To test the model’s dependence on galaxy color, the study divides the samples into blue and red categories and models the effective surface density profiles using Navarro-Frenk-White (NFW) profiles. Using the group catalog from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), the study extracts a value of $Q=2.138^{+0.952}_{-0.516}times 10^{-5},$Mpc$^{-2}$ at sigma$ confidence. This result suggests that $f(T)$ corrections on top of general relativity are preferred.
The study further applies information criteria such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). While acknowledging that the optimality of $f(T)$ gravity requires careful examination due to its dependence on the off-center effect, the analysis demonstrates that $f(T)$ gravity provides a better fit to the data compared to both general relativity and the $Lambda$CDM paradigm. Therefore, it poses a challenge to the latter.
Future Roadmap: Challenges and Opportunities
The results of this study open up several avenues for future research in the field of gravity theories and cosmology. Here is a roadmap that outlines potential challenges and opportunities:
1. Further Investigation of $f(T)$ Theory
The $f(T)$ theory, with its quadratic correction, has shown promise in explaining deviations from general relativity. However, its optimality needs to be thoroughly examined, especially in terms of the off-center effect. Researchers should conduct in-depth studies to understand the limitations and potential improvements of $f(T)$ gravity.
2. Testing the Model across Different Galaxy Types
While this study considered the dependence of $f(T)$ gravity on galaxy color by dividing the samples into blue and red, future research should explore the applicability of the model to other galaxy types as well. Investigating the effects of $f(T)$ gravity on a wider range of galaxies can provide valuable insights into its universality and suitability for different astrophysical environments.
3. Refining the Measurement of $Q$ Parameter
Improving the accuracy and precision of the measurement of the $Q$ parameter is crucial for a more robust evaluation of $f(T)$ gravity. Researchers should develop innovative observational techniques and data analysis methods to obtain more precise estimates of this parameter.
4. Comparison with Other Gravity Theories
While $f(T)$ gravity has shown advantages over general relativity and $Lambda$CDM paradigm based on the current analysis, it is important to compare it with other alternative gravity theories as well. Investigating how $f(T)$ gravity fares against competing theories can provide a comprehensive understanding of its strengths and weaknesses.
5. Incorporating Cosmological Observations
Expanding the scope of research to include cosmological observations can enhance our understanding of how $f(T)$ gravity operates on larger scales. By investigating the compatibility of $f(T)$ theory with cosmological data, researchers can assess its validity in a broader cosmological context.
In conclusion, the results of this study indicate that $f(T)$ gravity provides a more efficient fit to galaxy-galaxy lensing data compared to general relativity and $Lambda$CDM paradigm. However, further investigations are needed to fully understand the limitations and potential applications of $f(T)$ gravity. Through ongoing research and the exploration of new avenues, scientists can continue to push the boundaries of our understanding of gravity and its implications for our universe.
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