by jsendak | Jan 10, 2024 | GR & QC Articles
The nature of dark energy is one of the fundamental problems in cosmology.
Introduced to explain the apparent acceleration of the Universe’s expansion,
its origin remains to be determined. In this paper, we illustrate a result that
may significantly impact understanding the relationship between dark energy and
structure formation in the late-epoch Universe. Our analysis exploits a
scale-dependent energy functional, initially developed for image visualization,
to compare the physical and geometrical data that distinct cosmological
observers register on their celestial spheres. In the presence of late-epoch
gravitational structures, this functional provides a non-perturbative technique
that allows the standard Friedmann-Lema^itre-Robertson-Walker (FLRW) observer
to evaluate a measurable, scale-dependent difference between the idealized FLRW
past light cone and the physical light cone. From the point of view of the FLRW
observer, this difference manifests itself as a redshift-dependent correction
$Lambda^{(corr)}(z)$ to the FLRW cosmological constant $Lambda^{(FLRW)}$. At
the scale where cosmological expansion couples with the local virialized
dynamics of gravitational structures, we get $Lambda^{(corr)}(z)sim
10^{-52},m^{-2}$, indicating that the late-epoch structures induce an
effective cosmological constant that is of the same order of magnitude as the
assumed value of the FLRW cosmological constant, a result that may lead to an
interpretative shift in the very role of dark energy.
The Nature of Dark Energy and its Relationship to Structure Formation
The nature of dark energy is a fundamental question in cosmology. It was introduced to explain the apparent acceleration of the Universe’s expansion, but its origin is still unknown. In this paper, we present a result that could significantly impact our understanding of the relationship between dark energy and structure formation in the late-epoch Universe.
An Energy Functional for Comparing Cosmological Observer Data
Our analysis utilizes a scale-dependent energy functional, which was initially developed for image visualization. We use this functional to compare the physical and geometrical data that cosmological observers detect on their celestial spheres.
The Impact of Gravitational Structures
When late-epoch gravitational structures are present, our energy functional provides a non-perturbative technique. This technique allows the standard Friedmann-Lema^itre-Robertson-Walker (FLRW) observer to evaluate a measurable, scale-dependent difference between the idealized FLRW past light cone and the physical light cone.
A Redshift-Dependent Correction
From the perspective of the FLRW observer, this difference manifests as a redshift-dependent correction to the FLRW cosmological constant. This correction is denoted as $Lambda^{(corr)}(z)$.
Implications of the Correction
At the scale where cosmological expansion couples with the local virialized dynamics of gravitational structures, we find that $Lambda^{(corr)}(z)sim 10^{-52},m^{-2}$. This indicates that the late-epoch structures induce an effective cosmological constant that is comparable in magnitude to the assumed value of the FLRW cosmological constant.
A Potential Interpretative Shift
This result may lead to a shift in the interpretation of the role of dark energy. The fact that the late-epoch structures induce a cosmological constant of the same order of magnitude as the assumed value suggests that the role of dark energy may need to be reevaluated.
Future Roadmap: Challenges and Opportunities
Challenges
- Determining the exact nature and origin of dark energy remains a challenge in cosmology.
- Further validating the scale-dependent energy functional for comparing cosmological observer data.
- Investigating the implications of the redshift-dependent correction and its effects on other cosmological models.
Opportunities
- The potential for a deeper understanding of the relationship between dark energy and structure formation in the late-epoch Universe.
- The opportunity to refine and expand upon the non-perturbative technique provided by the scale-dependent energy functional.
- The possibility of new interpretations and theories regarding the role of dark energy based on the similarity in magnitude between the induced cosmological constant and the assumed value.
In summary, this research highlights a significant result in understanding the connection between dark energy and structure formation. However, further investigation and validation are needed to fully grasp its implications and potential impact on our current understanding of cosmology.
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by jsendak | Jan 10, 2024 | GR & QC Articles
Starting from Post-Newtonian predictions for a system of $N$ infalling masses
from the infinite past, we formulate and solve a scattering problem for the
system of linearised gravity around Schwarzschild as introduced in [DHR19]. The
scattering data are posed on a null hypersurface $mathcal C$ emanating from a
section of past null infinity $mathcal I^-$, and on the part of $mathcal I^-$
that lies to the future of this section: Along $mathcal C$, we implement the
Post-Newtonian theory-inspired hypothesis that the gauge-invariant components
of the Weyl tensor $alpha$ and $underline{alpha}$ (a.k.a. $Psi_0$ and
$Psi_4$) decay like $r^{-3}$, $r^{-4}$, respectively, and we exclude incoming
radiation from $mathcal I^-$ by demanding the News function to vanish along
$mathcal I^-$.
We also show that compactly supported gravitational perturbations along
$mathcal I^-$ induce very similar data, with $alpha$, $underline{alpha}$
decaying like $r^{-3}$, $r^{-5}$ along $mathcal C$.
After constructing the unique solution to this scattering problem, we provide
a complete analysis of the asymptotic behaviour of projections onto fixed
spherical harmonic number $ell$ near spacelike $i^0$ and future null infinity
$mathcal I^+$. Using our results, we also give constructive corrections to
popular historical notions of asymptotic flatness such as Bondi coordinates or
asymptotic simplicity. In particular, confirming earlier heuristics due to
Damour and Christodoulou, we find that the peeling property is violated both
near $mathcal I^-$ and near $mathcal I^+$, with e.g. $alpha$ near $mathcal
I^+$ only decaying like $r^{-4}$ instead of $r^{-5}$. We also find that the
resulting solution decays slower towards $i^0$ than often assumed, with
$alpha$ decaying like $r^{-3}$ towards $i^0$.
The issue of summing up the fixed angular mode estimates in $ell$ is dealt
with in forthcoming work.
Conclusions and Future Roadmap
Conclusions:
- The article presents a scattering problem for a system of linearized gravity around Schwarzschild.
- The scattering data are posed on a null hypersurface emanating from past null infinity.
- The gauge-invariant components of the Weyl tensor decay along the null hypersurface.
- Gravitational perturbations along past null infinity induce similar data.
- A unique solution to the scattering problem is constructed.
- An analysis of the asymptotic behavior of projections onto fixed spherical harmonic number is provided.
- Corrections to popular historical notions of asymptotic flatness are given.
- The peeling property is found to be violated near both past and future null infinity.
- The resulting solution decays slower towards spacelike infinity than previously assumed.
Future Roadmap:
- Further work is needed to address the issue of summing up the fixed angular mode estimates in ell.
- Explore and develop the implications of the constructed solution to other areas of study.
- Investigate the impact of violating the peeling property near past and future null infinity on gravitational phenomena.
- Study the consequences of slower decay towards spacelike infinity on the understanding of black hole dynamics.
- Continuously compare and refine the corrections to asymptotic flatness notions, such as Bondi coordinates or asymptotic simplicity.
Overall, the article provides valuable insights into the behavior of a system of linearized gravity around Schwarzschild and its implications for the understanding of asymptotic flatness and gravitational perturbations. It opens up avenues for further research and invites exploration of the consequences of violating the peeling property and slower decay towards spacelike infinity.
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by jsendak | Jan 10, 2024 | GR & QC Articles
We present an analytic frequency-domain gravitational waveform model for an
inspiraling binary whose center-of-mass undergoes a small acceleration, assumed
to be constant during the detection, such as when it orbits a distant tertiary
mass. The center-of-mass acceleration along the line of sight is incorporated
as a new parameter that perturbs the standard TaylorF2 model. We calculate the
wave phase to 3rd post-Newtonian order and first order in the acceleration. It
is shown that acceleration most significantly modifies the wave phase in the
low frequency portion of the signal, so ground-based detectors with a good
sensitivity at low frequencies are the most effective at detecting this effect.
We present a Fisher information calculation to quantify the detectability of
this effect at advanced LIGO A Plus, Cosmic Explorer, and Einstein Telescope
over the mass range of neutron stars and stellar-mass black holes, and discuss
degeneracy between acceleration and other parameters. We also determine the
parameter space where the acceleration is large enough that the wave phase
model would have to be extended to nonlinear orders in the acceleration.
Conclusions:
- An analytic frequency-domain gravitational waveform model for an inspiraling binary with a small constant acceleration has been developed.
- Acceleration significantly modifies the wave phase in the low-frequency portion of the signal.
- Ground-based detectors with good sensitivity at low frequencies are most effective at detecting this acceleration effect.
- A Fisher information calculation has been used to quantify the detectability of this effect at advanced LIGO A Plus, Cosmic Explorer, and Einstein Telescope.
- The analysis considers the mass range of neutron stars and stellar-mass black holes.
- Parameter degeneracy between acceleration and other parameters has been discussed.
- The parameter space where the acceleration is large enough to require extending the wave phase model to nonlinear orders in the acceleration has been determined.
Future Roadmap:
To further investigate the impact of acceleration on inspiraling binaries and improve the detection of this effect, future research should focus on the following points:
1. Experimental Upgrades:
- Develop and implement improvements to ground-based detectors, particularly focusing on enhancing sensitivity at low frequencies, to increase the effectiveness of detecting acceleration effects.
- Consider enhancing technology and capabilities of advanced LIGO A Plus, Cosmic Explorer, and Einstein Telescope for better detection in the mass range of neutron stars and stellar-mass black holes.
2. Parameter Degeneracy:
- Explore methods to overcome parameter degeneracy between acceleration and other parameters to improve accuracy in determining the effects of acceleration on inspiraling binaries.
3. Nonlinear Wave Phase Model:
- Investigate and develop a nonlinear wave phase model that incorporates higher orders in acceleration for cases where the acceleration is large enough to require such extensions.
Challenges and Opportunities:
Challenges:
- Developing and implementing improvements to ground-based detectors can be resource-intensive and may require significant technological advancements.
- Overcoming parameter degeneracy can be challenging and may require advanced statistical methods and sophisticated algorithms.
- Creating a reliable and accurate nonlinear wave phase model may pose computational challenges due to the complexity of the calculations involved.
Opportunities:
- The detection of acceleration effects on inspiraling binaries can provide valuable insights into the behavior and dynamics of these systems, enhancing our understanding of gravitational waves.
- Advancements in detector technology and modeling techniques can lead to improved accuracy and sensitivity, enabling more precise measurements and analysis of gravitational wave signals.
- Overcoming challenges in parameter degeneracy and extending wave phase models can open new avenues for research and contribute to the development of more comprehensive theories in astrophysics.
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by jsendak | Jan 10, 2024 | GR & QC Articles
This paper is the fourth in a series dedicated to the mathematically rigorous
asymptotic analysis of gravitational radiation under astrophysically realistic
setups. It provides an overview of the physical ideas involved in setting up
the mathematical problem, the mathematical challenges that need to be overcome
once the problem is posed, as well as the main new results we obtain in the
companion paper [KM24].
From the physical perspective, this includes a discussion of how
Post-Newtonian theory provides a prediction on the gravitational radiation
emitted by $N$ infalling masses from the infinite past in the intermediate
zone, i.e. up to some finite advanced time.
From the mathematical perspective, we then take this prediction, together
with the condition that there be no incoming radiation from $mathcal{I}^-$, as
a starting point to set up a scattering problem for the linearised Einstein
vacuum equations around Schwarzschild and near spacelike infinity, and we
outline how to solve this scattering problem and obtain the asymptotic
properties of the scattering solution near $i^0$ and $mathcal{I}^+$.
The full mathematical details are presented in the companion paper [KM24].
Conclusions:
This paper provides an overview of the physical and mathematical aspects involved in the rigorous asymptotic analysis of gravitational radiation under realistic astrophysical setups. From a physical perspective, the paper discusses the prediction of gravitational radiation emitted by multiple infalling masses in the intermediate zone. From a mathematical perspective, it sets up a scattering problem for the linearized Einstein vacuum equations around Schwarzschild and near spacelike infinity.
Roadmap for Future Readers:
1. Understanding the Physical Predictions:
The first step for readers is to grasp the concepts of Post-Newtonian theory and how it predicts the gravitational radiation emitted by infalling masses. This prediction is limited to a finite advanced time in the intermediate zone. Understanding these physical ideas is crucial to delve into the mathematical challenges that follow.
2. Mathematical Challenges and Solution Overview:
Once readers have a grasp of the physical predictions, they can move on to understanding the mathematical challenges involved in setting up a scattering problem for the linearized Einstein vacuum equations. One important condition is that there should be no incoming radiation from $mathcal{I}^-$.
The paper outlines how to solve this scattering problem and obtain the asymptotic properties of the scattering solution near $i^0$ and $mathcal{I}^+$. The full mathematical details are presented in the companion paper [KM24].
3. Reading the Companion Paper:
To gain a comprehensive understanding of the mathematical details, readers should refer to the companion paper [KM24]. It provides a detailed explanation of the methodology, equations, and results obtained in solving the scattering problem for the linearized Einstein vacuum equations.
Potential Challenges:
- The mathematical analysis involved in the rigorous asymptotic analysis of gravitational radiation may be complex and require familiarity with advanced mathematical concepts.
- Understanding the physical predictions of gravitational radiation and their limitations may require a strong background in astrophysics.
- Navigating through the companion paper [KM24] to grasp the full mathematical details may be time-consuming and challenging.
Potential Opportunities:
- This series of papers provides valuable insights into the rigorous mathematical analysis of gravitational radiation under astrophysical setups. Readers interested in this field can deepen their knowledge and contribute to further research.
- Understanding the physical predictions and mathematical challenges opens doors to exploring other aspects of gravitational radiation and related phenomena.
- The companion paper [KM24] presents new results, offering opportunities for researchers to build upon these findings and advance the field.
References:
- [KM24] – Placeholder for the companion paper. Readers should refer to this paper for the full mathematical details.
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by jsendak | Jan 10, 2024 | GR & QC Articles
We use the recent statistics of dual active galactic nuclei (AGN) in the
$James Webb Space Telescope$ (JWST) data at $z sim 3.4$ to address two
aspects of the feedback and evolution scenarios of supermassive black hole
binaries (SMBHB). We find that the JWST data provide evidence for the members
of a binary black hole being ‘lit’ at the same time, rather than independently
— a scenario which is consistent with gas-rich mergers being responsible for
concurrent AGN activity. This conclusion is supported by the recent NANOGrav
Pulsar Timing Array (PTA) measurements, whose upper limits on the stochastic
gravitational wave strain amplitude lie below those expected from extrapolating
the dual AGN fraction. The results indicate either a ‘stalling’ of the binaries
at the separations probed by NANOGrav, or rapid gas-driven inspirals.
Conclusions:
The recent statistics from the James Webb Space Telescope (JWST) data at z ~ 3.4 have provided evidence for the members of a binary black hole being active at the same time, rather than independently. This suggests that gas-rich mergers may be responsible for concurrent activity in supermassive black hole binaries (SMBHB). These findings are consistent with the recent measurements by the NANOGrav Pulsar Timing Array (PTA), which indicate upper limits on the gravitational wave strain amplitude below what would be expected from extrapolating the dual AGN fraction. This suggests that the binaries may either be stalling at the separations probed by NANOGrav or undergoing rapid gas-driven inspirals.
Future Roadmap:
Looking ahead, further research and observation in the field of dual active galactic nuclei (AGN) and supermassive black hole binaries (SMBHB) are essential to gain a deeper understanding of their feedback mechanisms and evolution scenarios. Here is a potential roadmap for readers interested in this topic:
1. Investigate Gas-rich Mergers:
One avenue for future research is to explore the role of gas-rich mergers in triggering concurrent AGN activity in SMBHB. Researchers can analyze more data from JWST and other observatories to gather additional evidence supporting this scenario. This would help validate the conclusion drawn from the current JWST data.
2. Study Binary Black Hole Stalling:
Another important area of research is to investigate the possibility of binaries stalling at specific separations. To address this, scientists could conduct simulations and modeling studies to understand the physical processes that might cause this stalling effect. By comparing theoretical predictions with observational data, insights into this phenomenon can be gained.
3. Explore Rapid Gas-driven Inspirals:
The idea of rapid inspirals driven by gas is also worth further investigation. Researchers can study the dynamics of gas accretion onto SMBHB and explore how it affects their inspiral rates. This could involve numerical simulations and theoretical modeling to understand the conditions under which rapid inspirals can occur. Observational data from a variety of telescopes, including JWST, can be used to test these theoretical predictions.
4. Validate NANOGrav PTA Measurements:
The upper limits on gravitational wave strain amplitude provided by the NANOGrav Pulsar Timing Array (PTA) measurements may indicate important insights into the behavior of SMBHB. Future studies could focus on validating these measurements and determining whether the observed gaps between the expected and measured values are indicative of a stalling scenario or rapid inspirals. This could involve refining the measurements or exploring alternative explanations for the discrepancies.
Challenges and Opportunities:
While conducting research in the field of dual AGN and SMBHB, there are several challenges and opportunities on the horizon:
- Data Limitations: The availability and quality of observational data might pose limitations to further research. Efforts should be made to collect more high-resolution data from observatories like JWST and future space missions.
- Complexity of Simulations: Simulating the dynamics of gas-rich mergers and binary black hole inspirals can be computationally intensive and require advanced modeling techniques. Researchers should focus on developing more efficient and accurate simulation methods to address these challenges.
- Collaboration and Interdisciplinary Approach: Addressing the open questions in this field may require collaboration between astronomers, astrophysicists, and experts in numerical simulations and data analysis. Interdisciplinary approaches can provide different perspectives and advance our understanding of the subject.
- New Observational Techniques: The development of novel observational techniques and instruments will be crucial in observing and studying dual AGN and SMBHB with higher precision. Researchers should explore opportunities to propose and develop new observational facilities or modifications to existing ones.
- Human-made Gravitational Wave Detectors: The current limitations of gravitational wave observations from sources like NANOGrav PTA could be overcome by the development of more sensitive, human-made gravitational wave detectors. Advancements in this technology would greatly contribute to studying the behavior and properties of SMBHB.
By addressing these challenges and embracing the opportunities, researchers can make significant progress in unraveling the feedback and evolution scenarios of supermassive black hole binaries and improving our understanding of the processes that shape the universe.
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by jsendak | Jan 9, 2024 | GR & QC Articles
We investigate the warm inflationary scenario within the context of the
linear version of f (Q, T ) gravity, coupled with both the inflaton scalar
field and the radiation field, under the conditions of the strong dissipation
regime. First, we calculate the modified Friedmann equations and the modified
slow-roll parameters. Subsequently, we apply the slow-roll approximations to
derive the scalar power spectrum and the tensor power spectrum. Also, we
develop formulations of the scalar and tensor perturbations for the f (Q, T )
gravity with warm inflation scenario. Furthermore, we scrutinize two different
forms of the dissipation coefficient, a constant and a function of the inflaton
field to determine the scalar spectral index, the tensor-to-scalar ratio and
the temperature for the power-law potential case. By imposing some constraints
on the free parameters of the model, we attain results in good agreement with
both the Planck 2018 data and the joint Planck, BK15 and BAO data for the
tensor-to-scalar ratio, and consistent results aligned with the Planck 2018
data for the scalar spectral index. Consequently, we are able to revive the
power-law potential that was previously ruled out by observational data.
Moreover, for the variable dissipation coefficient, the model leads to the
scalar spectral index with the blue and red tilts in agreement with the WMAP
three years data.
Future Roadmap: Challenges and Opportunities
1. Exploring Further Constraints on Free Parameters
- The current study has successfully obtained results in good agreement with the Planck 2018 data and other observational data for certain parameters.
- Future research should focus on exploring additional constraints on the free parameters of the model.
- This will help to further refine the model and enhance its compatibility with observational data.
2. Investigating Alternative Forms of the Dissipation Coefficient
- The study has examined two different forms of the dissipation coefficient, a constant and a function of the inflaton field.
- Future investigations should explore other possible forms of the dissipation coefficient.
- This will provide a more comprehensive understanding of its impact on the scalar spectral index and further improve the model’s alignment with observational data.
3. Assessing the Viability of Power-Law Potential
- The study has successfully revived the previously ruled out power-law potential by obtaining results consistent with observational data.
- Further research should assess the viability of the power-law potential in more detail.
- This will involve investigating its implications in different cosmological scenarios and exploring potential implications for other inflationary models.
4. Comparing Results with Alternative Data Sets
- The current study has focused on comparing results with the Planck 2018 data and the joint Planck, BK15 and BAO data for the tensor-to-scalar ratio.
- Future research should aim to compare and validate the model’s predictions with alternative data sets.
- This will ensure robustness and reliability of the model’s predictions across different data sources.
5. Further Analysis of Scalar Spectral Index
- The study has obtained scalar spectral index results in alignment with the WMAP three years data.
- Future investigations should conduct further analysis of the scalar spectral index.
- Exploring its implications in more cosmological scenarios and comparing with additional observational data will enhance our understanding of the inflationary dynamics.
Conclusion
The warm inflationary scenario within the context of the linear version of f (Q, T ) gravity, coupled with both the inflaton scalar field and the radiation field, has shown promise in aligning with observational data. However, there are several challenges and opportunities that need to be addressed in future research. By focusing on refining free parameters, investigating alternative forms of the dissipation coefficient, assessing the viability of the power-law potential, comparing with alternative data sets, and further analyzing the scalar spectral index, we can enhance our understanding of warm inflation in f (Q, T ) gravity and its implications for cosmology.
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