by jsendak | Jan 20, 2024 | GR & QC Articles
Recently we showed that in FLRW cosmology, the contribution from higher
curvature terms in any generic metric gravity theory to the energy-momentum
tensor is of the perfect fluid form. Such a geometric perfect fluid can be
interpreted as a fluid remaining from the beginning of the universe where the
string theory is thought to be effective. Just a short time after the beginning
of the Universe, it is known that the Einstein-Hilbert action is assumed to be
modified by adding all possible curvature invariants. We propose that the
observed late-time accelerating expansion of the Universe can be solely driven
by this geometric fluid. To support our claim, we specifically study the
quadratic gravity field equations in $D$-dimensions. We show that the field
equations of this theory for the FLRW metric possess a geometric perfect fluid
source containing two critical parameters $sigma_1$ and $sigma_2$. To analyze
this theory concerning its parameter space $(sigma_1, sigma_2)$, we obtain
the general second-order nonlinear differential equation governing the
late-time dynamics of the deceleration parameter $q$. Hence using some
present-day cosmological data as our initial conditions, our findings for the
$sigma_2=0$ case are as follows: $ (i)$ In order to have a positive energy
density for the geometric fluid $rho_g$, the parameter $sigma_1$ must be
negative for all dimensions up to $D = 11$, $(ii)$ For a suitable choice of
$sigma_1$, the deceleration parameter experiences signature changes in the
past and future, and in the meantime it lies within a negative range which
means that the current observed accelerated expansion phase of the Universe can
be driven solely by the curvature of the spacetime, $(iii)$ $q$ experiences a
signature change and as the dimension $D$ of spacetime increases, this
signature change happens at earlier and later times, in the past and future,
respectively.
Conclusions
The article presents a proposal that the observed late-time accelerating expansion of the Universe can be explained solely by the presence of a geometric perfect fluid, which is a remnant from the beginning of the universe when string theory is effective. The authors specifically analyze the quadratic gravity field equations in $D$-dimensions and find that the field equations possess a geometric perfect fluid source with two critical parameters, $sigma_1$ and $sigma_2$. They study the dynamics of the deceleration parameter $q$ and find that with suitable choices of $sigma_1$, $q$ experiences signature changes in the past and future, indicating a potential explanation for the current accelerated expansion phase of the Universe driven by spacetime curvature.
Future Roadmap
While the proposal presented in this article provides an intriguing explanation for the late-time acceleration of the Universe, there are several challenges and potential opportunities on the horizon.
Challenges
- The validity of the proposal relies on the assumption that the contribution from higher curvature terms in any generic metric gravity theory takes the form of a geometric perfect fluid. This assumption may need to be further tested and supported by additional theoretical and observational evidence.
- The parameter space $(sigma_1, sigma_2)$ governing the late-time dynamics of the deceleration parameter $q$ needs to be thoroughly explored. The authors have only considered the case where $sigma_2 = 0$, and it remains to be seen how varying values of $sigma_2$ may affect the results.
- Further investigations are needed to understand the implications of this proposal in the context of other cosmological theories and models. The authors have focused on FLRW cosmology and quadratic gravity field equations, but it would be valuable to explore its compatibility with different frameworks.
Opportunities
- Experimental and observational tests can be conducted to gather data that can support or challenge the proposal. Analyzing present and future cosmological data can provide insights into the behavior of the deceleration parameter $q$ and help validate the theoretical predictions.
- Exploring the dependence of the proposal on the dimension of spacetime ($D$) can open up new avenues for research. Investigating how the signature change of $q$ varies with increasing dimensions can lead to a deeper understanding of the relationship between curvature and the observed accelerated expansion.
- This proposal has the potential to bridge the gap between string theory and cosmology, as it suggests that the geometric perfect fluid originates from the beginning of the universe when string theory is effective. Further exploration of this connection may offer new insights into the fundamental nature of our universe.
Note: The roadmap outlined above is based on the information presented in the article. It is important to conduct further research and analysis to address the challenges and explore the opportunities discussed.
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by jsendak | Jan 20, 2024 | GR & QC Articles
The Equivalence Principle is considered in the framework of metric-affine
gravity. We show that it naturally emerges as a Noether symmetry starting from
a general non-metric theory. In particular, we discuss the Einstein Equivalence
Principle and the Strong Equivalence Principle showing their relations with the
non-metricity tensor. Possible violations are also discussed pointing out the
role of non-metricity in this debate.
Conclusions
The Equivalence Principle is examined within the framework of metric-affine gravity. The study shows that the Equivalence Principle naturally emerges as a Noether symmetry in a general non-metric theory. The discussion focuses on the Einstein Equivalence Principle and the Strong Equivalence Principle and their relations with the non-metricity tensor. The study also considers potential violations of the Equivalence Principle and highlights the role of non-metricity in this ongoing debate.
Future Roadmap
Looking ahead, there are several potential challenges and opportunities on the horizon related to the Equivalence Principle and its connection to non-metricity:
- Further exploration of metric-affine gravity: Researchers should continue investigating and developing the metric-affine framework to gain a deeper understanding of its implications for the Equivalence Principle.
- Experimental verification: Ongoing experiments should be conducted to test the Equivalence Principle and its potential violations. These experiments can further inform our understanding of the role of non-metricity in the debate.
- Theoretical development: Theoretical advancements are needed to establish a comprehensive theory that combines metric-affine gravity, non-metricity, and the Equivalence Principle.
- Alternative theories: Exploring alternative gravitational theories beyond metric-affine gravity could shed light on the Equivalence Principle and its connections to non-metricity. Comparisons and analyses of these theories can provide a broader perspective on the topic.
- Interdisciplinary collaboration: Collaboration among physicists, mathematicians, and cosmologists is crucial to addressing the challenges and opportunities related to the Equivalence Principle and non-metricity. Joint efforts can lead to innovative solutions, methodologies, and insights.
Challenges and Opportunities
The following challenges and opportunities may arise as researchers delve into the Equivalence Principle and non-metricity:
- Technological limitations: Experimental tests of the Equivalence Principle may face technological limitations in terms of precision, sensitivity, and scale. Overcoming these limitations will be crucial to achieve more accurate results.
- Theoretical complexities: Non-metric theories and their connections to the Equivalence Principle can involve intricate mathematical frameworks. Researchers must tackle these complexities to shape a coherent theoretical understanding.
- Interpretation of results: Analyzing experimental and theoretical findings require careful interpretation to draw meaningful conclusions and rule out potential confounding factors.
- Data availability: Access to high-quality experimental data is essential for driving advancements in the field. Researchers should actively collaborate and establish data-sharing initiatives to fuel progress.
In summary, the Equivalence Principle and its connection to non-metricity present exciting avenues for exploration. By continuing to investigate metric-affine gravity, conducting experiments, advancing theories, exploring alternative theories, and fostering interdisciplinary collaboration, researchers can make significant progress in understanding the Equivalence Principle and its implications for the fundamental laws of physics.
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by jsendak | Jan 20, 2024 | GR & QC Articles
The effective action in renormalizable quantum theory of gravity provides
entropy because the total Hamiltonian vanishes. Since it is a renormalization
group invariant that is constant in the process of cosmic evolution, we can
show conservation of entropy, that is an ansatz in the standard cosmology. Here
we study renormalizable quantum gravity that exhibits conformal dominance at
high energy beyond the Planck scale. The current entropy of the universe is
derived by calculating the effective action under the scenario of quantum
gravity inflation caused by its dynamics. We then argue that ghost modes must
be unphysical, but necessary for the Hamiltonian to vanish and for entropy to
exist in gravitational systems.
In this article, we examine the conclusions regarding the effective action in renormalizable quantum theory of gravity and its relationship to entropy. We also explore the concept of conformal dominance at high energy beyond the Planck scale in the context of renormalizable quantum gravity. Finally, we discuss the role of ghost modes in gravitational systems and their connection to the existence of entropy.
Conclusion 1: Conservation of Entropy in Standard Cosmology
The total Hamiltonian in renormalizable quantum theory of gravity vanishes, leading to the emergence of entropy. This conservation of entropy is a fundamental assumption in standard cosmology. By showing that the total Hamiltonian is a renormalization group invariant that remains constant throughout cosmic evolution, we can establish the conservation of entropy as an ansatz.
Conclusion 2: Quantum Gravity Inflation and the Current Entropy of the Universe
By calculating the effective action under the scenario of quantum gravity inflation, we can derive the current entropy of the universe. Quantum gravity inflation refers to the inflationary period caused by the dynamics of renormalizable quantum gravity. This calculation allows us to understand the contribution of quantum gravity to the overall entropy of the universe.
Conclusion 3: Unphysical Ghost Modes and the Vanishing Hamiltonian
We argue that ghost modes in renormalizable quantum gravity are unphysical but necessary for the Hamiltonian to vanish. Ghost modes are peculiar states that exist within gravitational systems and play a crucial role in allowing for the existence of entropy. Understanding the nature of ghost modes is essential for comprehending the relationship between gravity, entropy, and quantum effects.
Future Roadmap: Challenges and Opportunities
As we move forward in our understanding of renormalizable quantum gravity and its implications for entropy, several challenges and opportunities lie ahead:
- Development of More Precise Calculations: Further research is needed to improve the accuracy of calculating the effective action and determining the contribution of quantum gravity to the current entropy of the universe. This will require advancements in theoretical models and computational techniques.
- Investigation of Consequences of Conformal Dominance: The concept of conformal dominance at high energy beyond the Planck scale introduces intriguing possibilities for understanding the behavior of gravity and entropy. Exploring the consequences and implications of conformal dominance will open new avenues for future research.
- Resolution of the Nature of Ghost Modes: Understanding the nature of ghost modes in gravitational systems remains a challenge. Further investigations and theoretical breakthroughs are necessary to clarify their role in the vanishing Hamiltonian and the existence of entropy.
- Experimental Verification: While much of the discussion is theoretical, experimental verification is crucial to validate the conclusions and predictions made in this field. The development of experimental techniques and observational data that can test the concepts presented here will be an important focus in the future.
By addressing these challenges and capitalizing on the opportunities presented by these conclusions, we can pave the way for a deeper understanding of renormalizable quantum gravity, its connection to entropy, and its implications for our understanding of the universe.
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by jsendak | Jan 20, 2024 | GR & QC Articles
Motivated by the warped conifold compactification, we model the infrared (IR)
dynamics of confining gauge theories in a Randall-Sundrum (RS)-like setup by
modifying the stabilizing Goldberger-Wise (GW) potential so that it becomes
large (in magnitude) in the IR and back-reacts on the geometry. We study the
high-temperature phase by considering a black brane background in which we
calculate the entropy and free energy of the strongly back-reacted solution. As
with Buchel’s result for the conifold (arXiv:2103.15188), we find a minimum
temperature beyond which the black brane phase is thermodynamically unstable.
In the context of a phase transition to the confining background, our results
suggest that the amount of supercooling that the metastable black brane phase
undergoes can be limited. It also suggests the first-order phase transition
(and the associated gravitational waves from bubble collision) is not
universal. Our results therefore have important phenomenological implications
for early universe model building in these scenarios.
Conclusions:
- We have modeled the infrared (IR) dynamics of confining gauge theories in a Randall-Sundrum (RS)-like setup by modifying the stabilizing Goldberger-Wise (GW) potential.
- The modified potential becomes large in the IR and back-reacts on the geometry.
- We have studied the high-temperature phase by considering a black brane background and calculating the entropy and free energy of the strongly back-reacted solution.
- Similar to Buchel’s result for the conifold, we have found a minimum temperature beyond which the black brane phase is thermodynamically unstable.
- Our results suggest that the amount of supercooling that the metastable black brane phase undergoes can be limited in the context of a phase transition to the confining background.
- Our results also suggest that the first-order phase transition and the associated gravitational waves from bubble collision are not universal.
- These findings have important phenomenological implications for early universe model building in these scenarios.
Future Roadmap:
Based on these conclusions, readers can expect several future research directions and potential developments:
1. Further Investigation of IR Dynamics:
Researchers may continue to explore and refine the modeling of IR dynamics in confining gauge theories using the modified stabilizing Goldberger-Wise potential. This could involve studying different variations of the potential and evaluating their impact on the back-reaction on the geometry.
2. Study of Phase Transitions:
There is potential for future research on the phase transitions from the black brane phase to the confining background. The suggested limitation on supercooling in this transition opens up avenues for understanding and manipulating the thermodynamic behavior of the system. Exploring the nature of this phase transition in various scenarios and its implications for early universe model building could be a fruitful area of investigation.
3. Understanding Non-Universality:
The observation that the first-order phase transition and the associated gravitational waves from bubble collision are not universal invites further exploration. Researchers might delve into the factors that contribute to this non-universality and investigate how it affects the overall behavior of the system. This could involve studying different gauge theories, modifications to the potential, or alternative setups.
4. Phenomenological Implications:
Considering the important phenomenological implications highlighted in the article, future research might focus on understanding the practical consequences and applications of these findings. This could involve exploring how these results impact early universe model building and cosmological scenarios, and how they align with observational data or experimental observations.
Potential Challenges and Opportunities:
While there are exciting prospects for future research based on the conclusions of this study, there are also some challenges and opportunities to consider:
- Complexity of Calculations: Further investigations may involve complex calculations and theoretical analyses, requiring advanced mathematical techniques and computational resources.
- Data and Observational Constraints: The phenomenological implications of these findings may need to be compared and reconciled with observational data and experimental constraints, which can present challenges in terms of validating or refining the models.
- Diverse Theoretical Approaches: Researchers might need to explore various theoretical approaches, alternative gauge theories, and different setups to fully understand and explore the non-universality and other novel phenomena arising from this study.
- Interdisciplinary Collaboration: Given the potential implications for early universe model building and cosmology, interdisciplinary collaborations between theoretical physicists, cosmologists, and observational astronomers could be valuable to fully explore and apply these findings.
In conclusion, the study’s conclusions open up exciting avenues for future research in understanding the IR dynamics of confining gauge theories, studying phase transitions, investigating non-universality, and exploring the phenomenological implications. However, researchers should be prepared to tackle challenges such as complex calculations, data constraints, diverse theoretical approaches, and the need for interdisciplinary collaborations.
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by jsendak | Jan 20, 2024 | GR & QC Articles
Adiabatic binary inspiral in the small mass ratio limit treats the small body
as moving along a geodesic of a large Kerr black hole, with the geodesic slowly
evolving due to radiative backreaction. Up to initial conditions, geodesics are
typically parameterized in two ways: using the integrals of motion energy $E$,
axial angular momentum $L_z$, and Carter constant $Q$; or, using orbit geometry
parameters semi-latus rectum $p$, eccentricity $e$, and (cosine of )
inclination $x_I equiv cos I$. The community has long known how to compute
orbit integrals as functions of the orbit geometry parameters, i.e., as
functions expressing $E(p, e, x_I)$, and likewise for $L_z$ and $Q$. Mappings
in the other direction — functions $p(E, L_z, Q)$, and likewise for $e$ and
$x_I$ — have not yet been developed in general. In this note, we develop
generic mappings from ($E$, $L_z$, $Q$) to ($p$, $e$, $x_I$). The mappings are
particularly simple for equatorial orbits ($Q = 0$, $x_I = pm1$), and can be
evaluated efficiently for generic cases. These results make it possible to more
accurately compute adiabatic inspirals by eliminating the need to use a
Jacobian which becomes singular as inspiral approaches the last stable orbit.
Mapping Orbit Integrals to Orbit Geometry Parameters
This article discusses the development of mappings from orbit integrals (energy E, axial angular momentum L_z, Carter constant Q) to orbit geometry parameters (semi-latus rectum p, eccentricity e, and inclination x_I). These mappings are essential for accurately computing adiabatic inspirals where a small body moves along the geodesic of a large Kerr black hole.
Current Understanding
The community has long been able to compute orbit integrals as functions of the orbit geometry parameters. However, the reverse mappings, i.e., functions that express p, e, and x_I in terms of E, L_z, and Q, have not yet been developed in general.
New Developments
In this article, the authors present generic mappings that translate E, L_z, and Q into p, e, and x_I. These mappings are particularly simple for equatorial orbits (Q = 0, x_I = ±1) and can be efficiently evaluated for generic cases.
Potential Opportunities
- Accurate Computation: The developed mappings provide a more accurate method to compute adiabatic inspirals, eliminating the need for a singular Jacobian as the inspiral approaches the last stable orbit.
- Improved Understanding: By bridging the gap between orbit integrals and orbit geometry parameters, researchers can gain a deeper understanding of the dynamics of small bodies moving in the vicinity of Kerr black holes.
Potential Challenges
- Validation: The newly developed mappings need to be validated through further research and comparison with existing methods. This will ensure their reliability and accuracy in various scenarios.
- Complex Scenarios: While the mappings are efficient for generic cases, there may be complex scenarios or extreme conditions where their applicability needs to be further studied.
Roadmap for Readers
- Understand the current state of knowledge regarding the computation of orbit integrals and their dependence on orbit geometry parameters.
- Explore the limitations and challenges faced in the absence of reverse mappings from orbit integrals to orbit geometry parameters.
- Examine the new developments presented in this article, focusing on the generic mappings that allow for accurate computation of adiabatic inspirals.
- Consider the potential opportunities stemming from these developments, such as improved accuracy and a deeper understanding of small body dynamics around Kerr black holes.
- Recognize the potential challenges in validating the mappings and their applicability in complex scenarios.
- Stay updated on further research in this field to gain insights into the refinement and expansion of the developed mappings.
In conclusion, this article presents a significant advancement in understanding adiabatic inspirals by developing mappings from orbit integrals to orbit geometry parameters. While offering opportunities for accurate computation and improved understanding, these mappings need validation and careful consideration of their applicability in various scenarios.
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by jsendak | Jan 20, 2024 | GR & QC Articles
The dynamics of the Local Group (LG), especially concerning the contributions
of the Milky Way (MW) and Andromeda (M31) galaxies, is sensitive to the
presence of dark energy. This work compares the evolution of the LG by
considering it as a two-body problem in a homogeneous and isotropic expanding
spacetime, i.e. the McVitte spacetime (McV) versus the spherically symmetric
metric for LG dynamics with the Cosmological Constant, i.e. the De
Sitter-Schwarzschild spacetime (DsS). Using the Timing Argument (which links LG
dynamics to LG mass), calibrated by the IllustrisTNG simulations, we find that
the McV spacetime predicts a lower mass for the LG: $left(4.20 pm 0.61right)
cdot 10^{12} M_{odot}$ for McV spacetime vs. $left(4.65 pm 0.75right)
cdot 10^{12} M_{odot}$ for DsS spacetime ($68 % ,$ CL). Due to uncertainties
in tangential velocity measurements, the masses are indistinguishable. However,
with future astrometric measurements, we demonstrate that the predicted masses
will be distinguishable, indicating different LG histories. By independently
estimating the total mass of MW and M31, we compare the possible upper bounds
for the Cosmological Constant in these scenarios. We find a tighter upper bound
for the DsS spacetime model, $Lambda < 3.3 ,Lambda_{text{CMB}}$, compared
to $Lambda < 8.4, Lambda_{text{CMB}}$ for the McV spacetime (where
$Lambda_{text{CMB}}$ is the mean value from Planck). Future astrometric
measurements, such as those from JWST, hold the potential to independently
detect dark energy for both spacetime models independent from Planck’s value.
Future Roadmap: Challenges and Opportunities
Potential Challenges:
- Tangential Velocity Measurements: The current uncertainties in tangential velocity measurements make it difficult to distinguish between the predicted masses of the Local Group (LG) in the McVitte spacetime (McV) and the De Sitter-Schwarzschild spacetime (DsS).
- Indistinguishable LG Histories: Without more precise astrometric measurements, it is not currently possible to determine the different histories of the LG predicted by the two spacetime models.
- Upper Bound Estimation: While the comparison of upper bounds for the Cosmological Constant in the two scenarios is informative, there are uncertainties in independently estimating the total mass of the Milky Way (MW) and Andromeda (M31) galaxies, which could affect the reliability of these bounds.
Potential Opportunities:
- Future Astrometric Measurements: With advancements in astrometric measurements, particularly from the James Webb Space Telescope (JWST), there is the potential to overcome the challenges mentioned above. More precise measurements can help distinguish between the predicted masses in the McV and DsS spacetime models, revealing different LG histories.
- Independent Detection of Dark Energy: Future astrometric measurements, such as those from JWST, hold the potential to independently detect dark energy for both spacetime models, regardless of Planck’s value. This could provide valuable insights into the nature and properties of dark energy.
Note: It is important to acknowledge that further research and advancements in observational techniques are necessary to overcome the current challenges in determining the dynamics and contributions of the Milky Way and Andromeda galaxies to the Local Group. Continued investigations into the LG’s evolution and the presence of dark energy will deepen our understanding of the cosmos.
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