Semi-Symmetric Metric Gravity: A Comprehensive Review and Cosmological Applications

Concetti Chiave

Semi-Symmetric Metric Gravity (SSMG), a modified gravity theory incorporating torsion, offers a compelling alternative to the standard cosmological model by potentially explaining cosmic acceleration and galactic dynamics without invoking dark matter or a cosmological constant.

Sintesi

• Bibliographic Information: Chaudhary, H., Csillag, L., & Harko, T. (2024). Semi-Symmetric Metric Gravity: A Brief Overview. arXiv preprint arXiv:2411.03060v1.

• Research Objective: This paper reviews the theoretical framework of Semi-Symmetric Metric Gravity (SSMG) and explores its cosmological implications, particularly its potential to address limitations of General Relativity.

• Methodology: The authors derive the field equations of SSMG, analyze its Newtonian limit, and investigate its cosmological consequences. They examine specific cosmological models within SSMG and compare their predictions with observational data from Cosmic Chronometers, supernovae, and Baryon Acoustic Oscillations.

• Key Findings:

  • SSMG introduces torsion, a geometric concept, through a semi-symmetric connection, leading to non-conservation of the energy-momentum tensor.
  • This non-conservation can be interpreted as particle creation, potentially offering insights into quantum field processes in curved spacetimes.
  • The Newtonian limit of SSMG yields corrections to the Newtonian potential and force, which could explain galactic rotation curves without dark matter.
  • Cosmological models within SSMG generate an effective dark energy contribution, potentially explaining cosmic acceleration without a cosmological constant.

• Main Conclusions: SSMG presents a promising alternative to General Relativity, potentially resolving cosmological puzzles like dark matter and cosmic acceleration through geometric modifications. The authors suggest that SSMG warrants further investigation and observational testing.

• Significance: This research contributes to the ongoing exploration of modified gravity theories as potential solutions to fundamental questions in cosmology and astrophysics.

• Limitations and Future Research: The paper primarily focuses on theoretical aspects and cosmological applications of SSMG. Further research should explore its astrophysical implications in greater detail, including the study of galaxy clusters and gravitational lensing. Additionally, observational tests to constrain the theory's parameters and distinguish it from General Relativity are crucial for its validation.

Statistiche

The Hubble constant H0, as measured by the Planck satellite, is 66.93 ± 0.62 km/s/Mpc.
The SH0ES collaboration obtained a value of 73.24 ± 1.74 km/s/Mpc for H0.
There is a difference of more than 3σ between these values of the Hubble constant.
The abundance of 7Li is overestimated by a factor of ∼2.5 when calculated theoretically in the standard model of Big Bang Nucleosynthesis.
Dark matter is estimated to represent 90% of the mass of galaxy clusters.

Citazioni

"The Riemann geometry, used by Einstein and Hilbert to build general relativity is metric, with the metric tensor gµν satisfying the condition ◦∇λgµν = 0, where ◦∇λ is the covariant derivative defined with the help of the Levi-Civita connection."
"Hence, the presence of torsion may explain the galactic dynamics without resorting to the mysterious and not detected dark matter, which may prove to be a purely geometric effect induced by the torsion vector πµ."
"Our results suggest that the Semi-Symmetric Metric Gravity cosmology has the potential of explaining cosmological dynamics without the need of introducing a cosmological constant in the theory, by means of a geometrically generated dark energy term."

Approfondimenti chiave tratti da

Semi-Symmetric Metric Gravity: A Brief Overview

by Himanshu Cha... alle arxiv.org 11-06-2024

https://arxiv.org/pdf/2411.03060.pdf

Domande più approfondite

How might future advancements in observational cosmology, such as the use of gravitational wave astronomy, contribute to testing the validity of SSMG?

Answer: Gravitational wave astronomy offers a novel avenue for testing the validity of modified gravity theories like SSMG. Here's how:

Speed of Gravitational Waves: General Relativity predicts that gravitational waves propagate at the speed of light. SSMG, with its modified geometry due to torsion, might predict subtle deviations in this speed. Future observations of gravitational waves coincident with electromagnetic counterparts from distant events could precisely measure this speed and potentially constrain SSMG parameters.
Polarization Modes: General Relativity permits only two tensor polarization modes for gravitational waves. Theories like SSMG, by introducing additional degrees of freedom (the torsion vector in this case), might allow for extra polarization modes. Detecting these extra modes would be a smoking gun signature of deviations from GR and could lend support to SSMG or other modified gravity models.
Stochastic Gravitational Wave Background: The stochastic gravitational wave background is a faint "hum" of gravitational waves from the early universe and astrophysical sources. SSMG could leave a distinct imprint on this background, differing from the predictions of GR. Future space-based gravitational wave detectors, with their enhanced sensitivity, could potentially detect these subtle differences.
Strong-Field Tests: Gravitational wave observations from merging black holes and neutron stars provide a glimpse into the strong-field regime of gravity, where SSMG effects might be more pronounced. Analyzing the waveforms of these mergers and comparing them to GR predictions could constrain the torsion parameters of SSMG.
In essence, the high precision and novel information encoded in gravitational waves make them powerful tools for testing the fundamental nature of gravity and probing the validity of theories like SSMG.

Could the introduction of additional fields or modifications to the SSMG Lagrangian further enhance its explanatory power regarding other cosmological or astrophysical phenomena?

Answer: Yes, introducing additional fields or modifying the SSMG Lagrangian could potentially enhance its explanatory power. Here are some possibilities:

Scalar Fields: Coupling a scalar field to the torsion vector in the SSMG Lagrangian could lead to richer phenomenology. This scalar field could play the role of dark energy, driving the late-time accelerated expansion of the universe, or it could even be a candidate for dark matter. The specific form of the coupling would determine the cosmological implications.
Vector Fields: Introducing a new vector field coupled to torsion could lead to interesting effects. For example, it could potentially modify the dynamics of galaxies and clusters, offering an alternative explanation for the observed rotation curves and mass discrepancies without invoking dark matter.
Non-minimal Coupling to Matter: Currently, SSMG assumes minimal coupling between the torsion and matter fields. Introducing non-minimal couplings could lead to variations in fundamental constants, violations of the equivalence principle, or other effects that could be tested experimentally or observationally.
Higher-Order Torsion Terms: The current SSMG Lagrangian focuses on the simplest linear coupling of the torsion vector. Including higher-order terms in the torsion tensor could lead to more complex dynamics in strong gravity regimes, potentially affecting the evolution of the early universe or the behavior of compact objects.
It's important to note that any modifications to SSMG must be carefully considered to ensure consistency with existing observational constraints and to avoid introducing theoretical inconsistencies. However, the potential for enhancing the theory's explanatory power by incorporating new fields or interactions is a promising avenue for future research.

If the universe can be described as a self-organizing system, how might the concept of torsion in SSMG relate to the emergence of complexity and structure at cosmological scales?

Answer: The concept of torsion in SSMG, when viewed through the lens of a self-organizing universe, offers intriguing possibilities for understanding the emergence of cosmic structure:

Torsion as a Source of Asymmetry: In SSMG, torsion introduces an inherent asymmetry into spacetime geometry. This departure from the symmetric spacetime of General Relativity could act as a seed for breaking the homogeneity and isotropy of the early universe, potentially contributing to the formation of the first density fluctuations.
Torsion and Spin Interaction: Torsion is often associated with the spin of matter. In a self-organizing universe, the interaction between torsion and the intrinsic spin of particles could lead to the formation of large-scale structures. For example, regions with aligned spins might experience different gravitational dynamics compared to regions with random spin orientations, potentially leading to the clustering of matter.
Torsion and Entropy Production: As discussed in the context, SSMG allows for non-conservation of the energy-momentum tensor, which can be interpreted as particle creation. This process, driven by torsion, could be linked to entropy production in the early universe. The increase in entropy, a hallmark of self-organizing systems, could drive the universe towards higher complexity and the formation of structures.
Torsion and Feedback Mechanisms: In a self-organizing system, feedback mechanisms play a crucial role in driving the emergence of order. Torsion, through its influence on the dynamics of matter, could participate in such feedback loops. For example, the formation of structures could modify the torsion field, which in turn could influence the formation of subsequent structures, leading to a self-reinforcing process of structure formation.
While these ideas are speculative, they highlight the potential for torsion in SSMG to play a significant role in a self-organizing cosmological framework. Further research exploring the interplay between torsion, matter, and self-organization could provide deeper insights into the evolution of the universe and the emergence of its complex structures.