Exploring the Viability of f(T) Gravity as an Explanation for Dark Energy and Cosmic Acceleration

Concepts de base

This research paper investigates the potential of f(T) gravity, a modified theory of gravity, to explain the observed accelerated expansion of the universe and the nature of dark energy, concluding that the power law model of f(T) gravity aligns closely with the standard cosmological model (ΛCDM) when tested against observational data.

Résumé

• Bibliographic Information: S. R. Bhoyar and Y. B. Ingole, "Resolving FLRW cosmology through effective equations of state in f(T) gravity," arXiv:2408.13792v4 [gr-qc], Nov. 7, 2024.
• Research Objective: This study aims to resolve the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology within the framework of f(T) gravity, a modified theory of gravity, by employing an effective equation of state (EoS) parameterized with two parameters. The research seeks to constrain these parameters using observational data and analyze the cosmological implications of the model.
• Methodology: The authors utilize a power-law model of f(T) gravity and derive the effective EoS parameter. They then constrain the model parameters using a Markov Chain Monte Carlo (MCMC) analysis with three datasets: Cosmic Chronometers (CC), Pantheon+SH0ES supernovae, and a combined analysis of both. The study investigates the evolution of cosmological parameters like the deceleration parameter, effective EoS, jerk, snap, and lerk parameters. Additionally, the Om(z) diagnostic is employed to distinguish between different dark energy models.
• Key Findings: The research finds that the f(T) power-law model in the FLRW universe exhibits a transition from a decelerated to an accelerated expansion phase, aligning with the observed cosmic acceleration. The effective EoS parameter indicates that the model resides in the quintessence era and gradually approaches the behavior of the Einstein-de Sitter model. The Om(z) diagnostic suggests that the model aligns well with the standard ΛCDM model, particularly for the Pantheon+SH0ES and combined datasets.
• Main Conclusions: The authors conclude that the power-law model of f(T) gravity, when constrained by observational data, provides a viable description of dark energy and aligns closely with the standard ΛCDM model. The study highlights the potential of modified gravity theories like f(T) gravity to address fundamental questions in cosmology.
• Significance: This research contributes to the ongoing exploration of alternative gravity theories to explain the universe's accelerated expansion. The findings provide further support for f(T) gravity as a potential candidate for describing dark energy and its role in cosmic evolution.
• Limitations and Future Research: The study acknowledges the limitations of relying solely on specific datasets and the assumptions inherent in the chosen f(T) model. Future research could explore different f(T) functional forms, incorporate additional observational constraints, and investigate the model's implications for structure formation and other cosmological phenomena.

Stats

The analysis uses 31 data points from the Hubble (H(z)) datasets, extracted from the differential age (DA) approach in the redshift range 0.07 < z < 2.42.
The Pantheon+SH0ES sample collection comprises 1701 light curves of 1550 different Type Ia supernovae (SNeIa) with redshifts ranging from z = 0.00122 to 2.2613.

Citations

"By allowing the torsion scalar T to vary according to an arbitrary function, f(T) gravity offers a new framework for exploring gravitational phenomena, potentially providing new insights into the nature of cosmic acceleration and the evolution of the universe."
"In our current study, we aim to solve FLRW cosmology via the effective EOS parameter ωeff = −1/(1+m(1+z)k), as discussed previously [34], within the framework of f(T) gravity theory."
"In conclusion, the power law model of the f(T) gravity is consistent with the observational data and may serve as a potential description of dark energy."

Idées clés tirées de

Resolving FLRW cosmology through effective equations of state in $f(T)$ gravity

by S.R. Bhoyar,... à arxiv.org 11-08-2024

https://arxiv.org/pdf/2408.13792.pdf

Questions plus approfondies

How does the f(T) gravity model discussed in the paper compare to other modified gravity theories proposed to explain dark energy, such as f(R) gravity, in terms of their theoretical foundations, observational constraints, and cosmological predictions?

Both f(T) and f(R) gravity are intriguing modifications of General Relativity that aim to explain the observed cosmic acceleration without invoking the elusive dark energy. However, they differ significantly in their theoretical foundations, observational constraints, and cosmological predictions:
Theoretical Foundations:

f(R) gravity: This theory modifies the Einstein-Hilbert action by replacing the Ricci scalar (R) with an arbitrary function f(R). This introduces a new scalar degree of freedom, often interpreted as a "scalaron" field, which can drive cosmic acceleration. However, finding stable and ghost-free f(R) models that satisfy both cosmological and local gravity constraints remains a challenge.
f(T) gravity: Instead of curvature, f(T) gravity relies on torsion, a geometrical property of spacetime described by the Weitzenböck connection. The action is modified by replacing the torsion scalar (T) with an arbitrary function f(T). This approach often leads to second-order field equations, simplifying some calculations compared to f(R) gravity. However, f(T) gravity faces challenges regarding local Lorentz invariance, which is a fundamental symmetry of special relativity.
Observational Constraints:

f(R) gravity: Several f(R) models have been tightly constrained by observations, including solar system tests, the growth of large-scale structure, and the cosmic microwave background (CMB). While some models can reproduce the late-time acceleration, they often struggle to simultaneously fit all observational data without fine-tuning.
f(T) gravity: Observational constraints on f(T) gravity are less stringent than those on f(R) gravity. While some studies suggest that specific f(T) models might be compatible with current data, more precise measurements of the growth of structure and the Hubble parameter (H(z)) at high redshifts are needed to distinguish them from the standard cosmological model.
Cosmological Predictions:

f(R) gravity: Depending on the specific form of f(R), these models can predict various cosmological scenarios, including phantom-like behavior, future singularities, and deviations from General Relativity at early times.
f(T) gravity: Similar to f(R) gravity, f(T) models can also lead to diverse cosmological evolutions. Some models predict a crossing of the phantom divide line, while others, like the one discussed in the paper, remain in the quintessence regime.
In summary: Both f(T) and f(R) gravity offer exciting avenues for exploring modified gravity as an alternative to dark energy. While f(R) gravity is more mature and faces tighter observational constraints, f(T) gravity presents a simpler mathematical framework but grapples with theoretical issues like local Lorentz invariance. Ultimately, future observations, particularly at high redshifts, will be crucial in determining which, if any, of these modified gravity theories can successfully describe the Universe's evolution.

Could the apparent alignment of the f(T) model with the ΛCDM model be a consequence of the specific datasets used and the redshift range considered, and might deviations emerge with future, more precise observations or at higher redshifts?

Yes, the apparent alignment of the f(T) model with the ΛCDM model could indeed be a consequence of the specific datasets used, the redshift range considered, and the parameterization chosen for the effective equation of state. Here's why:

Datasets and Redshift Range: The paper primarily uses data from relatively low redshifts (z < 2.5). At these redshifts, the expansion history of the Universe is not dramatically different between many dark energy models and the ΛCDM model. Future observations probing higher redshifts, such as those from the James Webb Space Telescope (JWST), will be crucial in distinguishing between these models. The higher redshift data will provide a more extended and detailed picture of the expansion history, potentially revealing subtle deviations from the ΛCDM model that are not apparent at lower redshifts.
Parameterization Choice: The paper adopts a specific parameterization for the effective equation of state (EoS) of dark energy. This choice can influence the model's ability to fit the data and might mask potential deviations from the ΛCDM model. Exploring other parameterizations or non-parametric reconstructions of the dark energy EoS could reveal discrepancies.
Degeneracies: There might be parameter degeneracies within the f(T) model that are not fully broken by the current data. More precise measurements, particularly of the growth of structure, could help break these degeneracies and potentially reveal deviations from the ΛCDM model.
Future Prospects:
Several observational probes could provide more stringent tests of the f(T) model and its potential deviations from the ΛCDM model:

High-Redshift Surveys: Surveys like the JWST will provide crucial data on the expansion history and the growth of structure at high redshifts, where differences between dark energy models and the ΛCDM model are expected to be more pronounced.
CMB Observations: Future CMB experiments with higher sensitivity and resolution could constrain the growth of structure and the sum of neutrino masses, providing additional tests of modified gravity theories.
Gravitational Wave Astronomy: Observations of gravitational waves from merging binary systems offer a new window to probe gravity in the strong-field regime. Deviations from General Relativity predicted by modified gravity theories like f(T) gravity could be imprinted on the gravitational wave signals.
In conclusion, while the f(T) model presented in the paper appears consistent with current data, it's crucial to remember that this apparent agreement might be limited by the available observations and analysis techniques. Future, more precise observations, especially at higher redshifts, will be essential to definitively test the model and determine whether it offers a viable alternative to the standard ΛCDM model.

If f(T) gravity provides a more accurate description of gravity than General Relativity, what implications would this have for our understanding of fundamental physics and the nature of spacetime, particularly in extreme gravitational environments like black holes or the very early universe?

If f(T) gravity were proven to be a more accurate description of gravity than General Relativity, it would have profound implications for our understanding of fundamental physics and the nature of spacetime, especially in extreme environments:
1. Nature of Spacetime:

Torsion over Curvature: A shift from General Relativity to f(T) gravity would mean that the fundamental description of gravity is not solely based on the curvature of spacetime but also on its torsion. This would necessitate a re-evaluation of the geometric foundations of gravity and could lead to a richer understanding of the fabric of spacetime.
Local Lorentz Invariance: One of the significant challenges of f(T) gravity is its potential violation of local Lorentz invariance. If f(T) gravity is indeed a correct description, understanding how this fundamental symmetry is recovered or modified would be crucial. It might point towards new physics beyond the Standard Model.
2. Extreme Gravitational Environments:

Black Holes: The dynamics of black holes, regions of spacetime where gravity is extremely strong, could be significantly altered in f(T) gravity. The singularity at the center of black holes, predicted by General Relativity, might be avoided or modified in f(T) gravity. This could have implications for the information paradox and our understanding of black hole thermodynamics.
Early Universe: The very early universe, characterized by extremely high energy densities and temperatures, provides a unique testing ground for gravity theories. f(T) gravity could lead to different predictions for inflation, the period of rapid expansion in the early universe, and might leave observable imprints on the cosmic microwave background radiation.
3. Fundamental Physics:

Dark Matter and Dark Energy: The success of f(T) gravity in explaining cosmic acceleration without dark energy could point towards a deeper connection between gravity and the other fundamental forces. It might even offer new insights into the nature of dark matter, potentially unifying these mysterious components within a single framework.
Quantum Gravity: The quest for a theory of quantum gravity, unifying General Relativity with quantum mechanics, is one of the biggest challenges in modern physics. If f(T) gravity is a step in the right direction, it could provide valuable hints for constructing a consistent theory of quantum gravity.
4. New Physics:

Extra Dimensions: Some modified gravity theories, including certain f(T) models, can arise from higher-dimensional theories. If f(T) gravity is favored by observations, it might provide indirect evidence for the existence of extra spatial dimensions.
Varying Constants: Certain f(T) models allow for the variation of fundamental constants, such as the speed of light or the gravitational constant, over cosmological timescales. Observational confirmation of such variations would have profound implications for our understanding of the fundamental laws of physics.
In conclusion: While the current evidence for f(T) gravity is not conclusive, its potential implications are far-reaching. If confirmed, it would revolutionize our understanding of gravity, spacetime, and the evolution of the Universe. It could open new avenues for exploring the cosmos and unveil fundamental connections between gravity and the other forces of nature, ultimately leading to a more complete and profound picture of the physical world.