Can a Slowly Varying Newton's Constant Resolve Issues in Gravitational Theory?

Core Concepts

A slowly varying Newton's constant, consistent with existing bounds, could potentially explain various gravitational phenomena from planetary to cosmological scales without requiring dark matter or dark energy.

Abstract

• Bibliographic Information: Das, S., & Sur, S. (2024). Varying Newton’s constant: a cure for gravitational maladies? arXiv preprint arXiv:2411.06489v1.
• Research Objective: This paper explores whether a radially varying Newton's constant (G) can address challenges in explaining gravitational phenomena at different scales, potentially offering an alternative to dark matter and dark energy.
• Methodology: The authors propose a Taylor expansion of G as a function of radial distance (r), analyze its implications for galaxy rotation curves, gravitational lensing, the virial theorem, and cosmological dynamics. They derive modified Friedmann and Raychaudhuri equations incorporating the varying G and perform cosmological parameter estimation using observational data from Supernovae Type Ia and Hubble parameter measurements.
• Key Findings: The varying G model potentially explains the flatness of galaxy rotation curves, mass overestimation in gravitational lensing, and modifications to the virial theorem. Cosmological analysis suggests a significant reduction in the required cold dark matter content compared to the standard ΛCDM model. The study finds that a model with additional terms related to the varying G, particularly a logarithmic potential term and a constant force term, is favored by observational data.
• Main Conclusions: A varying Newton's constant offers a promising avenue for addressing challenges in gravitational theory, potentially explaining observations without relying heavily on dark matter or dark energy. The proposed model suggests a dynamic dark energy component and requires further investigation within a covariant theoretical framework.
• Significance: This research challenges the standard cosmological model and proposes a novel approach to understanding gravity at various scales. If validated, it could revolutionize our understanding of the Universe's composition and evolution.
• Limitations and Future Research: The study primarily employs a quasi-Newtonian framework for cosmological analysis. Future research should focus on embedding the varying G concept within a fully covariant theory, such as non-local gravity, and analyzing cosmological perturbations to reconcile the model with observations of the cosmic microwave background and baryon acoustic oscillations. Further investigation is needed to understand the implications of a varying G at very short distances and its potential impact on quantum gravity theories.

Stats

|G(r) −G0|/G0 ≪ 10−N, ∀r < L0, where N ≳ 5.
Typical galaxy mass M ≃ 10^42 Kg.
Typical galaxy rotation curve velocity v ≃ 10^5 m/s.
Apparent mass estimated via lensing can exceed the actual gravitating mass by a factor of up to 10.
The Pantheon+SH0ES data-set consists of 1701 light curves of Supernovae type Ia.
The observational Hubble data-set (OHD) consists of 51 measurements of H(z).
Baryonic matter constitutes about 5% of the Universe.

Quotes

"The logarithmic correction term in the potential (5) is well-known and has been considered by numerous authors."
"In other words, the apparent mass M′ estimated via lensing, if considered without the 1/r term in Eq.(4) or the logarithmic term in Eq.(5), can exceed the actual gravitating mass M by a factor of up to 10."
"Therefore, when quantum effects are expected to be dominant, i.e. for r → 0, a de facto vanishing coupling constant would preclude any problematic quantum gravity effects, or for that matter any quantum gravity effects !"

Key Insights Distilled From

Varying Newton's constant: a cure for gravitational maladies?

by Saurya Das, ... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.06489.pdf

Deeper Inquiries

How would a varying Newton's constant affect our understanding of the early Universe and its evolution through inflation?

Answer:
A varying Newton's constant (G) would have profound implications for our understanding of the early Universe and its evolution through inflation. Here's how:

Inflationary Dynamics: Inflation, a period of rapid expansion in the early Universe, is highly sensitive to the strength of gravity. A varying G would directly impact the expansion rate during inflation, potentially altering the duration of this epoch and the resulting density fluctuations.
Scalar Field Dynamics: Most inflationary models rely on a scalar field, the inflaton, driving the rapid expansion. A varying G would couple to this scalar field, potentially affecting its potential and dynamics. This could lead to different inflationary scenarios with distinct observational signatures in the Cosmic Microwave Background (CMB).
Primordial Density Fluctuations: Inflation is believed to be responsible for seeding the primordial density fluctuations that later gave rise to galaxies and large-scale structures. A varying G would modify the growth of these fluctuations during inflation, potentially leaving a distinct imprint on the CMB power spectrum and the matter power spectrum.
Big Bang Nucleosynthesis: The abundance of light elements produced during Big Bang Nucleosynthesis (BBN) is sensitive to the expansion rate of the Universe. A varying G during BBN could alter the predicted abundances of these elements, potentially conflicting with current observations.
In summary, a varying G in the early Universe would necessitate a reevaluation of inflationary models and our understanding of the generation of primordial density fluctuations. It could also have observable consequences for the CMB and the abundance of light elements.

Could the observed effects attributed to a varying Newton's constant be explained by other modifications to General Relativity, such as alternative theories of gravity?

Answer:
Yes, the observed effects attributed to a varying Newton's constant could potentially be explained by other modifications to General Relativity (GR) and alternative theories of gravity. Here are some examples:

Scalar-Tensor Theories: These theories introduce a scalar field alongside the metric tensor of GR. The scalar field can couple to gravity, leading to an effective variation of G in space and time. Brans-Dicke theory is a well-known example.
f(R) Gravity: These theories modify the Einstein-Hilbert action of GR by replacing the Ricci scalar (R) with a function of R, f(R). This modification can lead to an effective variation of G and mimic the effects of dark matter and dark energy.
MOND (Modified Newtonian Dynamics): MOND posits a modification of Newtonian dynamics at low accelerations, typically relevant for galactic scales. While not directly modifying G, it can explain the flat rotation curves of galaxies without invoking dark matter.
TeVeS (Tensor-Vector-Scalar Gravity): TeVeS is a relativistic generalization of MOND that introduces additional vector and scalar fields. It can reproduce MOND-like behavior on galactic scales while also being consistent with GR on larger scales.
Distinguishing between these alternatives and a varying G requires careful analysis of observational data across a wide range of scales, from the solar system to cosmology. The specific predictions for the growth of structure, gravitational lensing, and the CMB can differ between these theories, offering potential avenues for testing and discrimination.

If the strength of gravity changes over time and distance, what are the philosophical implications for our understanding of fundamental constants and the universality of physical laws?

Answer:
If the strength of gravity, as determined by Newton's constant G, changes over time and distance, it raises profound philosophical questions about our understanding of fundamental constants and the universality of physical laws:

The Nature of Fundamental Constants: A varying G challenges the very notion of what constitutes a fundamental constant. If G is not constant, what other "constants" might vary? This could point towards a deeper underlying theory where these constants are not fundamental but emerge from more fundamental entities or principles.
The Universality of Physical Laws: A cornerstone of modern physics is the assumption that physical laws are universal, holding true everywhere and at all times. A varying G could imply that the strength of gravity, and potentially other physical laws, might be different in different parts of the Universe or at different epochs. This raises questions about the uniformity of the Universe and the applicability of our locally derived laws on cosmological scales.
The Anthropic Principle: If fundamental constants can vary, it raises the question of why our Universe has the specific values we observe. The anthropic principle suggests that the observed values are fine-tuned for the existence of life, as even slight variations could have resulted in a vastly different Universe.
In conclusion, a varying G challenges our understanding of the fundamental building blocks of physics and the universality of physical laws. It compels us to reconsider the nature of physical reality and the possibility of a Universe governed by more complex and dynamic principles than we currently comprehend.