I'd like to join this discussion because I am currently finalizing the latest updates to my work, with the paper titled:
ON THE EXISTENCE OF DARK MATTER AND DARK ENERGY
Dark matter and dark energy are functional to the LCDM model:
1.Dark Energy (Λ): Explaining Cosmic Acceleration Einstein’s Cosmological Constant (Λ): In General Relativity (GR), Λ represents a geometric term acting as a repulsive "vacuum energy.", In ΛCDM, Λ (dark energy) explains the observed cosmic acceleration discovered in 1998 (Type Ia supernovae data). Without dark energy, cosmic expansion would decelerate due to gravity from matter. Observations unambiguously show acceleration.
2.Dark Matter: The Scaffolding of Cosmic Structure (Non-baryonic, non-relativistic ("cold") matter interacting only via gravity. Without dark matter, ordinary (baryonic) matter would lack sufficient time to clump into galaxies within the universe’s age (13.8 billion years). Dark Matter provides the gravitational "seeds" for structure growth. Density fluctuations in the CMB (measured by Planck) require dark matter to evolve into galaxies and galaxy clusters.
I ask whether, outside of this model, but particularly excluding its FLRW metric, they are still necessary to explain physical phenomena.
We question here their very existence.
Key Points: The Einstein Field Equations, the Action Principle, and the Role of Λ.
The Einstein field equations are derived from a variational principle (specifically, the Einstein-Hilbert action).
Λ does not alter the fundamental variational principle itself. Instead, it introduces a constant term into gravitational action.
Physically, Λ represents a vacuum energy density that contributes to spacetime curvature even in the absence of matter. Without Λ, the action would produce the original Einstein equations, with Λ, the equations include an additional term, driving cosmic acceleration.
Historical and Conceptual Implications:
Einstein initially added Λ "by hand" to his equations to achieve a static universe. After Edwin Hubble’s discovery of the universe’s expansion (1929), Einstein dismissed Λ as his "greatest blunder," deeming it unnecessary.
It later became a natural part of the action formalism. In modern physics indeed, Λ is interpreted as dark energy, an intrinsic property of spacetime encoded in the action itself.
Λ is often linked to quantum vacuum energy, but its theoretical value (predicted by quantum field theory) and observed value (from cosmology) differ by 120 orders of magnitude – one of the greatest unsolved mysteries in physics (the "cosmological constant problem").
Key Points: Estimating the Presence of Dark Matter through the Study of Gravitational Lenses.
In gravitational lensing systems, analogous to classical optics, the lens equation depends on the geometric relationships between the observer, lensing mass, and light source. Specifically:
A). The deflection angle is derived from the relative distances between:
- The observer and the source plane (where the background star/galaxy resides).
- the observer and the lens plane (where the foreground mass is located).
B). These distances are typically estimated using redshift data, interpreted through a chosen cosmological metric (e.g., FLRW).
Note that, under extreme conditions, in the lens equation, the smaller the ratio between the distances from the "lens" and from the "source", the more the mass of the "lens" and its distance from us become directly proportional.
Concerning my study performed on the article:
arXiv:astro-ph/0701589 – The Sloan Lens ACS Survey. IV. The Mass Density Profile of Early-Type Galaxies out to 100 Effective Radii, a confirmation of 4-Sphere model (my OSF Project) was not achieved: I was unable to obtain the mass of the gravitational lens through an independent observation. This is due to the complexity of the estimation, which requires a model-based refinement, and the difficulty in obtaining the observational data.
Nevertheless the discussion highlights that distance assumptions—tied to recession velocity models—play an underestimated role in mass calculations.
Key Points: Key Points: Estimating the Presence of Dark Matter through the Study of Galaxy Rotation Curves.
When challenging the presence of Dark Matter based on galaxy rotation curves, the discussion becomes more complex:
The rotation curve of galaxies is often traced by observing gas (HI, CO) as well as stars. If present, magnetic fields can influence the motion of gas, altering the observed rotation curve. Additionally, the galaxy’s density may not be uniform.
Certainly, these two factors alone cannot fully account for the observed deviations. However, the assumed model used to theorize the rotation curve might play a crucial role.
Inside galaxies, classical mechanics is typically used, but a more appropriate approach would be applying the Schwarzschild metric for the interior solution of a rotating sphere of fluid, as a first approximation of a mixture of gas, dust, and stars. This brings into play the study published in
The European Physical Journal C, Volume 81, Article Number: 186 (2021) — Galactic rotation curve and dark matter according to gravitomagnetism.
This study presents a new approach where, due to the coexistence of stars, gas, and dust in a galaxy, the classical concept of equilibrium between gravitational and centrifugal forces is replaced by a set of equations governing the motion of a perfect fluid in a gravitational field. The approximation used is that of weak fields, employing the analogy known as Gravitoelectromagnetism.
These are the conclusions:
“The effects attributed to dark matter can be simply explained by the gravitomagnetic field produced by the mass currents.”
Key Points: Dark Matter detection.
My goal is not to refute the existence of Dark Matter—since it is not a directly measurable entity, it is up to others to prove its existence.
Direct dark matter detection has made significant progress in recent years, although definitive results have not yet been obtained. Here’s an update on the main ongoing experiments:
- XENON1T Experiment:
XENON1T was one of the most sensitive detectors for direct dark matter detection. In 2020, it reported an excess of events that sparked interest in the scientific community. However, further analysis suggested that this excess might be due to statistical fluctuations or contamination from cosmic radiation, rather than dark matter signals.
- LUX-ZEPLIN (LZ) Experiment:
LZ is a next-generation detector designed to be more sensitive than XENON1T. In 2022, it began operations, aiming to detect rare interactions between dark matter particles and atomic nuclei. Preliminary results have not shown any dark matter signals but have contributed to further narrowing down the limits on dark matter candidate parameters.
- CRESST-III Experiment:
CRESST-III uses scintillating crystals to detect interactions between dark matter particles and atomic nuclei. In 2017, it published results that excluded a wide range of possible dark matter masses, helping to constrain theoretical models.
- DarkSide-50 Experiment:
DarkSide-50 uses ultra-pure liquid argon to detect dark matter signals. In 2018, it published results that excluded a wide range of possible interactions between dark matter and ordinary matter, contributing to further narrowing theoretical models.
- CERN Experiments:
At CERN, experiments like SND@LHC and SHiP are designed to search for dark matter particles produced in high-energy collisions. These experiments are either still being prepared or have just begun operations, and definitive results are expected in the coming years.
In summary, while no direct signals of dark matter have been detected yet, the ongoing experiments are helping to narrow the parameters of theoretical models and improve our understanding of the possible interactions of dark matter with ordinary matter.