Varying Newton Gravitational “Constant” Cosmology

Hello, my name is Clovis de Matos, and I am with the European Space Agency in Paris, France. I collaborated with Nicolas Lori from the Algorithmic Lab at the University of Minho in Portugal on an article titled "Varying Newton Gravitational Constant Cosmology." This article has been accepted for publication in the journal Annals of Physics, which has graciously invited us to present a seminar on our findings.

You may wonder why it is important to read an article that explores the physical implications of a varying Newton's gravitational constant in astrophysics and cosmology. Traditionally, Newton's gravitational constant has been regarded as a fixed value since Newton's formulation of the law of universal gravitation. However, our research challenges this notion.

In this presentation, I will outline our key arguments supporting the concept of a varying gravitational constant and discuss its potential implications for black hole physics and the standard cosmological model. We hope this overview will encourage you to explore our article further. The accompanying image features one of the oldest and most distant black holes observed by the James Webb Space Telescope.

Newton assumed that the gravitational constant, G, was constant in his law of universal gravitation primarily because he viewed space and time as absolute. This perspective allowed for the possibility of defining a universal present moment, suggesting that the speed of gravitation, like other interactions in Newtonian mechanics, could be infinite. Consequently, gravitation could always escape its own pull, meaning there was no gravitational cutoff length. This notion implies that black holes cannot exist within the framework of classical mechanics.

In contrast, Einstein's theory of relativity introduces a four-dimensional geometric continuum known as the space-time continuum. In this framework, gravitational interactions propagate at a finite speed—the speed of light. This leads to the existence of a gravitational cutoff length, specifically the Schwarzschild radius, thereby making black holes feasible within relativistic mechanics.

If G remains constant, black holes would be unable to interact gravitationally with the universe, as their gravitational pull would not allow for escape. However, if G fluctuates, gravitation could escape from black holes when the value of G permits escape speeds that are less than the speed of light. In this scenario, black holes could interact with the universe, potentially behaving as scintillating objects that emit flashes of light and gravitational waves.

To account for a varying gravitational constant, we propose a relationship between quantum gravity and the gravitational cutoff length of a system, equating the quantum length that characterizes a quantum system with this cutoff length.

In various theories of quantum gravity, the concept of the gravitational cutoff length differs significantly. In string theory, it is defined as the size of the string. In loop quantum gravity, it corresponds to the diameter of the loop. Additionally, in the recently developed PC approach to quantum gravity, proposed by my co-author Nicolas Lori, the gravitational cutoff length is linked to the diameter of what we refer to as the physics cell, abbreviated as PC.

Regardless of the quantum gravity theory employed, it is consistently observed that Newton's gravitational constant, G, is influenced by the gravitational cutoff length scale. Variations in this scale can lead to fluctuations in the value of G. By applying the Heisenberg uncertainty principle to the gravitational length scale, we find that the relative fluctuation of G is constrained to be less than or equal to 1/2π.

The Heisenberg uncertainty principle has significant implications for the vacuum state. It facilitates the spontaneous creation and annihilation of electron-positron pairs within the vacuum.

Consider a vacuum influenced by fluctuating gravitational fields. At a specific moment (T1), fluctuations in the gravitational constant (G) lead to the creation of an electron-positron pair at an initial energy level (E_initial) when G is at value G1. This pair subsequently falls a quantum wavelength to a lower energy level. Upon reaching this lower level, the gravitational constant has changed to G2, resulting in the spontaneous annihilation of the pair into gamma rays. These gamma rays then ascend back to the original energy level, where they generate a new electron-positron pair at event 3, with the gravitational constant now at G3.

During the transition from event 1 to event 2, the electron-positron pair experiences a change in gravitational potential energy, which should ideally be balanced by the gravitational Doppler shift of the gamma rays. This balance is only achieved if the gravitational constant remains constant across events 1, 2, and 3. In such a scenario, the initial and final energies of the electron-positron pair would be equal, resulting in no net radiation emission.

However, if G fluctuates—taking values G1 at event 1, G2 at event 2, and G3 at event 3—the initial and final energies of the electron-positron pair will differ, leading to an imbalance that prevents the gravitational Doppler shift from compensating. This variation in gravitational potential energy allows for the emission of Hawking radiation, indicating that all massive objects, not just black holes, can produce such radiation.

In contrast, Unruh radiation is not observable in relation to G fluctuations; it is instead associated with constant mechanical acceleration or with equivalent constant gravitational fields that do not involve fluctuations in G.

The horizon of events of a Schwarzschild black hole, defined by its Schwarzschild radius, will fluctuate in response to variations in the gravitational constant G. These random fluctuations, denoted as ±δ Rs, will cause corresponding changes in the kinetic energy of the orbiting plasma of ions within the accretion disk surrounding the black hole. As a result, the observed luminosity of the accretion disk near the black hole horizon will also exhibit fluctuations.

The fluctuations of the Schwarzschild horizon, assuming that 100% of the accretion rest mass is converted into energy, indicate that the relative fluctuation of the gravitational constant ( G ) near a black hole's horizon is directly proportional to the volumetric luminosity of the accretion disk and inversely proportional to the accretion mass rate.

When applying this relationship to observed black holes in Active Galactic Nuclei (AGN) across various redshifts, we observe a Gaussian distribution for the relative variation of ( G ) in relation to the galactic redshift ( z ), as illustrated in the bottom left of the slide. This distribution represents the best statistical fit for the calculated ( \delta G / G ). The analysis is based on observational data from multiple AGN at varying redshifts, indicating their distances from Earth.

The oscillations of the event horizon in Schwarzschild black holes, caused by fluctuations in the gravitational constant (G), introduce a novel mechanism for the emission of gravitational waves. We assume that the amplitudes of these gravitational waves correspond to those detected by various Pulsar timing array teams, which have been associated with the Stochastic Gravitational Wave Background.

Our analysis reveals a linear relationship between the mass of black holes and redshift, illustrated in green on the graph. The continuous red line represents the linear fit of the experimentally observed masses of different black holes across varying redshifts, which aligns closely with the theoretical predictions depicted by the continuous green line, falling within the standard error of the mean.

Furthermore, the variation of G in Einstein's field equations necessitates a re-evaluation of the Friedmann-Lemaître-Robertson-Walker cosmological equation concerning the universe's matter and energy content. Our findings suggest that fluctuations in Newton's gravitational constant can account for approximately 24.24% of dark matter, with the remaining 2.16% attributable to torsion, as shown in the equation in the lower left corner of the slide. In this equation, δG represents the matter density resulting from variations in G, while ρₜ denotes the matter density due to torsion.

Additionally, the varying G concept addresses the Hubble tension by suggesting that G fluctuations were more pronounced during the Cosmic Microwave Background (CMB) epoch compared to the Cepheid period. Our approach also resolves the firewall paradox, demonstrating that an observer at rest on a black hole's event horizon perceives the same radiation as an observer in free fall through the horizon. This observation indicates that the radiation is solely dependent on the amplitude of gravitational field fluctuations at the horizon.

Further research on fluctuations of the gravitational constant (G) can be conducted through various experimental and observational methods. In terrestrial laboratories, advanced Cavendish-type experiments with enhanced accuracy, along with Earth-based gravitational wave detectors such as LIGO and Virgo, can be utilized.

In space, advanced telescopes like the James Webb Space Telescope can observe the first galaxies in the universe, while the Euclid mission will map the distribution of dark matter and dark energy. Additionally, the advent of gravitational wave astronomy will enable exploration of G fluctuations using the LISA gravitational wave detector and Pulsar timing arrays, which have recently highlighted the Stochastic Gravitational Wave Background.

There is also potential for new experiments to measure G by comparing advanced atomic clocks situated in space and on Earth. However, the precision of current atomic clocks is still inadequate to challenge G measurements obtained through traditional Cavendish balances.

Further research on gravitational (G) fluctuations, as discussed in this work, can be conducted using various experimental and observational methods.

On Earth, advanced Cavendish-type experiments with enhanced accuracy can be employed, along with Earth-based gravitational wave detectors such as LIGO and Virgo.

In space, we can utilize sophisticated telescopes like the James Webb Space Telescope, which observes the first galaxies in the universe, and the Euclid telescope, which maps the distribution of dark matter and dark energy.

Looking ahead, the emergence of gravitational wave astronomy will allow us to investigate G fluctuations using the LISA gravitational wave detector and pulsar timing arrays, which have recently highlighted the Stochastic Gravitational Wave Background.

Additionally, new experiments may be designed to measure G by comparing advanced atomic clocks in space with those in Earth's laboratory. However, current atomic clock technology is not yet precise enough to challenge G measurements obtained with traditional Cavendish balances.