# Exploring a Novel Solution to the Cosmological Constant Dilemma

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The cosmological constant remains a significant challenge for physicists, often cited as one of the most egregious theoretical miscalculations in the field. New strategies are urgently needed to address this cosmic puzzle.

Albert Einstein, renowned for his groundbreaking contributions, famously labeled the cosmological constant his "greatest blunder." This issue continues to elude resolution today.

Currently, the cosmological constant serves as the simplest explanation for dark energy, which constitutes approximately 70% of the universe's total energy, propelling its accelerated expansion. Rather than attracting, it acts as a counterforce to gravity, pushing matter apart.

A heated debate persists among scientists concerning the value of the cosmological constant, represented by the Greek letter Lambda. Researchers are investigating Einstein's general relativity equations from various angles to unravel this cosmic enigma.

This problem succinctly highlights the ongoing divide in physics between theory and experiment, as theoretical predictions vastly exceed observational values. This discrepancy is attributed to contributions from "empty space," where vacuum energy emerges from particles and antiparticles transiently appearing in the void.

Enter Lucas Lombriser, an assistant professor at the University of Geneva, who proposes a groundbreaking new approach to this issue.

Lombriser theorizes that the challenge with the cosmological constant may stem from another fundamental constant in physics—Newton's gravitational constant (big G)—which might not be a constant at all. Instead, it could vary across different universes, taking distinct values but remaining fixed in our universe at 6.673 x 10?¹¹ Nm² kg?².

"Efforts to elucidate the cosmological constant have been unsuccessful, suggesting we are missing a fundamental aspect of our cosmic understanding," Lombriser explains in a paper published in *Physical Letters B*.

> “I became increasingly unsatisfied with some of the main candidates that have been proposed to solve the problem.”

The unification of particle physics, general relativity, and quantum theory could potentially resolve the cosmological constant issue, but Lombriser believes that a precise value for vacuum energy lies elsewhere.

"We may have been overly focused on this concept," he says. "A new strategy is required to tackle this issue."

This led Lombriser to examine big G as a potential solution to the cosmological constant dilemma. While this choice may seem unusual given its extensive application in physics, Lombriser's new mechanism aligns with the predictions of Einstein's general relativity and standard gravity theory while providing a cosmological constant that corresponds with observations.

This approach narrows the gap by treating big G as a variable, thereby negating the contribution of vacuum energy to the cosmological constant. This method has not been previously attempted in the long-standing quest to resolve the cosmological constant issue.

## The Cosmological Constant: A Controversial History

Lombriser describes the cosmological constant problem as having two distinct phases: the old and the new.

Einstein initially incorporated the constant into his field equations of general relativity to counterbalance the prediction of an expanding universe, a notion that contradicted the scientific consensus of a static universe in 1917, shortly after the completion of general relativity. Edwin Hubble would later challenge this view, providing solid evidence of the universe's expansion.

Upon reviewing Hubble's findings, Einstein recognized his error; his original equations were indeed accurate, while the cosmological constant was a miscalculation.

In 1931, he eliminated the cosmological constant from his equations, famously dubbing it his "greatest blunder." However, the scientific community was not finished with Lambda.

The cosmological constant re-emerged in 1998 when cosmologists discovered that the universe's expansion was not only ongoing but accelerating. At this point, the cosmological constant was reintroduced to account for this acceleration.

Yet, the cosmological constant continues to perplex scientists. The theoretical value predicted by quantum field theory is astronomically higher than the values observed through supernova and cosmic background radiation studies, which are remnants of the early universe's "last scattering."

"The gap between theoretical predictions and experimental values is staggering, amounting to a factor of 10¹²¹," Lombriser notes.

> “It has been labeled as 'the worst theoretical prediction in the history of physics.'”

Lombriser warns that such a significant contribution from vacuum energy would likely have prevented the universe from forming in the first place, indicating that something fundamental is missing—a notion that fuels excitement and inspiration among researchers across various scientific disciplines, including Lombriser himself.

## Could Newton's Gravitational Constant Be the Key?

Lombriser's innovative approach to the cosmological constant issue focuses on big G, a constant with a long history and fewer controversies.

His methodology builds on models proposed by other researchers who have altered elements of Einstein's field equations from constants to variables, incorporating a "sequestering" mechanism introduced by Nemanja Kaloper and Antonio Padilla five years prior.

"My paper doesn't fundamentally alter the equations of general relativity," Lombriser clarifies. "Instead, it adds an additional equation to Einstein's field equations."

Lombriser notes that the elegance of his proposed mechanism lies in its ability to produce predictions for the cosmological constant that closely align with observational values, unlike previous models.

"The value of the cosmological constant is determined by the formation of structures, like galaxies, within the cosmos' matter distribution," Lombriser explains. "This can be conceptualized as a backreaction effect, where 'matter clumps' on smaller scales influence the universe's dynamics at larger scales."

This backreaction mechanism would prevent vacuum energy from gravitating, thereby eliminating its contribution to the theoretical cosmological constant, Lombriser asserts.

"Vacuum energy does not directly impact gravitational dynamics," he adds. "Instead, the cosmological constant that influences dynamics must correlate with the average matter content in our universe."

One of the strengths of Lombriser's perspective is its simplicity. "The components are remarkably straightforward," he states.

> “There are no new elements, except for a global variation of Newton's gravitational constant within the standard equations of gravity.”

Upon evaluating the new equation, Lombriser arrives at a predicted value for the cosmological constant that is in good agreement with observational data. By rendering the quantum contribution of vacuum energy gravitationally inert, the cosmological constant issues are addressed, but this raises the question: is it justified to modify the equations of general relativity?

## If It Works, Why Change It?

Lombriser's focus on Newton's gravitational constant was deliberate. He initially explored other methods to understand the universe's expansion before considering G. "I investigated gravity modifications as a possible cause of cosmic expansion," he explains.

> “I gradually became dissatisfied with this approach, as it didn't tackle the core issue of cosmic acceleration.”

The measurement of gravitational wave speeds also dismissed several alternative gravity models proposed to explain the accelerating expansion of the cosmos, according to Lombriser.

He acknowledges that while Kaloper and Padilla's approach is appealing, it does not clarify why the observed value of the cosmological constant is so small. In their original sequestering model, the universe should have ceased expanding billions of years ago to arrive at a precise fit for the cosmological constant's value.

"What I needed was a model of cosmic evolution that would conclude in the future while also yielding the correct cosmological constant value," he continues. "I could have accomplished this by introducing new fields throughout the universe or modifying gravity, but the results were not promising."

> “Moreover, the universe's future evolution appeared arbitrary, lacking a natural path to produce the required cosmic end.”

Lombriser realized that the formation of structures in the universe's matter distribution, particularly regarding galactic clusters, would supply his model with the collapse event necessary for a natural prediction of the cosmological constant.

"While I could make this idea compatible with the sequestering mechanism, it still required structure formation to cease at a specific time in the future to yield the observed cosmological constant values."

Investigating the sequestering mechanism's function led Lombriser to the conclusions presented in this paper—a generalization and simplification of the elements that enable the mechanism's functionality.

While promising, this new model is not without challenges. The pressing question remains: can cosmologists experimentally verify it?

## Future Prospects: A New Era in Cosmology or Another Dead End?

I inquire about the feasibility of verifying the variability of Newton's gravitational constant. "Regrettably, for the type of variation I propose, this will be a complex challenge," he responds. "Big G would not vary in the observable universe—it remains constant throughout."

However, this does not imply that his model is entirely untestable. "The appropriate inquiry to verify my model is to examine the effects these fundamental theories may have that can be tested," he adds. "Falsification through experimentation seems challenging given the current understanding of this model."

One advantage of this new model is its ability to replicate the observable success of standard cosmology, all while eliminating the cosmological constant problem and one less free parameter—making it statistically more favorable, according to Lombriser.

The model might also benefit from the unpredictable nature of scientific progress, allowing other cosmologists to find compelling elements in Lombriser's work to develop their own models.

"Researchers exploring new fundamental theories might use this mechanism as motivation to focus on those that can give rise to it," he agrees.

> “Ideally, these theories would also generate verifiable and falsifiable predictions.”

Lombriser emphasizes the importance of exploring different theories that produce the mechanism he proposes. By systematically ruling out these theories, a solution to the cosmological constant problem may emerge—or, Lombriser acknowledges, his mechanism could be entirely dismissed.

Robert Brandenberger, a theoretical cosmologist and physics professor at McGill University in Montreal, Canada, recognizes the merit of Lombriser's new model.

"I view this paper as an important and intriguing idea to address a crucial issue in fundamental physics," says Brandenberger, who is no stranger to proposing alternative cosmological theories as the co-founder of string gas cosmology.

"I would like to see this work extended to assess how the new equations impact the formation of structures in the universe," Brandenberger cautions. "It is essential to investigate the effects on small inhomogeneities that evolve into microwave anisotropies in the cosmic microwave background and the large-scale structure of galaxy distributions."

Only time will reveal whether Lombriser's theory will yield fruitful insights. If he has indeed identified the correct mechanism to resolve the cosmological constant problems, it may also raise further questions, such as what other universes with different values of big G might look like.

Alternatively, if Lombriser's work proves incorrect or incomplete, a future researcher may discover his paper and cultivate their own ideas.

The realm of theoretical physics remains a complex and intricate landscape.