As they observe the universe, astronomers can detect several effects that seem to contradict our present understanding of gravity. Among them are measurements of the speed at which galaxies rotate. According to general relativity, these rotation speeds should steadily slow down with increasing distance from the galactic centre – but in most galaxies we can observe, these speeds remain mostly constant, in stark contrast to theoretical predictions.

This appears to point to a universe permeated by an immense source of mass, named dark matter. This hypothetical substance does not interact with light or other electromagnetic radiation, but still exerts gravitational influence on visible matter. Today, astronomers widely assume that each observed galaxy is immersed in a dark matter halo, completely invisible even to the most advanced telescopes.

Additional evidence for these halos comes from the effect of gravitational lensing, where light from distant galaxies is bent by distortions in spacetime created by the mass of foreground galaxies. Often, this lensing appears stronger than general relativity can explain, again pointing to the need for more mass than we can observe.

Further mysteries arise from measurements of the universe’s expansion. According to the standard Big Bang model, with galaxies surrounded by dark matter halos, this acceleration should behave like a centripetal force, pulling inwards. Yet in contrast, by observing how quickly distant galaxies are moving away from us, astronomers find that the current acceleration of the universe’s expansion behaves like a centrifugal force, pushing outward.

Over the past few decades, scientists have developed a wide range of theories to explain the nature of dark matter, alongside numerous experiments to detect any interaction it may have with light or ordinary matter. Yet despite decades of searching, results have consistently come up short. While some physicists remain hopeful that experimental breakthroughs lie ahead, others are now questioning whether dark matter exists at all.

Instead, theorists such as Nesbet argue that the need for dark matter may have only emerged because Einstein’s theory of gravity is incomplete. If so, the answer to astronomers’ observations won’t come from elusive particles, but from a more fundamental rethink of gravity itself. This reconsideration has led researchers to explore alternative formulations of gravity, capable of reproducing cosmic observations without invoking unseen matter.

An alternative to general relativity has been established by requiring Weyl scaling symmetry. The fundamental gravitational tensor of Einstein is replaced by the traceless Weyl tensor. This defines Conformal Gravity, where conformal symmetry is such that physical laws remain the same even if all fields are scaled by a differentiable scalar quantity. Conformal symmetry has been found to explain the gravitational increment responsible for observed excessive galactic rotation velocities.

For example, an apple falling from a tree accelerates because it follows the curved spacetime shaped by Earth’s mass. Both the apple’s path and the measured distance and time of its fall are determined by this curvature. If the apple fell on another planet with a different mass, that curvature would change, altering the apple’s trajectory and the time it takes to hit the ground.

Under such transformations, spacetime distances can stretch or shrink depending on location. Imagine a grid of tiny squares drawn on a rubber sheet. If the sheet is stretched or compressed in places, the squares might grow or shrink. But their 90-degree angles stay the same, meaning their shape is preserved even as their size changes.

In this analogy, a falling apple still moves in the same direction under conformal gravity. However, the distance it falls, and the time it takes, may differ depending on how spacetime has been rescaled. Crucially, this allows for the preservation of certain physical laws while still enabling spacetime to evolve in ways that differ from general relativity.

This mathematical flexibility opens new possibilities for understanding gravity on both small and large scales. By extending symmetry principles that are already fundamental to quantum field theory, conformal gravity offers a framework that is more aligned with the scale-invariant behaviour observed in high-energy physics.

This broader framework raised hopes that astronomers’ observations – like flat galactic rotation curves – could be explained without dark matter. But one major obstacle remained. A key mathematical feature of conformal gravity is the Weyl tensor, which describes shape-changing aspects of spacetime curvature while ignoring changes in volume caused by mass and energy. However, a significant limitation emerges when considering the Hubble expansion model, which describes how the universe is expanding.

On cosmic scales, the Hubble model shows that matter and energy are spread out nearly evenly, with no large-scale variation. The universe also appears the same in every direction. In cosmological terms, the universe is homogeneous and isotropic. Under these conditions, the Weyl tensor becomes zero – meaning conformal gravity alone can’t explain the universe’s accelerating expansion.

Nesbet has proposed a solution to the issue, extending conformal symmetry to all elementary fields. This postulate of universal conformal symmetry, applied to the Higgs scalar field of elementary particle physics, implies the Conformal Higgs Model (CHM). The Higgs scalar field extends throughout the universe. The CHM is found to imply a Friedmann equation for centrifugal cosmic expansion in agreement with observations of the redshift of distant supernovae.

Beyond matching observations, CHM could also solve some of the deepest mysteries in cosmology. General relativity requires dark matter halos to explain why galaxies rotate the way they do and why gravitational lensing is so strong. But according to CHM, such halos may not be needed. When a galaxy forms from the collapse of a cloud of gas and dust, it leaves behind a spherical region around it – a ‘vacuum bubble’ – that lacks the mass and energy that was pulled into the galaxy.

According to CHM, this empty region naturally creates the observed galactic rotation speeds and lensing strengths. In other words, the effects previously attributed to dark matter halos arise as a direct consequence of how mass condenses and warps spacetime under conformal gravity.

Even more significantly, Nesbet argues that CHM provides an effective cosmological constant determined by the Higgs scalar field, offering an elegant explanation of observed cosmic acceleration. In general relativity, an energy source named ‘dark energy’ is needed to explain why the universe’s expansion is speeding up, and it would need to account for nearly 68% of the total energy in the universe. Yet like dark matter, its source remains mysterious.

CHM shows that the observed acceleration can be fully explained by the Higgs field’s properties and how it interacts with spacetime under Weyl symmetry. There is no need to invoke an additional, unseen energy source.

This result not only removes one of the biggest theoretical burdens in modern cosmology, but it also enhances the internal coherence of the gravitational model by uniting particle physics and cosmology in a single conformally symmetric framework.

The CHM does not imply a massive Higgs boson, but produces a neutral diboson formed by interacting gauge boson pairs. The mass is 125GeV, equal to that of the recently observed neutral particle.

For now, standard general relativity remains at the forefront of theoretical physics. But based on the success of its predictions so far, Nesbet is hopeful that conformal theory could become more widely accepted as a serious alternative.

If his ideas are correct, they would explain why dark matter and dark energy have remained so elusive. Rather than existing as real substances, they may simply be artefacts of an incomplete gravitational theory.

By eliminating the need for these entities altogether, the conformal theory could offer long-awaited solutions to some of cosmology’s most enduring puzzles – and may eventually reshape our understanding of the universe itself.

Ultimately, conformal gravity and CHM presents a striking example of how combining insights from high-energy physics with alternative gravitational theories can shed light on long-standing astronomical mysteries. As observational capabilities improve and theoretical tools evolve, the next decade could see conformal theory tested more rigorously, either confirming its bold predictions or refining our path toward a deeper, more complete theory of the cosmos.