Einstein’s theory of gravity — general relativity — has been very successful for greater than a century. Nonetheless, it has theoretical shortcomings. This shouldn’t be surprising: the speculation predicts its own failure at spacetime singularities inside black holes — and the Big Bang itself.
Unlike physical theories describing the opposite three fundamental forces in physics — the electromagnetic and the strong and weak nuclear interactions — the overall theory of relativity has only been tested in weak gravity.
Deviations of gravity from general relativity are on no account excluded nor tested all over the place within the universe. And, in accordance with theoretical physicists, deviation must occur.
Related: Was Einstein mistaken? The case against space-time theory
Deviations and quantum mechanics
In keeping with Einstein, our universe originated in a Big Bang. Other singularities hide inside black holes: Space and time stop to have meaning there, while quantities reminiscent of energy density and pressure develop into infinite. These signal that Einstein’s theory is failing there and should be replaced with a more fundamental one.
Naively, spacetime singularities must be resolved by quantum mechanics, which apply at very small scales.
Quantum physics relies on two easy ideas: point particles make no sense; and the Heisenberg uncertainty principle, which states that one can never know the worth of certain pairs of quantities with absolute precision — for instance, the position and velocity of a particle. It is because particles mustn’t be considered points but as waves; at small scales they behave as waves of matter.
That is enough to know that a theory that embraces each general relativity and quantum physics must be freed from such pathologies. Nonetheless, all attempts to mix general relativity and quantum physics necessarily introduce deviations from Einstein’s theory.
Due to this fact, Einstein’s gravity can’t be the last word theory of gravity. Indeed, it was not long after the introduction of general relativity by Einstein in 1915 that Arthur Eddington, best known for verifying this theory within the 1919 solar eclipse, began trying to find alternatives simply to see how things might be different.
Einstein’s theory has survived all tests so far, accurately predicting various results from the precession of Mercury’s orbit to the existence of gravitational waves. So, where are these deviations from general relativity hiding?
Cosmology matters
A century of research has given us the usual model of cosmology often known as the Λ-Cold Dark Matter (ΛCDM) model. Here, Λ stands for either Einstein’s famous cosmological constant or a mysterious dark energy with similar properties.
Dark energy was introduced ad hoc by astronomers to elucidate the acceleration of the cosmic expansion. Despite fitting cosmological data extremely well until recently, the ΛCDM model is spectacularly incomplete and unsatisfactory from the theoretical perspective.
Prior to now five years, it has also faced severe observational tensions. The Hubble constant, which determines the age and the space scale within the universe, will be measured within the early universe using the cosmic microwave background and within the late universe using supernovae as standard candles.
These two measurements give incompatible results. Much more vital, the character of the primary ingredients of the ΛCDM model — dark energy, dark matter and the sector driving early universe inflation (a really temporary period of extremely fast expansion originating the seeds for galaxies and galaxy clusters) — stays a mystery.
From the observational perspective, probably the most compelling motivation for modified gravity is the acceleration of the universe discovered in 1998 with Type Ia supernovae, whose luminosity is dimmed by this acceleration. The ΛCDM model based on general relativity postulates a particularly exotic dark energy with negative pressure permeating the universe.
Problem is, this dark energy has no physical justification. Its nature is totally unknown, although a plethora of models has been proposed. The proposed alternative to dark energy is a cosmological constant Λ which, in accordance with quantum-mechanical back-of-the-envelope (but questionable) calculations, must be huge.
Nonetheless, Λ must as a substitute be incredibly fine-tuned to a tiny value to suit the cosmological observations. If dark energy exists, our ignorance of its nature is deeply troubling.
Alternatives to Einstein’s theory
Could or not it’s that troubles arise, as a substitute, from wrongly attempting to fit the cosmological observations into general relativity, like fitting an individual right into a pair of trousers which might be too small? That we’re observing the primary deviations from general relativity while the mysterious dark energy simply doesn’t exist?
This concept, first proposed by researchers on the University of Naples, has gained tremendous popularity while the contending dark energy camp stays vigorous.
How can we tell? Deviations from Einstein gravity are constrained by solar system experiments, the recent observations of gravitational waves and the near-horizon images of black holes.
There’s now a large literature on theories of gravity alternative to general relativity, going back to Eddington’s 1923 early investigations. A extremely popular class of alternatives is the so-called scalar-tensor gravity. It’s conceptually quite simple because it only introduces one additional ingredient (a scalar field corresponding to the only, spinless, particle) to Einstein’s geometric description of gravity.
The implications of this program, nevertheless, are removed from trivial. A striking phenomenon is the “chameleon effect,” consisting of the incontrovertible fact that these theories can disguise themselves as general relativity in high-density environments (reminiscent of in stars or within the solar system) while deviating strongly from it within the low-density environment of cosmology.
Consequently, the additional (gravitational) field is effectively absent in the primary form of systems, disguising itself as a chameleon does, and is felt only at the biggest (cosmological) scales.
The present situation
Nowadays the spectrum of alternatives to Einstein gravity has widened dramatically. Even adding a single massive scalar excitation (namely, a spin-zero particle) to Einstein gravity —and keeping the resulting equations “easy” to avoid some known fatal instabilities — has resulted within the much wider class of Horndeski theories, and subsequent generalizations.
Theorists have spent the last decade extracting physical consequences from these theories. The recent detections of gravitational waves have provided a method to constrain the physical class of modifications of Einstein gravity allowed.
Nonetheless, much work still must be done, with the hope that future advances in multi-messenger astronomy result in discovering modifications of general relativity where gravity is amazingly strong.