Physicists sometimes come up with crazy stories that sound like science
fiction. Some turn out to be true, like how the curvature of space and time
described by Einstein was eventually borne out by astronomical measurements.
Others linger on as mere possibilities or mathematical curiosities.

In a new paper in Physical Review Research, JQI Fellow Victor Galitski and
JQI graduate student Alireza Parhizkar have explored the imaginative
possibility that our reality is only one half of a pair of interacting
worlds. Their mathematical model may provide a new perspective for looking
at fundamental features of reality—including why our universe expands the
way it does and how that relates to the most miniscule lengths allowed in
quantum mechanics. These topics are crucial to understanding our universe
and are part of one of the great mysteries of modern physics.

The pair of scientists stumbled upon this new perspective when they were
looking into research on sheets of graphene—single atomic layers of carbon
in a repeating hexagonal pattern. They realized that experiments on the
electrical properties of stacked sheets of graphene produced results that
looked like little universes and that the underlying phenomenon might
generalize to other areas of physics. In stacks of graphene, new electrical
behaviors arise from interactions between the individual sheets, so maybe
unique physics could similarly emerge from interacting layers
elsewhere—perhaps in cosmological theories about the entire universe.

"We think this is an exciting and ambitious idea," says Galitski, who is
also a Chesapeake Chair Professor of Theoretical Physics in the Department
of Physics. "In a sense, it's almost suspicious that it works so well by
naturally 'predicting' fundamental features of our universe such as
inflation and the Higgs particle as we described in a follow up preprint."

Stacked graphene's exceptional electrical properties and possible connection
to our reality having a twin comes from the special physics produced by
patterns called moirÃ© patterns. MoirÃ© patterns form when two repeating
patterns—anything from the hexagons of atoms in graphene sheets to the grids
of window screens—overlap and one of the layers is twisted, offset, or
stretched.

The patterns that emerge can repeat over lengths that are vast compared to
the underlying patterns. In graphene stacks, the new patterns change the
physics that plays out in the sheets, notably the electrons' behaviors. In
the special case called "magic angle graphene," the moirÃ© pattern repeats
over a length that is about 52 times longer than the pattern length of the
individual sheets, and the energy level that governs the behaviors of the
electrons drops precipitously, allowing new behaviors, including
superconductivity.

Galitski and Parhizkar realized that the physics in two sheets of graphene
could be reinterpreted as the physics of two two-dimensional universes where
electrons occasionally hop between universes. This inspired the pair to
generalize the math to apply to universes made of any number of dimensions,
including our own four-dimensional one, and to explore if similar phenomenon
resulting from moirÃ© patterns might pop up in other areas of physics. This
started a line of inquiry that brought them face to face with one of the
major problems in cosmology.

"We discussed if we can observe moirÃ© physics when two real universes
coalesce into one," Parhizkar says. "What do you want to look for when
you're asking this question? First you have to know the length scale of each
universe."

A length scale—or a scale of a physical value generally—describes what level
of accuracy is relevant to whatever you are looking at. If you're
approximating the size of an atom, then a ten-billionth of a meter matters,
but that scale is useless if you're measuring a football field because it is
on a different scale. Physics theories put fundamental limits on some of the
smallest and largest scales that make sense in our equations.

The scale of the universe that concerned Galitski and Parhizkar is called
the Planck length, and it defines the smallest length that is consistent
with quantum physics. The Planck length is directly related to a
constant—called the cosmological constant—that is included in Einstein's
field equations of general relativity. In the equations, the constant
influences whether the universe—outside of gravitational influences—tends to
expand or contract.

This constant is fundamental to our universe. So to determine its value,
scientists, in theory, just need to look at the universe, measure several
details, like how fast galaxies are moving away from each other, plug
everything into the equations and calculate what the constant must be.

This straightforward plan hits a problem because our universe contains both
relativistic and quantum effects. The effect of quantum fluctuations across
the vast vacuum of space should influence behaviors even at cosmological
scales. But when scientists try to combine the relativistic understanding of
the universe given to us by Einstein with theories about the quantum vacuum,
they run into problems.

One of those problems is that whenever researchers attempt to use
observations to approximate the cosmological constant, the value they
calculate is much smaller than they would expect based on other parts of the
theory. More importantly, the value jumps around dramatically depending on
how much detail they include in the approximation instead of homing in on a
consistent value. This lingering challenge is known as the cosmological
constant problem, or sometimes the "vacuum catastrophe."

"This is the largest—by far the largest—inconsistency between measurement
and what we can predict by theory," Parhizkar says. "It means that something
is wrong."

Since moirÃ© patterns can produce dramatic differences in scales, moirÃ©
effects seemed like a natural lens to view the problem through. Galitski and
Parhizkar created a mathematical model (which they call moirÃ© gravity) by
taking two copies of Einstein's theory of how the universe changes over time
and introducing extra terms in the math that let the two copies interact.
Instead of looking at the scales of energy and length in graphene, they were
looking at the cosmological constants and lengths in universes.

Galitski says that this idea arose spontaneously when they were working on a
seemingly unrelated project that is funded by the John Templeton Foundation
and is focused on studying hydrodynamic flows in graphene and other
materials to simulate astrophysical phenomena.

Playing with their model, they showed that two interacting worlds with large
cosmological constants could override the expected behavior from the
individual cosmological constants. The interactions produce behaviors
governed by a shared effective cosmological constant that is much smaller
than the individual constants. The calculation for the effective
cosmological constant circumvents the problem researchers have with the
value of their approximations jumping around because over time the
influences from the two universes in the model cancel each other out.

"We don't claim—ever—that this solves cosmological constant problem,"
Parhizkar says. "That's a very arrogant claim, to be honest. This is just a
nice insight that if you have two universes with huge cosmological
constants—like 120 orders of magnitude larger than what we observe—and if
you combine them, there is still a chance that you can get a very small
effective cosmological constant out of them."

In preliminary follow up work, Galitski and Parhizkar have started to build
upon this new perspective by diving into a more detailed model of a pair of
interacting worlds—that they dub "bi-worlds." Each of these worlds is a
complete world on its own by our normal standards, and each is filled with
matching sets of all matter and fields. Since the math allowed it, they also
included fields that simultaneously lived in both worlds, which they dubbed
"amphibian fields."

The new model produced additional results the researchers find intriguing.
As they put together the math, they found that part of the model looked like
important fields that are part of reality. The more detailed model still
suggests that two worlds could explain a small cosmological constant and
provides details about how such a bi-world might imprint a distinct
signature on the cosmic background radiation—the light that lingers from the
earliest times in the universe.

This signature could possibly be seen—or definitively not be seen—in real
world measurements. So future experiments could determine if this unique
perspective inspired by graphene deserves more attention or is merely an
interesting novelty in the physicists' toy bin.

"We haven't explored all the effects—that's a hard thing to do, but the
theory is falsifiable experimentally, which is a good thing," Parhizkar
says. "If it's not falsified, then it's very interesting because it solves
the cosmological constant problem while describing many other important
parts of physics. I personally don't have my hopes up for that— I think it
is actually too big to be true."

### Reference:

Alireza Parhizkar et al, Strained bilayer graphene, emergent energy scales,
and moirÃ© gravity, Physical Review Research (2022).
DOI: 10.1103/PhysRevResearch.4.L022027

Alireza Parhizkar, Victor Galitski, MoirÃ© Gravity and Cosmology.
arXiv:2204.06574v1 [hep-th],
arxiv.org/abs/2204.06574