[All forms of energy affect the expanding Universe. But if matter
and radiation slow the expansion down, how does dark energy speed it
up?]
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SUNDAY SCIENCE: HOW DOES DARK ENERGY ACCELERATE THE UNIVERSE?  
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Ethan Siegel
April 28, 2023
Big Think
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_ All forms of energy affect the expanding Universe. But if matter
and radiation slow the expansion down, how does dark energy speed it
up? _

For the first several billion years the Universe's expansion rate was
decreasing. However, for the past ~6 billion years, distant galaxies
have been speeding up in their recession, and the expansion rate,
though still dropping, is not headed toward zero, NASA/STSci/Ann Feild


 

* In our Universe, there's only one factor that determines the cosmic
expansion rate: the sum total of all the different forms of energy
contained within it. 
* And yet, perhaps puzzlingly, we'd observe distant galaxies
receding ever more slowly from the Milky Way for the first ~7.8
billion years, but speeding up over the past ~6 billion. 
* We sometimes refer to this latter stage as dark energy domination,
or the accelerated expansion of the Universe. But if dark energy is
just energy, how does it accelerate the Universe?

It’s all too easy to accept what we know — or think we know —
without examining it too critically. But when it comes to the great
mysteries of our cosmic reality, that close, critical examination is
exactly what’s required to help us truly, deeply understand what’s
at play. At first pass, the expanding Universe might seem like an easy
thing to accept: some sort of rapid, initial expansion started off our
Universe, while the gravitational effects of all the matter and energy
within it work to bring things back together. If gravitation won,
we’d end in a Big Crunch; if the expansion won, we’d end in a Big
Freeze.

Only, when we examined our Universe in sufficient detail, we found
that not only is the expansion going to win, but that distant objects
are actually speeding up as they recede from us. Somehow, they’re
moving away faster and faster as time goes on. How do we make sense of
this? That’s what Patreon supporter
[[link removed]] Bob Schier wants to know,
asking:

“How does dark energy produce increasing acceleration.. away from
itself? Is it a kind of ‘negative gravity’ in which matter repels
matter similar to the way that like charges repel each other? Or does
it stretch the ‘fabric of space-time’ or simply of space?”

There are many ways to conceptualize the expanding Universe and dark
energy, but “repulsion” isn’t one of them. Let’s start at the
beginning: with the concept of cosmic expansion.

This simplified animation shows how light redshifts and how distances
between unbound objects change over time in the expanding Universe.
Note that the objects start off closer than the amount of time it
takes light to travel between them, the light redshifts due to the
expansion of space, and the two galaxies wind up much farther apart
than the light-travel path taken by the photon exchanged between them.
Credit: Rob Knop

It’s all too easy to accept what we know — or think we know —
without examining it too critically. But when it comes to the great
mysteries of our cosmic reality, that close, critical examination is
exactly what’s required to help us truly, deeply understand what’s
at play. At first pass, the expanding Universe might seem like an easy
thing to accept: some sort of rapid, initial expansion started off our
Universe, while the gravitational effects of all the matter and energy
within it work to bring things back together. If gravitation won,
we’d end in a Big Crunch; if the expansion won, we’d end in a Big
Freeze.

Only, when we examined our Universe in sufficient detail, we found
that not only is the expansion going to win, but that distant objects
are actually speeding up as they recede from us. Somehow, they’re
moving away faster and faster as time goes on. How do we make sense of
this? That’s what Patreon supporter
[[link removed]] Bob Schier wants to know,
askin“How does dark energy produce increasing acceleration.. away
from itself? Is it a kind of ‘negative gravity’ in which matter
repels matter similar to the way that like charges repel each other?
Or does it stretch the ‘fabric of space-time’ or simply of
space?”

There are many ways to conceptualize the expanding Universe and dark
energy, but “repulsion” isn’t one of them. Let’s start at the
beginning: with the concept of cosmic expansion.

When Einstein first put forth his new theory of gravitation to replace
Newtonian gravity, his theory of General Relativity, it was a radical
way of viewing the Universe. Instead of viewing space and time as
independent, absolute entities — where space is a static,
three-dimensional grid and time is simply an inexorable,
forward-moving line — three great advances came along, hand-in-hand,
in the early 20th century.

* First, there was the notion that arrived with Special Relativity in
1905: that neither space nor time were absolutes, but that they were
only experienced relative to the observer. Whenever two observers were
either at different locations or had different motions through space,
they experienced space and time differently from one another.
* Second, there was a way to “weave” space and time together:
discovered by Einstein’s former teacher, Hermann Minkowski, in 1908.
This fabric, spacetime, would replace the independent notions of space
and time, individually.
* And third, there was the notion that gravitation could be included
in the spacetime picture as well, where matter-and-energy curved the
fabric of spacetime, and that curved spacetime told matter and energy
how to move.

An animated look at how spacetime responds as a mass moves through it
helps showcase exactly how, qualitatively, it isn’t merely a sheet
of fabric but all of space itself that gets curved by the presence and
properties of the matter and energy within the Universe. Note that
spacetime can only be described if we include not only the position of
the massive object, but where that mass is located throughout time.
Both instantaneous location and the past history of where that object
was located determine the forces experienced by objects moving through
the Universe, making General Relativity’s set of differential
equations even more complicated than Newton’s. Credit:; LucasVB

But here was the kicker: if matter and energy curved the fabric of
spacetime, then that implied the fabric wouldn’t be static, but
would change over time. Most of us think of curvature as having three
possibilities, where you could be curved positively, like a sphere, or
you could be curved negatively, like a Pringles’ chip or a horse’s
saddle, or you could have zero curvature, being flat like a sheet of
paper. Those three examples are all true: curvature could mean any of
those three things.

But curvature could also lead to something else entirely: expansion or
contraction.

One of Einstein’s first thought experiments in the context of
General Relativity was to imagine what would happen if you had a
Universe — i.e., a spacetime — that was uniformly filled with what
he thought of as dust: massive particles, evenly distributed, at rest
with respect to one another and to the backdrop of spacetime. When you
calculate what happens in the context of General Relativity, you find
that space curves in such a way that these dust particles all get
closer and closer, with the distance between them decreasing, until
they all meet at a single point. It seemed inevitable that what
you’d get was the solution that Karl Schwarzschild derived just
months after General Relativity was put forth in its final form: a
black hole.

If you begin with a bound, stationary configuration of mass, and there
are no non-gravitational forces or effects present (or they’re all
negligible compared to gravity), that mass will always inevitably
collapse down to a black hole. It’s one of the main reasons why a
static, non-expanding Universe is inconsistent with Einstein’s
General Relativity. Credit: E. Siegel/Beyond the Galaxy

Einstein went further than this, and realized that it didn’t matter
what the extent of the matter distribution was, nor did the geometry
matter. Whether the matter was distributed in a sphere, a cube, a
pyramid, a potato-like structure, or any geometrical shape, it
didn’t matter: you’d still collapse down to a black hole.

But it wasn’t simply because spacetime curved in such a way that it
caused the matter to move through space and accelerate into a single
point; as intuitive as that explanation is, it doesn’t accurately
depict what’s going on.

Instead, what’s happening is that spacetime curves in such a way
that the fabric itself actually “flows” inward into itself, so
that the entire fabric — or, at least, the fabric within this region
of space — contracts. It’s as though there’s an invisible,
omnidirectional “moving walkway” that drags these particles
inward. Even if space were absolutely infinite, and it was infinitely
filled with this dust everywhere, the entire fabric of spacetime would
get pulled inward, as though it were contracting. If this situation
did encapsulate the entire Universe, it would end in a singularity: a
“point” where all of spacetime reached arbitrary, infinite
density. If this scenario only applied to a finite region of the
Universe, you’d get a black hole, where this “moving walkway”
analogy continued to draw not just matter, but spacetime, into it.

Both inside and outside the event horizon of a Schwarzschild black
hole, space flows like either a moving walkway or a waterfall,
depending on how you want to visualize it. At the event horizon, even
if you ran (or swam) at the speed of light, there would be no
overcoming the flow of spacetime, which drags you into the singularity
at the center. Outside the event horizon, though, other forces (like
electromagnetism) can frequently overcome the pull of gravity, causing
even infalling matter to escape. Credit: Andrew
Hamilton/JILA/University of Colorado

It was still in the very early days of General Relativity that
Einstein realized this pathology: we lived in a Universe that was
filled with matter. But if your Universe is filled with matter, it
won’t remain static and stable; the fabric of spacetime will
collapse inward on itself, leading to a Big Crunch scenario in short
order. Therefore — in a move that Einstein would later tout as his
“biggest blunder” — Einstein realized that another form of
energy must be “holding the Universe up against gravitational
collapse,” so he introduced what we know today as either a
cosmological constant or as dark energy: the only way he could think
of to balance out this otherwise inevitable gravitational collapse.

This brings us to the big question: how does “dark energy”
actually do this? How does it prevent the Universe from collapsing?
How does it resist the gravitational attraction of matter and other
forms of energy? And, after all, if dark energy is just another form
of energy, wouldn’t it also cause the Universe to gravitate, leading
to gravitational collapse anyway?

In order to answer this, we have to get quantitative.

A photo of Ethan Siegel at the American Astronomical Society’s
hyperwall in 2017, along with the first Friedmann equation at right.
The first Friedmann equation details the Hubble expansion rate squared
on the left hand side, which governs the evolution of spacetime. The
right side includes all the different forms of matter and energy,
along with spatial curvature (in the final term), which determines how
the Universe evolves in the future. This has been called the most
important equation in all of cosmology and was derived by Friedmann in
essentially its modern form back in 1922. Credit: Harley Thronson
(photograph) and Perimeter Institute (composition)

What you see, above, is sometimes known as the first Friedmann
equation: what I myself have often called the most important equation
in the Universe
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In any Universe that you can imagine that is:

* governed by Einstein’s General Relativity,
* that’s isotropic (i.e., the same in all directions),
* and that’s homogeneous (i.e., the same at all locations),

Einstein’s field equations can be solved, exactly, to give you a
series of equations. One of them is this very equation, and its power
is that it relates the change in the scale of the Universe, on the
left hand side, to the matter, energy, and curvature (and cosmological
constant, if you include it) on the right hand side.

The simplest way to deal with this equation is to assume there’s no
curvature and no cosmological constant, and to imagine that you’ve
got a Universe that’s filled with only one type of matter-or-energy
in it. You’re going to get a much simpler equation: one that simply
says that the change in the scale of the Universe (given by _H_ on
the left hand side, which technically is the “change in scale”
squared, since it’s _H_²) to some form of energy density (given
by _ρ_ on the right hand side, since we’re setting the
curvature, _k_, and the cosmological constant, Λ, to zero), and
let’s not even worry about those constants in front of the _ρ_.

Then, I want us to imagine three possibilities for what sort of energy
could be in this imaginary Universe: matter, radiation, and “dark
energy.”

This diagram shows, to scale, how spacetime evolves/expands in equal
time increments if your Universe is dominated by matter, radiation, or
the energy inherent to space itself (i.e., during inflation or dark
energy dominance), with the latter corresponding to the inflationary
phase that preceded and set up the hot Big Bang. Although all of these
model universes expand toward infinite size, they approach it at
different rates, with the “space itself” solution approaching
infinity in a fundamentally more quick fashion than the other two.
Credit: E. Siegel/Beyond the Galaxy

What’s going to happen is that the “change in scale, squared”
(_H_²) is going to change in proportion to how the energy density
(_ρ_) changes. Let’s break them down, one by one.

* For matter, density is just mass over volume. Because particles
have a fixed mass and a fixed number, then the density changes
inversely proportional to the volume: double the “scale” of the
Universe and your density becomes 1/8 of what it was initially; halve
the “scale” of the Universe and your density increases by a factor
of 8. So the “change in scale” is just the square root of that.
* For radiation, those quanta are massless, so density is just
energy over volume. While the number of quanta (say, photons) is
fixed, the energy of each quantum is defined by its wavelength, and
the “length” of one wave is dependent on the scale of the
Universe. As a result, not only does volume change if you double or
halve the scale of your Universe, but the energy-per-quantum halves or
doubles, respectively. If you double the scale of your Universe, the
density becomes 1/16 of what it was initially; if you halve the scale
instead, your density increases by a factor of 16. And again, the
“change in scale” is the square root of that.
* But for dark energy, this behaves as a form of energy intrinsic to
space itself: its energy density is always constant. Whether you
change the volume or not, that density term, _ρ_, remains unchanged.
If you halve or double the scale of the Universe, the “change in
scale” is simply the square root of a constant: it does not change.

How matter (top), radiation (middle), and dark energy (bottom) all
evolve with time in an expanding Universe. As the Universe expands,
the matter density dilutes, but the radiation also becomes cooler as
its wavelengths get stretched to longer, less energetic states. Dark
energy’s density, on the other hand, will truly remain constant if
it behaves as is currently thought: as a form of energy intrinsic to
space itself. Credit E. Siegel/Beyond the Galaxy

Because we’re not dealing with an equation about the “change in
scale” but rather an equation that tells us something about the
“change in scale, squared,” there’s an important caveat here:
the value of the “change in scale” itself could be either positive
or negative, and we’d get the same answer either way. If the
“change in scale” were positive, the Universe would be expanding;
if the “change in scale” were negative, the Universe would be
contracting.

What Einstein’s initial (and flawed) reasoning told him was, “Hey,
if you start your Universe off static and neither expanding nor
contracting, then if you sprinkle matter into it, it must begin
contracting. So if we don’t want it to contract, we can add in
another form of energy that behaves differently (like dark energy, or
a cosmological constant), and watch the Universe expand instead. And
if we tune the matter and the other form of energy just right,
they’ll balance, and we’ll get a static Universe instead!”

But observationally, as was first borne out in the 1920s and that’s
been confirmed ever since to much greater precision and to
extraordinary distances, the Universe is actually expanding, and
contains all three of these species: matter, radiation, and dark
energy.

A plot of the apparent expansion rate (y-axis) vs. distance (x-axis)
is consistent with a Universe that expanded faster in the past, but
where distant galaxies are accelerating in their recession today. This
is a modern version of, extending thousands of times farther than,
Hubble’s original work. Note the fact that the points do not form a
straight line, indicating the expansion rate’s change over time. The
fact that the Universe follows the curve it does is indicative of the
presence, and late-time dominance, of dark energy. Credit: Ned
Wright/Betoule et al. (2014)

If we want to know, then, how the Universe expands, and how the
expansion accelerates, all we have to do is solve that same governing
equation, the first Friedmann equation, for a Universe with all three
types of energy, and choose the positive, expanding solution.

That’s actually a fairly straightforward task! It turns out that the
expansion rate itself — what we define as the “change in scale”
parameter, or _H_ — actually always decreases over time. This
value is not something that accelerates, but rather something that
decreases: rapidly early on, when the Universe is dominated by
radiation, then a little less rapidly later, when the Universe is
dominated by matter, and then eventually, when dark energy takes over,
slowing down further and approaching a finite, positive, non-zero
value.

The reason we say the expansion is accelerating isn’t because _H_,
the expansion rate, is increasing over time; it is not. The reason is
because the things we observe are galaxies within the Universe, and we
can see these galaxies receding from us. If we watched these galaxies
recede over time, then we’d find:

* when the Universe is dominated by radiation, the apparent recession
speed of these galaxies would decrease,
* when the Universe is dominated by matter, their apparent recession
speed would decrease, but more slowly,
* and when the Universe is dominated by dark energy, their apparent
recession speed increases.

It’s that — the rate at which galaxies appear to recede from us
— that’s accelerating, not the expansion rate of the Universe
itself.

The scale of the Universe (y-axis) versus the age of the Universe
(x-axis) on logarithmic scales. Some size and time milestones are
marked, as appropriate. The transition between radiation and matter
domination is subtle; the transition to dark energy domination is easy
to see. Credit: E. Siegel

It’s important to recognize that dark energy isn’t some type of
“negative energy” or “repulsive gravity,” although there are
certainly people out there who attempt to interpret it in that
fashion. Instead, it’s just a form of energy like any other, and
that it’s part of that great cosmic balance between the expansion of
the Universe and the sum of all the different forms of energy within
it. The biggest difference is that while matter’s and radiation’s
energy densities both drop as the Universe expands, dark energy’s
energy density doesn’t: it remains constant instead, and that
“lack of dropping” is why the individual galaxies caught up in our
cosmic expansion are seen to speed away from us faster and faster as
time goes on.

At the same time, however, it’s important to remember that we
aren’t 100% certain that dark energy truly behaves as though its
energy density is constant: like a true cosmological constant. Dark
energy could, ever so slightly, increase or decrease in density or in
strength as time progresses. Part of the reason for NASA’s next
upcoming flagship mission, the Nancy Roman Space Telescope
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tell us, to the greatest precision ever, how dark energy truly
behaves. After all, the ultimate fate of the Universe depends on it!

_ETHAN SIEGEL is a Ph.D. astrophysicist and author of "Starts with a
Bang!" He is a science communicator, who professes physics and
astronomy at various colleges. He has won numerous awards for science
writing since 2008 for his blog, including the award for best science
blog by the Institute of Physics. His two books "Treknology: The
Science of Star Trek from Tricorders to Warp Drive"
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the Galaxy: How humanity looked beyond our Milky Way and discovered
the entire Universe"
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available for purchase at Amazon. Follow him on
Twitter @startswithabang [[link removed]]._

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