Image Credit: ESA/Hubble & NASA, Acknowledgement: Flickr user Det58
Cosmologists are intellectual time travelers. Looking back over billions
of years, these scientists are able to trace the evolution of our
Universe in astonishing detail. 13.8 billion years ago, the Big Bang
occurred. Fractions of a second later, the fledgling Universe expanded
exponentially during an incredibly brief period of time called
inflation. Over the ensuing eons, our cosmos has grown to such an
enormous size that we can no longer see the other side of it.
But how can this be? If light’s velocity marks a cosmic speed limit, how
can there possibly be regions of spacetime whose photons are forever
out of our reach? And even if there are, how do we know that they
exist at all?
The Expanding Universe
Like everything else in physics, our Universe strives to exist in the lowest possible energy state possible. But around 10-36 seconds
after the Big Bang, inflationary cosmologists believe that the cosmos
found itself resting instead at a “false vacuum energy” – a low-point
that wasn’t really a low-point. Seeking the true nadir of vacuum energy,
over a minute fraction of a moment, the Universe is thought to have
ballooned by a factor of 1050.
Since that time, our Universe has continued to expand, but at a much
slower pace. We see evidence of this expansion in the light from distant
objects. As photons emitted by a star or galaxy propagate across the
Universe, the stretching of space causes them to lose energy. Once the
photons reach us, their wavelengths have been redshifted in accordance
with the distance they have traveled.
Two sources of redshift: Doppler and cosmological expansion; modeled
after Koupelis & Kuhn. Bottom: Detectors catch the light that is
emitted by a central star. This light is stretched, or redshifted, as
space expands in between. Credit: Brews Ohare.
This is why cosmologists speak of redshift as a function of distance in
both space and time. The light from these distant objects has been
traveling for so long that, when we finally see it, we are seeing the
objects as they were billions of years ago.
The Hubble Volume
Redshifted light allows us to see objects like galaxies as they existed in the distant past; but we cannot see allevents
that occurred in our Universe during its history. Because our cosmos is
expanding, the light from some objects is simply too far away for us
ever to see.
The physics of that boundary rely, in part, on a chunk
of surrounding spacetime called the Hubble volume. Here on Earth, we
define the Hubble volume by measuring something called the Hubble
parameter (H0),
a value that relates the apparent recession speed of distant objects to
their redshift. It was first calculated in 1929, when Edwin Hubble
discovered that faraway galaxies appeared to be moving away from us at a
rate that was proportional to the redshift of their light.
Fit of redshift velocities to Hubble’s law. Credit: Brews Ohare
Dividing the speed of light by H0,
we get the Hubble volume. This spherical bubble encloses a region where
all objects move away from a central observer at speeds less than the
speed of light. Correspondingly, all objects outside of the Hubble
volume move away from the center faster than the speed of light.
Yes, “faster than the speed of light.” How is this possible?
The Magic of Relativity
The answer has to do with the difference between special relativity and
general relativity. Special relativity requires what is called an
“inertial reference frame” – more simply, a backdrop. According to this
theory, the speed of light is the same when compared in all inertial
reference frames. Whether an observer is sitting still on a park bench
on planet Earth or zooming past Neptune in a futuristic high-velocity
rocket ship, the speed of light is always the same. A photon always
travels away from the observer at 300,000,000 meters per second, and he
or she will never catch up.
General relativity, however, describes the fabric of spacetime itself.
In this theory, there is no inertial reference frame. Spacetime is not
expanding with respect to anything outside of itself, so the the speed
of light as a limit on its velocity doesn’t apply. Yes, galaxies outside
of our Hubble sphere are receding from us faster than the speed of
light. But the galaxies themselves aren’t breaking any cosmic speed
limits. To an observer within one of those galaxies, nothing violates
special relativity at all. It is the space in between us and those
galaxies that is rapidly proliferating and stretching exponentially.
The Observable Universe
Now for the next bombshell: The Hubble volume is not the same thing as the observable Universe.
To understand this, consider that as the Universe gets older, distant
light has more time to reach our detectors here on Earth. We can see
objects that have accelerated beyond our current Hubble volume because
the light we see today was emitted when they were within it.
Strictly speaking, our observable Universe coincides with something called the particle horizon.
The particle horizon marks the distance to the farthest light that we
can possibly see at this moment in time – photons that have had enough
time to either remain within, or catch up to, our gently expanding
Hubble sphere.
And just what is this distance? A little more than 46 billion light
years in every direction – giving our observable Universe a diameter of
approximately 93 billion light years, or more than 500 billion
trillion miles.
Image credit: Htwins
(A quick note: the particle horizon is not the same thing as the cosmological event horizon.
The particle horizon encompasses all the events in the past that we can
currently see. The cosmological event horizon, on the other hand,
defines a distance within which a future observer will be able to see
the then-ancient light our little corner of spacetime is emitting today.
In other words, the particle horizon deals with the distance to past
objects whose ancient light that we can see today; the cosmological
event horizon deals with the distance that our present-day light that
will be able to travel as faraway regions of the Universe accelerate
away from us.)
Dark Energy
Thanks to the expansion of the Universe, there are regions of the cosmos
that we will never see, even if we could wait an infinite amount of
time for their light to reach us. But what about those areas just beyond
the reaches of our present-day Hubble volume? If that sphere is also
expanding, will we ever be able to see those boundary objects?
This depends on which region is expanding faster – the Hubble volume or
the parts of the Universe just outside of it. And the answer to that
question depends on two things: 1) whether H0 is
increasing or decreasing, and 2) whether the Universe is accelerating
or decelerating. These two rates are intimately related, but they are
not the same.
In fact, cosmologists believe that we are actually living at a time when H0 is decreasing; but because of dark energy, the velocity of the Universe’s expansion is increasing.
That may sound counter-intuitive, but as long as H0 decreases at a slower rate than
that at which the Universe’s expansion velocity is increasing, the
overall movement of galaxies away from us still occurs at an accelerated
pace. And at this moment in time, cosmologists believe that the
Universe’s expansion will outpace the more modest growth of the Hubble
volume.
So even though our Hubble volume is expanding, the influence of dark
energy appears to provide a hard limit to the ever-increasing observable
Universe.
Our Earthly Limitations
Cosmologists seem to have a good handle on deep questions like what our
observable Universe will someday look like and how the expansion of the
cosmos will change. But ultimately, scientists can only theorize the
answers to questions about the future based on their present-day
understanding of the Universe. Cosmological timescales are so
unimaginably long that it is impossible to say much of anything concrete
about how the Universe will behave in the future. Today’s models fit
the current data remarkably well, but the truth is that none of us will
live long enough to see whether the predictions truly match all of the
outcomes.
Disappointing? Sure. But totally worth the effort to help our puny
brains consider such mind-bloggling science – a reality that, as usual,
is just plain stranger than fiction.
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