Do Dark Matter and Dark Energy Exist?

Numerous searches for the particle or particles responsible for dark matter have so far come up empty.  What if dark matter doesn’t really exist?  Could there be alternative explanation for the phenomena attributed to dark matter?

In the November 10, 2017 issue of the Astrophysical Journal, Swiss astronomer André Maeder presents an intriguing hypothesis that non-baryonic dark matter need not exist, nor dark energy either.  In “Dynamical Effects of the Scale Invariance of the Empty Space: The Fall of Dark Matter?” he suggests that scale invariance of empty space (i.e. very low density) over time could be causing the phenomena we attribute to dark matter and dark energy.

What is scale invariance?  In the cosmological context, it means that empty space and its properties do not change following an expansion or contraction.  Scales of length, time, mass, energy, and so on are defined by the presence of matter.  In the presence of matter, space is not scale invariant.  But take the matter away, and empty space may have some non-intuitive properties.  The expanding universe may require adding a small acceleration term that opposes the force of gravity.  In the earlier denser universe, this acceleration term was tiny in comparison to the rate at which the expansion was slowing down, but in the later emptier universe, the acceleration term dominates.  Sound like dark energy, doesn’t it?  But maybe it is an inherent property of empty space itself.

The existence of dark matter is primarily suggested by two  observed dynamical anomalies:

  1. Flat outer rotation curve of spiral galaxies (including the Milky Way)
  2. Motions of galaxies within galaxy clusters

Many spiral galaxies have a well-known property that  beyond a certain distance from their centers, their rotation rate (the orbital velocity of stars at that distance) stays nearly constant rather than decreasing as one would expect from Keplerian motion / Newtonian dynamics (think planets orbiting the Sun in our own solar system— the farther the planet is from the Sun, the slower it orbits).  Only there seems to be evidence that the rotation curves of galaxies when they are young (as seen in the high-redshift universe) do have a Keplerian gradient, but in the present-day universe the rotation curve is flat.  So, it appears, flat rotation curves could be an age effect.  In other words, in the outer regions of spiral galaxies, stars may be orbiting at the same velocity as they did in the past when they were closer to the galactic center.  Maeder writes:

…the relatively flat rotation curves of spiral galaxies is an age effect from the mechanical laws, which account for the scale invariant properties of the empty space at large scales.  These laws predict that the circular velocities remain the same, while a very low expansion rate not far from the Hubble rate progressively extends the outer layers, increasing the radius of the Galaxy and decreasing its surface density like 1/t.

We need to study the rotation curves (as a function of galactocentric radius all the way out to the outermost reaches of the galaxy) of many more galaxies at different redshifts (and thus ages) to help us test the validity of the scale invariant vs. dark matter hypotheses.  Maeder suggests a thorough rotation study of two massive and fast-rotating galaxies, UGC 2953 (a.k.a. IC 356; 50-68 Mly) and UGC 2487 (a.k.a. NGC 1167; 219-225 Mly), would be quite interesting.

The observed motions of galaxies within many galaxy clusters seems to indicate there is a substantial amount of unseen mass within these clusters, through application of the virial theorem.  However, the motions within some galaxy clusters such as Coma (336 Mly) and Abell 2029 (1.1 Gly) may be explainable without the need to resort to “exotic” dark matter.

Then there’s the AVR (Age-Velocity Dispersion Relation) problem which, incidentally, has nothing to do with dark matter.  But it may offer evidence for the scale invariant hypothesis.  It is convenient to specify the motion of a star in a spiral galaxy such as the Milky Way in a galactocentric coordinate system.

U = component of velocity towards the galaxy center

V = component of velocity in the direction of galactic rotation

W = component of velocity orthogonal to the galactic plane

Maeder writes:

The AVR problem is that of explaining why the velocity dispersion, in particular for the W-component, considerably increases with the age of the stars considered … Continuous processes, such as spiral waves, collisions with giant molecular clouds, etc… are active in the disk plane and may effectively influence the stellar velocity distributions.  However…vertical heating (the increase of the dispersion σW) is unexpected, since the stars spend most of their lifetime out of the galactic plane.

There may be more to “empty” space than meets the eye…

References
Maeder, A., 2017, ApJ, 849, 158
arXiv:1710.11425

Constants of Nature

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

The constants of nature are indeed invariant, with one possible exception: the fine structure constant, where there is claimed to be evidence of a very small change over astronomical timescales.  That issue is still under investigation.  Testing such invariance is fundamentally important, precisely because cosmology usually assumes as a ground rule that physics is the same everywhere in the universe.  If this were not true, local physics would not guide us adequately as to the behaviour of matter elsewhere or at other times, and cosmology would become an arbitrary guessing game.

The fine structure constant (α) is a unitless number, approximately equal to 1/137, that characterizes the strength of the electromagnetic force between electrons.  Its value is the same no matter what system of measurement one chooses.  If the value of α were just a little smaller, molecular bonds would be less stable.  If the value of α were just a little larger, carbon—which is essential to life—could no longer be produced inside of stars.

Do constants of nature, specifically dimensionless physical constants such as α, the fine structure constant, and μ, the proton-to-electron mass ratio1, vary with time?  This is an active topic of investigation.  If constants of nature change at all, they change so slowly that it presents a formidable challenge to measure that change.  But if they do indeed change, it would have profound implications for our understanding of the universe.  A lot can happen in 13.8 billion years that might not be at all obvious in the infinitesimal interval of a human life or even human civilization.

“Despite the incessant change and dynamic of the visible world, there are aspects of the fabric of the universe which are mysterious in their unshakeable constancy.  It is these mysterious unchanging things that make our universe what it is and distinguish it from other worlds we might imagine.” – J.D. Barrow, The Constants of Nature. (Vintage, 2003).

I’d like to conclude this discussion of constancy and change with a poem I wrote about the possibility of sentient life having a very different sense of time than we humans do.

Life On a Cold, Slow World

Life on a cold, slow world
On Europa, perhaps, or even Mars
On distant moons and planets of other stars.

A minute of time for some anti-freeze being
Might span a year for us human folk
(A greeting could take a week, if spoke.)

How fast our busy lives would seem to pass
Through watchful eyes we cannot see
Curious about our amative celerity.

The heartbeat of the universe runs slow and deep
We know only violent change, the sudden leap
But that which is most alive appears to sleep.

David Oesper

1μ = mp / me ≅ 1836

References
Barrow, J.D., Webb, J.K., 2005, Scientific American, 292, 6, 56-63

Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

The Hidden Universe

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

Thesis B6: Observational horizons limit our ability to observationally determine the very large scale geometry of the universe.
We can only see back to the time of decoupling of matter and radiation, and so have no direct information about earlier times; and unless we live in a “small universe”, most of the matter in the universe is hidden behind the visual horizon.  Conjectures as to its geometry on larger scales cannot be observationally tested.  The situation is completely different in the small universe case: then we can see everything there is in the universe, including our own galaxy at earlier times.

What an intriguing idea.  If the entire universe (or the self-contained section we find ourselves in) is substantially smaller than the distance light has traveled since the universe became transparent to radiation (“decoupling”, about 380,000 years after the Big Bang), we might be able to see our Milky Way galaxy (and other galaxies) at various points in the past.

The key point here is that unless we live in a small universe, the universe itself is much bigger than the observable universe.  There are many galaxies—perhaps an infinite number—at a greater distance than the horizon, that we cannot observe by any electromagnetic radiation.  Furthermore, no causal influence can reach us from matter more distant than our particle horizon—the distance light can have travelled since the creation of the universe, so this is the furthest matter with which we can have had any causal connection.  We can hope to obtain information on matter lying between the visual horizon and the particle horizon by neutrino or gravitational radiation observatories; but we can obtain no reliable information whatever about what lies beyond the particle horizon.  We can in principle feel the gravitational effect of matter beyond the horizon because of the force it exerts (for example, matter beyond the horizon may influence velocities of matter within the horizon, even though we cannot see it).  This is possible because of the constraint equations of general relativity theory, which are in effect instantaneous equations valid on spacelike surfaces.  However we cannot uniquely decode that signal to determine what matter distribution outside the horizon caused it: a particular velocity field might be caused by a relatively small mass near the horizon, or a much larger mass much further away.  Claims about what conditions are like on very large scales—that is, much bigger than the Hubble scale—are unverifiable, for we have no observational evidence as to what conditions are like far beyond the visual horizon.  The situation is like that of an ant surveying the world from the top of a sand dune in the Sahara desert.  Her world model will be a world composed only of sand dunes—despite the existence of cities, oceans, forests, tundra, mountains, and so on beyond her horizon.

Let us now define some terms that Ellis uses above.

visual horizon – the distance beyond which the universe was still opaque to photons due to high temperature and density

particle horizon – the distance beyond which light has not yet had time to reach us in all the time since the Big Bang; our particle horizon is, therefore, farther away than our visual horizon

spacelike surface – a three-dimensional surface in four-dimensional space-time where no event on the surface lies in the past or future of any other event on that surface; every point on the surface as it exists at one instant of time

Hubble scale – a cosmological distance unit equal to the reciprocal of the Hubble constant times the speed of light; see derivation below

A reasonable value for the Hubble constant H0 is 70 km/s/Mpc.  A galaxy one megaparsec distant has a cosmological recession velocity of 70 km/s, two megaparsecs distant 140 km/s, and so on.

You may notice that there are two units of distance in H0: kilometers and megaparsecs.  We can thus rewrite H0 in units of s-1 (reciprocal seconds of time) as follows:

The Hubble time is defined as the inverse of the Hubble constant:

Converting this into more convenient units of years, we get

The Hubble scale is now simply the Hubble time multiplied by the speed of light.

Converting this into more convenient distance units of light years, and then parsecs, we get

As Ellis says, we are like ants in the Sahara desert that cannot see their Earth-universe beyond the sand dunes.  Like the ant, is there a limit to our intellect as well?

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Homogeneity and Isotropy

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

4.2.2 Indirect determination: justifying a Friedmann-Lemaître geometry
Considered on a large enough angular scale, astronomical observations are very nearly isotropic about us, both as regards source observations and background radiation; indeed the latter is spectacularly isotropic, better than one part in 104 after a dipole anisotropy, understood as resulting from our motion relative to the rest frame of the universe, has been removed.

No matter what direction we look, the universe looks statistically the same at a scale of hundreds of millions of light years.  We call this property isotropy.  Case in point: when compared one to the other, the Hubble Deep Fields look remarkably similar, even though they are about 135° apart in the sky.

Hubble eXtreme Deep Field in the constellation Fornax
Hubble Deep Field in the constellation Ursa Major

Taken individually, both of these deep fields also exhibit homogeneity, that is, they generally show a fairly uniform distribution of galaxies across the field.

Does the dipole anisotropy in the cosmic background radiation (CBR), due to our motion with respect the rest frame of the universe, indicate an absolute frame of reference?  Not at all.  Though the rest frame of the universe is the preferred frame for cosmology, it is not a particularly good frame of reference to use, for example, in describing the motion of the planets in our solar system.  The laws of physics are the same in all inertial (unaccelerated) reference frames, so none of them can be “special”—or absolute.  An absolute frame of reference would be one in which the laws of physics would be different—indeed simpler—but no such reference frame exists.  And any non-inertial (accelerated) reference frame indicates there is an external force outside the system acting on the system, so it can never be used as an absolute frame of reference.

We’re moving toward Leo and away from Aquarius, relative to the cosmic background radiation
Top: CBR with nothing subtracted; Middle: CBR with dipole anisotropy subtracted; Bottom: CBR with both dipole anisotropy and galactic emission subtracted
Cosmic Background Radiation from the Planck spacecraft with anisotropies removed

If all observers see an isotropic universe, then spatial homogeneity follows; indeed homogeneity follows if only three spatially separated observers see isotropy.  Now we cannot observe the universe from any other point, so we cannot observationally establish that far distant observers see an isotropic universe.  Hence the standard argument is to assume a Copernican Principle: that we are not privileged observers.  This is plausible in that all observable regions of the universe look alike: we see no major changes in conditions anywhere we look.  Combined with the isotropy we see about ourselves, this implies that all observers see an isotropic universe.

The Copernican principle states that we are not privileged observers of the universe.  Any observer elsewhere in the universe will see the same universe that we do.  The laws of physics, chemistry, and biology are truly universal.  The Copernican principle is a good example of the application of Occam’s razor: unless there is evidence to the contrary, the simplest explanation that fits all the known facts is probably the correct one.

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Beginnings, Quantum Gravity, and Inflation

We continue our series on the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

2.6  Inflation
Particle horizons in inflationary FL models will be much larger than in the standard models with ordinary matter, allowing causal connection of matter on scales larger than the visual horizon, and inflation also will sweep topological defects outside the visible domain.

The particle horizon is the distance beyond which light would have not yet had time to reach us in all the time since the Big Bang.  The visual horizon is the distance beyond which the universe was still opaque to photons due to high temperature and density.  The visual horizon, therefore, is not as far away as the particle horizon.  FL stands for Friedmann-Lemaître, the standard models of a flat, open, or closed universe.

What is inflation?  At the moment of the Big Bang, the expansion of the universe accelerated exponentially for a very short period of time.  This caused portions of space that had been close enough together to be causally connected to become causally disconnected.  While inflation does a very good job of explaining many observed features of our universe, such as its uniformity in all directions, at this point it is an untestable hypothesis (unlike special and general relativity), and the underlying physical principles are completely unknown.

2.7  The very early universe
Quantum gravity processes are presumed to have dominated the very earliest times, preceding inflation.  There are many theories of the quantum origin of the universe, but none has attained dominance.  The problem is that we do not have a good theory of quantum gravity, so all these attempts are essentially different proposals for extrapolating known physics into the unknown.  A key issue is whether quantum effects can remove the initial singularity and make possible universes without a beginning.  Preliminary results suggest that this may be so.

We currently live in a universe where the density may be too low to observe how gravity behaves at the quantum level.  Though we may never be able to build a particle accelerator with energies high enough to explore quantum gravity, quantum gravity might possibly play a detectable role in high-density stars such as white dwarfs, neutron stars, or black holes.  At the time of the Big Bang, however, the density of the universe was so high that quantum gravity certainly must have played a role in the subsequent development of our universe.

Do we live in the universe that had no beginning and will have no end?  A universe that is supratemporal—existing outside of time—because it has always existed and always will exist?  Admittedly, this is an idea that appeals to me, but at present it is little more than conjecture, or, perhaps, even wishful thinking.

2.7.1  Is there a quantum gravity epoch?
A key issue is whether the start of the universe was very special or generic.

Will science ever be able to answer this question?  I sincerely hope so.

2.8.1  Some misunderstandings
Two distantly separated fundamental observers in a surface {t = const} can have a relative velocity greater than c if their spatial separation is large enough.  No violation of special relativity is implied, as this is not a local velocity difference, and no information is transferred between distant galaxies moving apart at these speeds.  For example, there is presently a sphere around us of matter receding from us at the speed of light; matter beyond this sphere is moving away from us at a speed greater than the speed of light.  The matter that emitted the CBR was moving away from us at a speed of about 61c when it did so.

Thus, there are (many) places in our universe that are receding from us so fast that light will never have a chance to reach us from there.  Indeed, the cosmic background radiation that pervades our universe today was emitted by matter that was receding from us at 61 times the speed of light at that time.  That matter never was nor ever will be visible to us, but the electromagnetic radiation it emitted then, at the time of decoupling, is everywhere around us.  Think of it as an afterglow.

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

A Small, Big, or Really Big Universe?

George F. R. Ellis writes in section 2.4.2 of his outstanding survey paper, Issues in the Philosophy of Cosmology:

Clearly we cannot obtain any observational data on what is happening beyond the particle horizon; indeed we cannot even see that far because the universe was opaque before decoupling.  Our view of the universe is limited by the visual horizon, comprised of the worldlines of furthest matter we can observe—namely, the matter that emitted the CBR at the time of last scattering.

The picture we obtain of the LSS by measuring the CBR from satellites such as COBE and WMAP is just a view of the matter comprising the visual horizon, viewed by us at the time in the far distant past when it decoupled from radiation.

Visual horizons do indeed exist, unless we live in a small universe, spatially closed with the closure scale so small that we can have seen right around the universe since decoupling.

The major consequence of the existence of visual horizons is that many present-day speculations about the super-horizon structure of the universe—e.g. the chaotic inflationary theory—are not observationally testable, because one can obtain no definite information whatever about what lies beyond the visual horizon.  This is one of the major limits to be taken into account in our attempts to test the veracity of cosmological models.

Let’s start by defining a few of the terms that Ellis uses above.

particle horizon – the distance beyond which light has not yet had time to reach us in all the time since the Big Bang

decoupling – the time after the Big Bang when the Universe had expanded and cooled enough that it was no longer a completely ionized opaque plasma; atoms could form and photons began traveling great distances without being absorbed

worldlines – the path of a photon (or any particle or object) in 4-dimensional spacetime: its location at each and every moment in time

CBRcosmic background radiation

LSS – last scattering surface

COBECosmic Background Explorer

WMAPWilkinson Microwave Anisotropy Probe

(And, Planck should be added now, too)

Now the question.  Do we live in a small, big, or really big universe?  The best answer we can give now (or, perhaps, even in the future) is that we live in a really big universe, though it is unlikely to be infinite.  Ellis himself provides a cogent argument in section 9.3.2 of the paper referenced here that infinity, while a very useful mathematical tool, does not ever exist in physical reality.  We shall investigate this topic in a future posting.

Even though general relativity shows us how matter defines the geometry of our observable universe, it tells us nothing about the topology of our universe, in other words, its global properties.  Do we live in a wrap-around universe where if we set off in one direction and traveled long enough, we’d eventually return to the same point in spacetime?  Is the topology of our universe finite or infinite?  At the moment it appears that we are not able to observe enough of the universe to discern its topology.  If that is true, we may never be able to understand what type of universe we live in.  But observational cosmologists will continue to search for the imprint of topology on our visible universe at the largest scales.

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Liddle, A.R. 2015, An Introduction to Modern Cosmology, 3rd ed., Wiley, ISBN: 978-1-118-50214-3.