What are dark energy and dark matter?
What are dark energy and dark matter? Michela Massimi and John Peacock
Introduction This week we look at a topic at the forefront of
contemporary research in cosmology, which raised interesting philosophical questions: i.e.
What are dark energy (DE) and dark matter (DM)? How justified are we in believing in them? Are there any alternative theories that do not involve dark matter and dark energy?
How do cosmologists go about choosing which theory to endorse?
The ‘concordance model’ or ΛCDM It asserts that we
live in an infinite universe, with approximately 5% ordinary matter (baryons), 25% Cold Dark Matter, and 70% Dark Energy.
It builds on
Einstein’s general relativity (GR) and the so-called FriedmannLemaîtreRobertson-Walker (FLRW) models.
Concordance model baryons cold dark matter dark energy
Back to Duhem and underdetermination of theory by evidence A famous example from the
history of astronomy: in 1846 the astronomers Le Verrier and Adams explained the observed anomalous precession of the planet Uranus by hypothesizing the existence of a new planet
The planet, called Neptune, was indeed observed on 23 September 2014. (Pictures: Le Verrier, top, and Couch Adams, bottom. Credit: Wikipedia)
A very similar anomalous phenomenon was
observed for the planet Mercury, and also in this case a new planet was hypothesized (called Vulcan).
But no planet was observed this time and a final
explanation of the anomaly came only by replacing Newtonian mechanics with General Relativity.
This historical example illustrates what
philosophers of science call the problem of underdetermination of theory by evidence
I.e., in the presence of more than one possible
scientific theory or hypothesis, the available experimental evidence may not be sufficient to determine the choice of one scientific theory (or hypothesis) over a rival one.
Philosophical problem: how
do scientists go about making their decisions and choosing among rival theories when the available evidence does not unequivocally point them in one clear direction?
Pierre Duhem’s answer (recall the Introduction to the course): scientists typically follow their ‘good sense’ in making decisions. (Picture: Pierre Duhem. Credit: Wikipedia)
A closer look at the underdetermination argument Scientists’ belief in a theory T1 is justified (i.e., they have good reasons for believing that theory T1 is true)
Scientific theory T1 has to be read literally (i.e., if the theory
talks about planetary motions, we must take what the theory says about planetary motions at face value)
T1 is empirically equivalent to another theory T2 when T1 and T2 have the same empirical consequences.
––––––––––––––––––––––––––––––––––––––––––––––––––––
Therefore, premise 1. must be false. Scientists are not justified in believing that a theory T1 is true (or corresponds to the way things are in nature), if there is another theory T2 which is empirically equivalent to T1.
Thomas Kuhn on the rationality of theory-choice In 1977 The Essential Tension, Kuhn pointed out that theory choice seems governed by the following criteria:
accuracy (i.e. the theory is in agreement with experimental evidence);
consistency (i.e., the theory is consistent with other accepted scientific theories);
broad scope (i.e., the theory has to go beyond the original phenomena it was designed to explain);
simplicity (i.e., the theory should give a simple account of the phenomena);
fruitfulness (i.e., the theory should be able to predict novel phenomena).
Kuhn: these criteria are either imprecise (e.g., how
to define ‘simplicity’?); or they conflict with one another (e.g., while Copernicanism seems preferable to Ptolemaic astronomy on the basis of accuracy; Ptolemaic astronomy fares better on the score of consistency with the AristotelianArchimedean tradition of the time).
These five joint criteria are not sufficient to determine theory choice.
Instead, external, sociological factors seem to play a decisive role in how scientists gather consensus around a given theory.
Going back to cosmology What is the current evidence for the concordance model, with dark matter and dark energy?
Are there viable alternatives to the concordance model?
How do cosmologists make their rational decision of endorsing the concordance model?
What are dark matter and dark energy?
The contents of the universe
The Friedmann equation: (dR/dt)2 − 8πG ρ(t) R(t)2 / 3 = −K K depends on curvature. But density higher in past so can measure K from change in expansion rate
The accelerating ΛCDM universe
Plus about 0.01% radiation: more important in the past
Evidence for dark energy from distant supernovae • SNe Ia look like stars superimposed on distant galaxies • Relative distances: 4 times fainter means twice as far away
SN94D observed on a ground based telescope and with the Hubble Space Telescope.
SN Ia Hubble Diagram Distance
Distant supernovae are fainter than expected if the universe just contained normal matter:
Hubble Diagram
The expansion must be accelerating, not slowing down A flat vacuumdominated universe:
Ωmatter = 0.3 Ωvacuum = 0.7
Velocity
But the first strong evidence for dark energy came from mapping the large-scale distribution of galaxies, using v = HD to make a 3D map The ‘Redshift Survey’
Billion-lightyear patterns in the galaxy distribution
2dF Galaxy redshift Survey: 220,000 redshifts
Why do galaxies, clusters, and superclusters exist? Simplest answer: because gravity can amplify density irregularities
Making structure in a computer Simulate the action of gravity on a mass distribution with small initial fluctuations in density
Weighing the universe - I density
matter radiation time Now: background radiation ‘weighs’ 1 / 3000 of matter t < 100,000 years (depending on matter density): radiation weighs more - affects growth of structure
Weighing the universe - II fractional variation in number density of galaxies
length-scale Density of the universe is ‘written on the sky’: Ω = 0.3 This is 6 x the density of normal material:
So ‘Dark matter’ dominates the universe?
Dark Matter
First seen via galaxy orbital speeds in clusters (Zwicky 1933) Now well probed via gravitational lensing: 6 X normal matter Collisionless, unlike gas. Relic WIMP simplest hypothesis
Observing fluctuations from the early universe: Furthest back we can see is the microwave background (z = 1100)
WMAP 2003: The sky at 1 mm (Milky Way subtracted) Superclusters waiting to be born
CMB and cosmic geometry Open geometries with negative curvature shift detail to small angles − not seen.
closed
open Boomerang
1990: evidence for ΛCDM from LSS + CMB
1996: still in denial
Dark energy means giving weight to the vacuum. How is this possible?
Physics of the subatomic realm: The uncertainty principle (1927)
Precise knowledge of both position and speed is impossible
The vacuum of fields: zero-point energy Energy in electromagnetic wave mode of frequency ν = (n+1/2) hν n photons and zeropoint energy (inevitable from uncertainty principle) – not the only contribution to vacuum energy
Empty space has antigravity Ordinary matter: expansion slows as it expands, since gravitational energy is less
A sphere of vacuum increases mass as it expands, so gravitational energy goes up
The Big Bang and cosmic acceleration
Size of universe
time
The Big Bang and cosmic acceleration
Size of universe Without gravity: D = v t and v = H D So t = 1/H
time The Big Bang: zero size and infinite density 1/H = 14 billion years ago
The Big Bang and cosmic acceleration
Size of universe But matter should cause the expansion to slow down
time
The Big Bang and cosmic acceleration
Size of universe Current picture: decelerating in the past, but accelerating now as vacuum energy starts to dominate
time
Is this the way the universe really is?
Just one more creation myth that will look as foolish as all the others in due course?
Bishop John Leslie (1578)
Alternatives to ΛCDM There may be new physics only detectable on cosmological scales − e.g. evidence for Dark Matter from galaxy rotation curves. MOND: Modified Newtonian Dynamics Suppose F = m a is wrong at low accelerations?
Bayesian approach to theories Probability P as degree of belief: P(theory given data) is proportional to P(theory) times P(data given theory) (i.e. prior times likelihood) MOND may have a better likelihood, but it has a lower prior probability, being an ad hoc. theory. So cosmologists can be justified in failing to adopt it
Dark energy or modified gravity? Dark energy: inferred assuming standard Friedmann equation. But if Einstein was wrong, the Friedmann equation may just need replacing
? But can look for other signs of modified gravity, e.g. rate of growth of galaxy clustering. So far, all in agreement with Einstein plus dark energy as a physical entity
What prospects for contemporary cosmology? Going back to Duhem and the underdetermination
problem. Does underdetermination loom in contemporary cosmology? (see Lahav and Massimi 2014) Anomaly
Reject a main theoretical assumption?
Add a new auxiliary hypothesis?
Galaxy flat rotation curves
Modify Newtonian dynamics (MOND)?
Halos of dark matter?
Accelerating Modify general expansion of the relativity (GR)? universe Retain GR but modify FLRW?
Dark energy?
Are there empirically equivalent rivals for DE and DM? Two possible rivals to Dark Energy: 1. Inhomogeneous Lemaitre-Tolman-Bondi (or LTB)
models (rather than the standard FLRW model, which assumes, with the Cosmological Principle, that the Universe is roughly homogeneous and isotropic, namely it has the same uniform structure in all spatial positions and directions).
LTB denies homogeneity (but retains isotropy), and
assumes that there are spatial variations in the distribution of matter in the Universe, and that we live in an underdense or ‘void’ region of the Universe (a ‘Hubble bubble’), which is expanding at a faster rate than the average.
Most cosmologists find LTB
models unappealing, because they place us in a very ‘special’ position (a ‘Hubble bubble’) in the Universe.
This violates the so-called
Copernican principle, i.e. the principle named after Copernicus that says that we are not likely to occupy any privileged position in the universe.
(Picture: Nicolaus Copernicus. Credit: Wikipedia)
2. Instead of modifying FLRW models, we could try to modify General Relativity itself (to avoid DE).
But GR works in the Solar System. If it fails on the scale of the cosmos as a whole, the largest objects such as superclusters should start to collapse at a non-standard rate but this is not seen.
Also, there is no well-motivated candidate theory to replace GR. Thus neither prior considerations nor evidence from data favour abandoning GR, although the possibility continues to be investigated.
Possible rivals to Dark Matter: Modified Newtonian Dynamics or MOND, first
proposed by Milgrom (1983), and in its relativistic form by Bekenstein (2010).
“for disk galaxies MOND is more economical, and more falsifiable, than the DM paradigm” (Bekenstein 2010, p. 5).
Is theory-choice underdetermined in cosmology? Was Kuhn right in claiming that neither simplicity,
nor any of the other criteria, will ever be sufficient to determine the rationality of theory choice?
Philosophers of science have sometimes appealed to the notion of empirical support as a more promising way of thinking about theory choice.
A glimpse at the philosopher’s notion of empirical support The concordance model is empirically supported
not just when there is direct experimental evidence for some of its main theoretical assumptions (dark energy and dark matter), but when the model is integrated / embedded into a broader theoretical framework.
In this way, the model receives indirect empirical
support from any other piece of evidence, which although not a direct consequence of the model itself, are nonetheless consequences of the broader theoretical framework in which the model is embedded.
Summary Dark energy and dark matter have been postulated to explain two anomalous phenomena (i.e. the accelerating expansion of the universe, and galaxies’ flat rotation curves, respectively).
But rival explanations for these two phenomena are possible.
This is an example of what philosophers call the problem of underdetermination of theory by evidence. Anomalous evidence can be the sign that either a new auxiliary hypothesis has to be introduced; or that the main theoretical assumptions need be modified.
The underdetermination argument challenges the rationality of theory-choice.
A philosophically promising way of bypassing the
underdetermination problem appeals to the notion of empirical support.
A theory or hypothesis is empirically well supported when integrated into a larger theoretical framework through which empirical support accrues via indirect pieces of evidence.
The DM+DE model took some time to be established.
Strong evidence for DE around 1990 was met with skepticism, based on a physical prejudice against nonzero vacuum density.
But evidence for accelerating expansion from type Ia
Supernovae in 1998 caused almost instant adoption of the DM+DE model. These results in themselves could have been (and were) challenged, but the consistency with other lines of argument was sufficient to trigger a paradigm shift.
Thank you for listening!
Introduction This week we look at a topic at the forefront of
contemporary research in cosmology, which raised interesting philosophical questions: i.e.
What are dark energy (DE) and dark matter (DM)? How justified are we in believing in them? Are there any alternative theories that do not involve dark matter and dark energy?
How do cosmologists go about choosing which theory to endorse?
The ‘concordance model’ or ΛCDM It asserts that we
live in an infinite universe, with approximately 5% ordinary matter (baryons), 25% Cold Dark Matter, and 70% Dark Energy.
It builds on
Einstein’s general relativity (GR) and the so-called FriedmannLemaîtreRobertson-Walker (FLRW) models.
Concordance model baryons cold dark matter dark energy
Back to Duhem and underdetermination of theory by evidence A famous example from the
history of astronomy: in 1846 the astronomers Le Verrier and Adams explained the observed anomalous precession of the planet Uranus by hypothesizing the existence of a new planet
The planet, called Neptune, was indeed observed on 23 September 2014. (Pictures: Le Verrier, top, and Couch Adams, bottom. Credit: Wikipedia)
A very similar anomalous phenomenon was
observed for the planet Mercury, and also in this case a new planet was hypothesized (called Vulcan).
But no planet was observed this time and a final
explanation of the anomaly came only by replacing Newtonian mechanics with General Relativity.
This historical example illustrates what
philosophers of science call the problem of underdetermination of theory by evidence
I.e., in the presence of more than one possible
scientific theory or hypothesis, the available experimental evidence may not be sufficient to determine the choice of one scientific theory (or hypothesis) over a rival one.
Philosophical problem: how
do scientists go about making their decisions and choosing among rival theories when the available evidence does not unequivocally point them in one clear direction?
Pierre Duhem’s answer (recall the Introduction to the course): scientists typically follow their ‘good sense’ in making decisions. (Picture: Pierre Duhem. Credit: Wikipedia)
A closer look at the underdetermination argument Scientists’ belief in a theory T1 is justified (i.e., they have good reasons for believing that theory T1 is true)
Scientific theory T1 has to be read literally (i.e., if the theory
talks about planetary motions, we must take what the theory says about planetary motions at face value)
T1 is empirically equivalent to another theory T2 when T1 and T2 have the same empirical consequences.
––––––––––––––––––––––––––––––––––––––––––––––––––––
Therefore, premise 1. must be false. Scientists are not justified in believing that a theory T1 is true (or corresponds to the way things are in nature), if there is another theory T2 which is empirically equivalent to T1.
Thomas Kuhn on the rationality of theory-choice In 1977 The Essential Tension, Kuhn pointed out that theory choice seems governed by the following criteria:
accuracy (i.e. the theory is in agreement with experimental evidence);
consistency (i.e., the theory is consistent with other accepted scientific theories);
broad scope (i.e., the theory has to go beyond the original phenomena it was designed to explain);
simplicity (i.e., the theory should give a simple account of the phenomena);
fruitfulness (i.e., the theory should be able to predict novel phenomena).
Kuhn: these criteria are either imprecise (e.g., how
to define ‘simplicity’?); or they conflict with one another (e.g., while Copernicanism seems preferable to Ptolemaic astronomy on the basis of accuracy; Ptolemaic astronomy fares better on the score of consistency with the AristotelianArchimedean tradition of the time).
These five joint criteria are not sufficient to determine theory choice.
Instead, external, sociological factors seem to play a decisive role in how scientists gather consensus around a given theory.
Going back to cosmology What is the current evidence for the concordance model, with dark matter and dark energy?
Are there viable alternatives to the concordance model?
How do cosmologists make their rational decision of endorsing the concordance model?
What are dark matter and dark energy?
The contents of the universe
The Friedmann equation: (dR/dt)2 − 8πG ρ(t) R(t)2 / 3 = −K K depends on curvature. But density higher in past so can measure K from change in expansion rate
The accelerating ΛCDM universe
Plus about 0.01% radiation: more important in the past
Evidence for dark energy from distant supernovae • SNe Ia look like stars superimposed on distant galaxies • Relative distances: 4 times fainter means twice as far away
SN94D observed on a ground based telescope and with the Hubble Space Telescope.
SN Ia Hubble Diagram Distance
Distant supernovae are fainter than expected if the universe just contained normal matter:
Hubble Diagram
The expansion must be accelerating, not slowing down A flat vacuumdominated universe:
Ωmatter = 0.3 Ωvacuum = 0.7
Velocity
But the first strong evidence for dark energy came from mapping the large-scale distribution of galaxies, using v = HD to make a 3D map The ‘Redshift Survey’
Billion-lightyear patterns in the galaxy distribution
2dF Galaxy redshift Survey: 220,000 redshifts
Why do galaxies, clusters, and superclusters exist? Simplest answer: because gravity can amplify density irregularities
Making structure in a computer Simulate the action of gravity on a mass distribution with small initial fluctuations in density
Weighing the universe - I density
matter radiation time Now: background radiation ‘weighs’ 1 / 3000 of matter t < 100,000 years (depending on matter density): radiation weighs more - affects growth of structure
Weighing the universe - II fractional variation in number density of galaxies
length-scale Density of the universe is ‘written on the sky’: Ω = 0.3 This is 6 x the density of normal material:
So ‘Dark matter’ dominates the universe?
Dark Matter
First seen via galaxy orbital speeds in clusters (Zwicky 1933) Now well probed via gravitational lensing: 6 X normal matter Collisionless, unlike gas. Relic WIMP simplest hypothesis
Observing fluctuations from the early universe: Furthest back we can see is the microwave background (z = 1100)
WMAP 2003: The sky at 1 mm (Milky Way subtracted) Superclusters waiting to be born
CMB and cosmic geometry Open geometries with negative curvature shift detail to small angles − not seen.
closed
open Boomerang
1990: evidence for ΛCDM from LSS + CMB
1996: still in denial
Dark energy means giving weight to the vacuum. How is this possible?
Physics of the subatomic realm: The uncertainty principle (1927)
Precise knowledge of both position and speed is impossible
The vacuum of fields: zero-point energy Energy in electromagnetic wave mode of frequency ν = (n+1/2) hν n photons and zeropoint energy (inevitable from uncertainty principle) – not the only contribution to vacuum energy
Empty space has antigravity Ordinary matter: expansion slows as it expands, since gravitational energy is less
A sphere of vacuum increases mass as it expands, so gravitational energy goes up
The Big Bang and cosmic acceleration
Size of universe
time
The Big Bang and cosmic acceleration
Size of universe Without gravity: D = v t and v = H D So t = 1/H
time The Big Bang: zero size and infinite density 1/H = 14 billion years ago
The Big Bang and cosmic acceleration
Size of universe But matter should cause the expansion to slow down
time
The Big Bang and cosmic acceleration
Size of universe Current picture: decelerating in the past, but accelerating now as vacuum energy starts to dominate
time
Is this the way the universe really is?
Just one more creation myth that will look as foolish as all the others in due course?
Bishop John Leslie (1578)
Alternatives to ΛCDM There may be new physics only detectable on cosmological scales − e.g. evidence for Dark Matter from galaxy rotation curves. MOND: Modified Newtonian Dynamics Suppose F = m a is wrong at low accelerations?
Bayesian approach to theories Probability P as degree of belief: P(theory given data) is proportional to P(theory) times P(data given theory) (i.e. prior times likelihood) MOND may have a better likelihood, but it has a lower prior probability, being an ad hoc. theory. So cosmologists can be justified in failing to adopt it
Dark energy or modified gravity? Dark energy: inferred assuming standard Friedmann equation. But if Einstein was wrong, the Friedmann equation may just need replacing
? But can look for other signs of modified gravity, e.g. rate of growth of galaxy clustering. So far, all in agreement with Einstein plus dark energy as a physical entity
What prospects for contemporary cosmology? Going back to Duhem and the underdetermination
problem. Does underdetermination loom in contemporary cosmology? (see Lahav and Massimi 2014) Anomaly
Reject a main theoretical assumption?
Add a new auxiliary hypothesis?
Galaxy flat rotation curves
Modify Newtonian dynamics (MOND)?
Halos of dark matter?
Accelerating Modify general expansion of the relativity (GR)? universe Retain GR but modify FLRW?
Dark energy?
Are there empirically equivalent rivals for DE and DM? Two possible rivals to Dark Energy: 1. Inhomogeneous Lemaitre-Tolman-Bondi (or LTB)
models (rather than the standard FLRW model, which assumes, with the Cosmological Principle, that the Universe is roughly homogeneous and isotropic, namely it has the same uniform structure in all spatial positions and directions).
LTB denies homogeneity (but retains isotropy), and
assumes that there are spatial variations in the distribution of matter in the Universe, and that we live in an underdense or ‘void’ region of the Universe (a ‘Hubble bubble’), which is expanding at a faster rate than the average.
Most cosmologists find LTB
models unappealing, because they place us in a very ‘special’ position (a ‘Hubble bubble’) in the Universe.
This violates the so-called
Copernican principle, i.e. the principle named after Copernicus that says that we are not likely to occupy any privileged position in the universe.
(Picture: Nicolaus Copernicus. Credit: Wikipedia)
2. Instead of modifying FLRW models, we could try to modify General Relativity itself (to avoid DE).
But GR works in the Solar System. If it fails on the scale of the cosmos as a whole, the largest objects such as superclusters should start to collapse at a non-standard rate but this is not seen.
Also, there is no well-motivated candidate theory to replace GR. Thus neither prior considerations nor evidence from data favour abandoning GR, although the possibility continues to be investigated.
Possible rivals to Dark Matter: Modified Newtonian Dynamics or MOND, first
proposed by Milgrom (1983), and in its relativistic form by Bekenstein (2010).
“for disk galaxies MOND is more economical, and more falsifiable, than the DM paradigm” (Bekenstein 2010, p. 5).
Is theory-choice underdetermined in cosmology? Was Kuhn right in claiming that neither simplicity,
nor any of the other criteria, will ever be sufficient to determine the rationality of theory choice?
Philosophers of science have sometimes appealed to the notion of empirical support as a more promising way of thinking about theory choice.
A glimpse at the philosopher’s notion of empirical support The concordance model is empirically supported
not just when there is direct experimental evidence for some of its main theoretical assumptions (dark energy and dark matter), but when the model is integrated / embedded into a broader theoretical framework.
In this way, the model receives indirect empirical
support from any other piece of evidence, which although not a direct consequence of the model itself, are nonetheless consequences of the broader theoretical framework in which the model is embedded.
Summary Dark energy and dark matter have been postulated to explain two anomalous phenomena (i.e. the accelerating expansion of the universe, and galaxies’ flat rotation curves, respectively).
But rival explanations for these two phenomena are possible.
This is an example of what philosophers call the problem of underdetermination of theory by evidence. Anomalous evidence can be the sign that either a new auxiliary hypothesis has to be introduced; or that the main theoretical assumptions need be modified.
The underdetermination argument challenges the rationality of theory-choice.
A philosophically promising way of bypassing the
underdetermination problem appeals to the notion of empirical support.
A theory or hypothesis is empirically well supported when integrated into a larger theoretical framework through which empirical support accrues via indirect pieces of evidence.
The DM+DE model took some time to be established.
Strong evidence for DE around 1990 was met with skepticism, based on a physical prejudice against nonzero vacuum density.
But evidence for accelerating expansion from type Ia
Supernovae in 1998 caused almost instant adoption of the DM+DE model. These results in themselves could have been (and were) challenged, but the consistency with other lines of argument was sufficient to trigger a paradigm shift.
Thank you for listening!
