So, going then back to
the underdetermination problem,
we may ask what is the available
evidence for the concordance model?
And here we will find replicated Pierre
Duhem's story about how a piece of negative
evidence may not necessarily speak
against the main theoretical hypothesis,
but may instead indicate the need of
introducing an auxiliary hypothesis.
If that's the case, then the problem
of underdetermination of theory by
evidence looms on the horizon
as the following table shows.
So if the underdetermination
argument is correct,
then the choice between
the concordance model and
some of its rivals must seem
to be not on rational ground.
And one might be tempted to bring
in a sociological explanation of
why scientists gather their consensus
around the concordance model and
the hypothesis of dark energy and
dark matter.
For example, one might argue that
it's easier to hold on to a well
established and well accepted
theory such as general relativity
plus the auxiliary hypothesis of dark
energy than trying to modify the theory.
And even in those cases where we do have
 a very well worked out alternative such
as MOND, people may prefer to hold on to
traditional Newtonian dynamics because of
the ad-hoc nature of the modification of
the Newtonian dynamics required by MOND.
Are scientists following their good
sense in taking those decisions, and
what counts as good sense?
For example, a MOND supporter would
argue that they have a very successful
theory to explain galaxy rotation curves
without resorting to dark matter.
From their point of view,
good sense would recommend accepting
relativistic MOND over
the concordance model.
To give an answer to these pressing
questions at the forefront of
contemporary research in cosmology, we
should go back to one of the premises of
the underdetermination argument, the
premise about empirical equivalence, and
ask whether we do have genuine
empirically equivalent competitors for
dark energy and dark matter.
For example, one rival dark
energy-free model is the so-called
Inhomogeneous Lemaitre-Tolman-Bondi,
or LTB model, rather than the FLRW
models of the concordance model, which
assumes, with the Cosmological Principle,
that our universe is roughly
homogenous and isotropic.
Namely, it assumes that
our universe has the same
uniform structure in all spatial
positions and in all spatial directions.
So if we deny homogeneity but retain
isotropy, we might be assuming that there
are variations, spatial variations in the
distribution of matter in our universe.
And we may want to assume that
we occupy an underdense, or
void region in our universe,
what cosmologists call the Hubble Bubble,
that is accelerating at a rate
faster than the average.
So the argument goes that our inference
to dark energy is flawed because
it's based on a flawed
homogeneous FLRW model.
Critics of dark energy argue that an LTB
model is a genuine empirically equivalent
rival to FLRW model, because it can
account for, for example, fluctuations
in cosmic microwave background, as well
as accounting for the same evidence
that dark energy typically explains,
namely supernova 1a data.
Although with an important caveat.
Supernova 1a data,
which is a typical evidence for
an accelerating expansion
of the universe for
which dark energy is usually introduced,
is now interpreted without acceleration.
Dark energy critics argue that light
traveling through an inhomogeneous
universe doesn't see the Hubble expansion,
and we make inferences about
an accelerating expansion using red shift
and light intensity, neither of which can
track any eventual inhomogeneities in the
universe through which the light travels.
However, many cosmologists find LTB models
unattractive because of the need to place
ourselves in a very special position in
our universe, a so-called Hubble Bubble.
And this violates what is called
the Copernican principle, namely,
the view named after Copernicus
that we don't occupy any special or
privileged position in our universe.
Moreover, one may retort
that the charge of
being ad hoc affects the interpretation
of supernova 1a data here as
implying no acceleration no less that it
affects the assumption of dark energy,
the assumption of a known zero vacuum
energy density to interpret the very
same data as data for
an accelerating expansion of the universe.
What if instead of modifying FLRW models,
we try to modify general relativity
instead, and go with dark energy?
Well, some physicists appeal to string
theory to speculate that there might be
many vacua with different energy
of the vacuum density, and
we might just be occupying
a very special vacuum
with a tiny positive value of
the vacuum energy density.
But it's fair to say,
that as of today, we don't really have
a genuine contender to general relativity.
Shifting to rivals of dark matter,
the best candidate we currently have is
Modified Newtonian Dynamics,
or MOND, first proposed by
Milgrom in the 1980's and
in its relativistic form by Bekenstein.
As we mentioned before, MOND was
introduced to explain the anomaly of
galaxy flat rotation curves
without introducing the auxiliary
hypothesis of dark matter, but
by modifying Newton's law instead.
MOND supporters appeal to arguments from
simplicity and mathematical elegance.
For example, Bekenstein argues that for
disk galaxies MOND provides
a more economical and more falsifiable
theory than the dark matter paradigm.
It's interesting that appeals should be
made here to Popper's falsifiability and
simplicity as arguments for
preferring MOND over dark matter,
which brings us back to the philosophical
topic of today's class.
Do we have genuine empirically equivalent
rivals to dark energy and dark matter?
Or is the theory choice
between dark energy and
dark matter on one hand and
rivals really underdetermined by evidence.
Was Thomas Kuhn right in thinking
that neither simplicity nor
any other criteria will
ever be sufficient to
explain how scientists go about making
decisions about which theory to support?
As a philosophical reply to those
questions, one might stress that there is
a lot more to theory choice than just the
ability of two rival theories to imply or
to entail the same piece of evidence.
It is within this context that
philosophers of science appeal to
the notion of empirical support as
a way forward in the debate about
underdetermination of theory by evidence
and the rationality of theory choice.
For example, the concordance model is
not just empirically supported by direct
empirical evidence that we may be able
to find one day about dark energy and
dark matter.
But the model is embedded into a larger
theoretical framework, general relativity.
And in so doing, the model receives
indirect empirical support from any other
piece of evidence that is a consequence of
the larger theoretical framework
within which the model is embedded.
Along similar lines,
although none of the phenomena of
terrestrial mechanics is directly
relevant to galaxy flat rotation curves,
one may appeal to the success of
Newtonian dynamics across this wide
range spectrum of phenomena as
an argument for Newtonian dynamics being
empirically very well supported, and
not in need of any ad-hoc modification,
such as those required by MOND, to
explain anomalous phenomena in cosmology.
