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HPS 2580 |
Cosmology | Spring 2018 |
Here is a brief survey of foundational problems in modern cosmology, divided according to the eras.
How did things look in 1997?
Vote on topics in 1997.
How should we react to an inconsistent theory?
A generic Newtonian cosmology has an infinite Euclidean space filled with a uniform matter distribution. Seeliger and others had found this cosmology inconsistent. A valid computation in Newtonian gravitational theory allowed the gravitational force on a test body to be a force of any nominated magnitude and direction.
There were many responses at the time. One was to augment Newton's inverse square law with a correction term that eliminated the inconsistency. Einstein used the precedent of such a correction term to motivate an analogous correction term to his theory: λ.
Later Development:
Is the paradox resolved by identifying a neglected relativity of acceleration in Newtonian cosmology?
Yes.
Is modern cosmology dependent on a epistemological analysis?
According to Einstein, classical mechanics and special relativity are marred by an epistemological defect, that is, one without an empirical grounding. The epistemological principle they violate is what he called "Mach's principle." According to it, the geometric structure of spacetime has to be determined completely by the distribution of matter. The principle is still violated in general relativity by the need fix Minkowskian values at spatial infinity.
It is finally resolved by Einstein's 1917 introduction of the Einstein universe, the first, general relativistic cosmology. The Einstein universe is spatially finite and so has no spatial infinity. The admissibility of the Einstein universe in general relativity in turn required the addition to his gravitational field equations of a new "cosmological" term employing the cosmological constant λ.
No sooner had Einstein proposed his new universe and his augmented gravitational field equations than the Dutch astronomer de Sitter found a serious problem. He pointed out that there are solutions of the augmented Einstein gravitational field equations without any matter at all, the de Sitter spacetimes.
General relativity fails if its quantities become singular. How should we treat such singularities?
Einstein and others, including Hermann Weyl, found singularities in de Sitter spacetime and identified them as "mass horizons," where the spacetime creating masses of the universe reside. We now identify these singularities as merely artefacts of the choice of spacetime coordinates. This was one of the first serious discussions of singularities in spacetime theories and not, by modern lights, handled well. Perhaps our modern lenses are distorting the issues of the late 1910s?
Is a cosmology with an initial singularity admissible?
Following Hubble's discovery of the recession of the galaxies, the simple projection into the past leads to an initial singularity. Do cogent cosmologies admit spacetime singularities?
How do we address inconsistencies between our best cosmology and other theories?
The simple projection of the recession of the galaxies into the past indicates an age of the universe that is younger than other processes. James Jeans had then estimated that stars need 1013 years to form, whereas then current estimates of the Hubble age of the universe were roughly 2 billion years.
How extravagant an inductive inference is admissible for a cogent science?
How can any cosmology be cogent when it depends on an extravagant inductive leap from the properties of the finite portion of the universe we can see to all of the infinite universe?
Do we develop our cosmological theories from observation and cautious inference or from the postulation of principles?
The foundation of cosmological theories is Milne's cosmological principle. It asserts that, on a suitably large scale, the universe look the same at every position in space. There is no empirical way to know that this is correct. It must be posited. So why not continue in this vein and posit the Perfect Cosmological Principle? According to it, the uniformity holds not just for positions in space, but also for all times. What results is a quite specific cosmology, the Bondi-Gold-Hoyle steady state cosmology. This cosmology dominated in England, whereas the American tradition favored an empirical approach and what Hoyle derisively labeled a "big bang" cosmology.
Are crucial experiments or observations possible?
The standard recounting is that Penzias and Wilson's discovery of the cosmic background radiation was the decisive experiment that killed steady state cosmology in favor of big bang cosmology. The history is a less definite. It took decades before this simple gloss came to be the standard, text book summary.
When are we authorized to infer from a gap in our equations to the existence of a novel form of matter?
We have two remarkable cases:
The luminous matter visible in galaxies provides insufficient gravitational attraction to return the observed motion of the stars of the galaxies. Should we accommodate this by modifying Newton's inverse square law of gravity? Or should we assume that there is considerable non-luminous matter in the galaxies, that is "dark matter"?
Starting in the 1990s distant galaxies were observed to be receding faster than we would expect from Einstein's gravitational field equations, unless his 1917 cosmological term was restored. Can we reinterpret this term as a matter term, "dark energy."
Is an inference to matter warranted in both cases? What principles guide our decisions?
Is a theory supported inductively if it explains uniformities in the initial state of the universe?
Present cosmological theories must suppose an initial state in which matter is nearly perfectly uniformly distributed, even though no causal connections between the parts of space could have homogenized it. Guth initially argued for his inflationary cosmology since they made these and other cosmic coincidences more likely. However there seems to be no cogent sense, probabilistic or otherwise, that makes sense of this "more likely."
If eternal inflation can be fitted to any present matter distribution, is it science?
The strongest argument for inflationary cosmology now offered by its supporters are no longer that is solves Guth's original problems. It is that it gives just the right amount of inhomogeneity in the matter distribution for the stars, planets and galaxies we now see to have formed. There has been a major defection among the founders of inflationary cosmology. These dissidents argue that this success with structure formation derives from working backwards to tune the properties of the inflaton field so that is gives what we see now. It is success by theft, not honest toil.
How does the quantum inflaton field collapse when there is no observer outside the universe to trigger the collapse?
The inhomogeneities inflationary cosmology brings to the matter distribution derive from quantum fluctuations being "frozen in" and becoming classical. Otherwise the inflaton field would simply remain in a homogeneous quantum state. How this quantum to classical transition happens remains a subject of dispute. It is the old measurement problem of quantum mechanics realized on a cosmic scale.
Can we know the global structure of spacetime?
In general relativity, our past light cone does not fix the rest of the structure of spacetime. This means that the fullest knowledge of what we can see in our past is insufficient to determine the structure of the remainder of spacetime.
How do we divide empirically respectable cosmology from fanciful conjecture?
Present cosmological theories spans a range from modest, observationally grounded theorizing to the wildest speculation. When have we passed beyond respectable science? What criteria do we use to decide?
From Max Tegmark's "The Multiverse Hierarchy," https://arxiv.org/pdf/0905.1283.pdf
"
• Level I: A generic prediction of cosmological
inflation is an infinite “ergodic” space, which contains Hubble volumes
realizing all initial conditions — including an identical copy of you
about 101029 m away.
• Level II: Given the fundamental laws of physics that
physicists one day hope to capture with equations on a T-shirt, different
regions of space can exhibit different effective laws of physics (physical
constants, dimensionality, particle content, etc.) corresponding to
different local minima in a landscape of possibilities.
• Level III: In unitary quantum mechanics, other
branches of the wavefunction add nothing qualitatively new, which is
ironic given that this level has historically been the most controversial.
• Level IV: Other mathematical structures give different
fundamental equations of physics for that T- shirt.
"
Is anthropic reasoning cogent?
Why are we so fortunate to be in a universe where the fundamental constants have just the values needed to admit matter forms like us, on a temperate planet, orbiting nicely behaved stars. Anthropic reasoning explains our good fortune by noting that, if the constants were otherwise, we would not be here to ask the question. Cosmological ideas are then introduced to bolster this approach. In multiverse theories, there are very many mini-universes, each with different combinations of values of the constants. We are in the one with the values we see since we could not be in any other.
Do inferences from observations always prevail over inferences from simulations?
There are two major trends in modern cosmology. One is the flood of new data coming from a range of observational sources, including observations of distant supernovae and the cosmic background radiation and its fluctuations. The second is a series of ever more sophisticated simulations, most commonly of structure formation in the cosmos. In other contexts, the philosophical debate concerns whether one has authority over the other. Do the issues of this debate arise in cosmology?
How do we integrate the many sciences that contribute to modern cosmology?
Modern cosmological theorizing draws on many sciences. There is the core cosmological theory that delivers the ΛCDM model. It draws on the spacetime geometry of general relativity; astronomy for its observation of stars and galaxes; on chemistry and nuclear physics for the transitions in the matter content of the cosmos; and much more. The science is more a collaborative of many sciences. How are the pieces to be fitted together?
http://www.preposterousuniverse.com/blog/2014/10/03/ten-questions-for-the-philosophy-of-cosmology/
here Sean Carroll laments that we do not yet have a proper field of study that can be called "philosophy of cosmology." In an effort to launch the field, he posed ten questions. Quoted from Carroll's blog: