What is the Standard Cosmological Model?

There’s a nice little paper – a summary of a talk – by Eric Linder on the arXiv here. The abstract is:

Reports of “cosmology in crisis” are in vogue, but as Mark Twain said, “the report of my death was an exaggeration”. We explore what we might actually mean by the standard cosmological model, how tensions – or their apparent resolutions – might arise from too narrow a view, and why looking at the big picture is so essential. This is based on the seminar “All Cosmology, All the Time”.

You can find a PDF here.

The paper discusses not only the question “what is the standard cosmological model?” in a fairly general way but also the more basic question “what is cosmology?” I’d think you’d be surprised how different would be the answers to that question from different cosmologists!

Anyway, I usually say when I give talks that the following are the six main ingredients of the standard model:

  1. General Relativity
  2. The Cosmological Principle
  3. Cold Dark Matter
  4. Cosmological Constant
  5. Primordial (nearly) Gaussian adiabatic fluctuations
  6. Inflation in the very early Universe

There are other ingredients of course, such as baryons and neutrinos but I don’t include them in a model because I feel one should distinguish at some level between the ingredients of a model and the  ingredients of the actual Universe. What I mean by that is that we know baryons exist (though we may not know their cosmic abundance precisely) but we don’t know for sure whether Cold Dark Matter exists.

Note that (1) isn’t really a model because it has no free parameters: it’s only when you add (2) that it comes a FLRW model with e.g. the curvature as a free parameter, and some assumed form of the energy-momentum tensor. The other ingredients have one or more free parameters, e.g. the density of CDM (3) and the value of Λ (4); these can be made more flexible by including, e.g., a dark energy term with equation of state w. Ingredient (5) needs the user to specify an initial power spectrum, which is at least two parameters (amplitude and slope), which may or may not be motivated by (6).

Anyway, the following items in the above list are – to a greater or lesser extent – open to question:

  1. General Relativity
  2. The Cosmological Principle
  3. Cold Dark Matter
  4. Cosmological Constant
  5. Primordial (nearly) Gaussian adiabatic fluctuations
  6. Inflation in the very early Universe

We’d be unwise to question only, e.g., 3 or 4 while ignoring the possibility that we may be wrong about the others!


39 Responses to “What is the Standard Cosmological Model?”

  1. 1. Yes.
    2. Now no longer a principle, but rather an observation.
    3. Probably in some form, but perhaps not everywhere it is invoked.
    4. This one is actually the most certain.
    5. Yes.
    6. Maybe; still unclear.

  2. “As an aside, one of the most fascinating aspects of this is that the argument could be made that the study of dark energy actually grew out of investigation of the radiation dominated era.”

    I don’t know what he means by that.

    An interesting paper. It is good to emphasize that one must fit all the data. It is easy to come up with alternative explanations for any one datum, or solutions to “tension” which address only one test at one redshift. It is much harder to fix problems without causing even greater problems elsewhere.

    • Not sure either, but I would guess it is the idea of inflation / observation of flatness from CMB constaining the sum of matter and dark energy densities in a cosmological model. Along with large scale structure data, one could infer that a non zero cosmological constant was required. Additionally, with CMB lensing one can determine the existence of a cosmological constant directly I think.

      • Maybe. Historically, it was the supernova magnitude-redshift relation which tipped the scales in favour of the cosmological constant. Back then (a bit more than 20 years ago), there was some evidence from the CMB that the Universe is flat, but due to the well known (almost) degeneracy, the CMB itself couldn’t say what that was. Some people still believed in the Einstein—de Sitter model (flat but no cosmological constant) at that time.

        However, at best one could get the cosmological constant from the CMB; any sort of more complicated “dark energy” needs data over a large redshift range. (Note that there is still no indication that dark energy is anything more than the cosmological constant.)

        As to flatness, the Universe is flat in that the sum of Ω and λ is 1 certainly to within a per cent or so but whether it is much flatter than that is still not clear.

      • Phillip, (I can’t put this in the right place it seems). Historically yes, the supernovae did it, but the large scale structure data suggested a matter density of about 0.3 before this. So, if one were to believe in flatness (even to a few percent), and a LCDM like model, this would put Omega Lambda to ~ 0.7. I don’t think flatness was clearly observed before the WMAP (after the supernova results), so this was more of a theoretical prior. Nevertheless, the point could be that this is possible.
        Regarding the ability of the CMB to constrain dark energy, this is possible because of the CMB passing through large scale structure at different redshifts with lensing (e.g. https://arxiv.org/abs/1105.0419) and ISW (e.g. https://arxiv.org/abs/astro-ph/0506396) being effects (that can help pin down properties of Dark Energy, even though the latter might be quite hard in practice.
        Obviously I agree that we don’t have any evidence of a dark energy beyond a cosmological constant yet.

      • Right; already at the beginning of the 1990s many people pointed out that something like the current concordance model was the best fit to all the data. Simulations didn’t like the Ω=1 CDM, but I think that it is fair to say that that alone wasn’t convincing, and certainly that alone didn’t convince the majority. The SN data are the first which, alone, point to a positive cosmological constant. Otherwise, it is combinations of constraints.

  3. The biggest problem I have with the Big Bang theory is that when they realized redshift increases proportional to distance in all directions, it was changed from an expansion in space, to an expansion of space, because spacetime!
    Which seems to ignore that that means intergalactic light is not constant to intergalactic space. More lightyears, not expanded lightyears.
    Two metrics are being derived from the same light. One based on the speed and one based on the spectrum. Given the speed is being used as the denominator, since if it was assumed to be the numerator, it would be a “tired light” model, that makes the speed the “ruler.”
    It has been shown multi spectrum light “packets” do redshift over distance, but that would mean we are observing a wave front, not individual photons, which would mean quantization of light is a function of absorption and that opens a Pandora’s box, but the fact remains the theory is still treating a stable light speed as the metric of space.

    • In general, redshift does not increase proportionally to distance in cosmology, so the rest of your comment is irrelevant.

      Velocity does increase with distance (valid for all distances and all redshifts and the velocity can be larger than the speed of light), but that just follows from the assumption of homogeneous and isotropic expansion, and needs no physics at all, much less GR.

      The word “because” needs “of” if the following word is a noun.

      With regard to your first claim: the principle of observational cosmology is that one examines how distance depends on redshift, because that can give us further information. If your claim were true, then that would not be possible.

      • How do we measure that velocity, other than as redshift?
        Ok, so things are just speeding away. We still appear to be at the center and the further things are in all directions, the faster they appear to recede.
        How could we measure that velocity/redshift, if there is nothing being used as comparison and if there is something used as comparison, isn’t that the metric of space, the “ruler,” with the velocity a function of increasing distance, in that space?
        With normal doppler effect, the train moving down the railroad tracks doesn’t stretch those tracks. The speed of light does seem to be the tracks. More lightyears, as those sources recede. Thus the explanation for the redshift.
        So we seem to be at the center, in space defined in terms of the speed of light. While the expansion is premised on the redshift of the very same intergalactic light.

      • The grammar was intentional.

      • It‘s too big too quote and fit into the comment box, so I recommend that you read Edward Harrison‘s textbook Cosmology: The Science of the Universe where he explains all this and more.

  4. Thanks. I’ll look it up.
    Though I think a simple yes, or no answer to the question of whether this expansion is calibrated in terms of lightyears wouldn’t be impossible.
    Whenever I hear descriptions of the process, it’s that eventually everything will be too far away for the light to cross, so the sky will be dark and I think What? Why doesn’t that mean space is being defined in terms of the speed of light, not the redshift of the spectrum of that light?
    Then when I think Inflation, Dark Matter, Dark Energy, I’m reminded of epicycles.
    I’ve also been referred to a fair number of other papers and books over the decades, by those in the know and they just seem to skip over this point.

  5. Jesus, that is 567 pages! It’s like asking what’s the fine for littering and being told to go read the criminal code. I would think that with all your knowledge of the field, you might be able to narrow the search down just a little bit.
    I might be off by a few years, but it seemed like the early 1920’s, when they decided to use the premise of spacetime, to explain why we appear to be at the center of the universe. If that’s any help in jogging your memory.
    Obviously I’ve just got the run around when I’ve asked this question previously, so I’m assuming this is par for the course. I realize that to be a member of the group, it doesn’t work to question the premises the group is working under, but this is supposed to be science, not politics.
    I guess I’d better just drop it.

    • There is no royal road to geometry.

    • There is no problem in being a member of the group and questioning the premises it is working under. However, in order to question them, whether or not one is a member, one has to understand them.

      If you are really interested in cosmology, Harrison‘s book is what you need to read.

      • If I was in my teens, early twenties, I’d take you up on it, but I work 6 days a week and there is quite a lot going on in the world today, that grabs my attention.
        How much of geometry evolved from modeling a geocentric cosmology? The math might be quite good and beautiful, but it doesn’t take much to throw it off. Butterfly’s wings effect.
        For instance;
        Consider the influence of monotheism on Western culture.
        Would a spiritual absolute be the essence of sentience, from which we rise, or an ideal of wisdom and judgement, from which we fell? The father figure lawgiver might be a useful social construct, but you would think the philosophers would question the logic of conflating the aspirational with the elemental.
        Are good and bad some cosmic conflict between righteousness and evil, or the basic biological binary of beneficial and detrimental? The 1/0 of sentience. Is it any wonder conflicts have a tendency to become a race to the bottom when all nuance and subjectivity is washed out by simplistic assumptions?
        Is money the social contract and accounting device enabling mass societies to function, or a commodity to mine from it?
        My sense has grown over the years that people are still fairly primitive in their understanding of reality and have a strong tendency to just make stuff up and run with it. Even the sciences.

      • telescoper Says:

        People do indeed tend to make stuff up. That’s often the people who can’t be bothered to study.

  6. I grew up in the horse racing industry and I will tell you, people study very industriously how to make stuff up.
    The thing about science is that it is out on the cutting edge of knowledge. The consequence of which is that it has to be somewhat self regulating.
    In many parts of the economy and society, it helps to have some outside regulation, like banking, healthcare, building airplanes, because there is a tendency to focus closely on one’s goals, putting together the parts that seem to fit and not step back to consider how it looks from the outside. The big picture.
    Remember, the people who run armies are called generals, while specialist is about one rank above private.
    For instance, the field in which math is most broadly used is accounting and in accounting, when they come across a gap in the books, it is somewhat frowned upon to just write in a figure and call it dark money. In accounting they understand that math is a tool, not God whispering in one’s ear and the complexity can obscure as easily as it can enlighten.
    Patches do have their uses, but when they cause more problems than they solve, like airplanes falling out of the sky, it is time to go back, tear apart the books and look at every figure.
    Does space expand in comparison to the speed of light?
    Yes, or no?

    • telescoper Says:

      I don’t understand your question. The speed of light is not expanding.

      • I know. My point is the theory still assumes the universe is expanding in comparison to the speed of light.
        What is the speed of light measuring, if not space? Or are space and the universe two separate dimensional constructs?
        The speed of light is not expanding, but the redshift of that light is presumably proof the overall universe is expanding.
        With normal doppler shift, it is a change of distance in stable space. The train moving down the tracks doesn’t stretch the tracks. It only increases the distance in terms of the tracks.
        The speed of light is the tracks, in this theory. More lightyears, as it expands. It is the stable metric of space, against which this expansion is occurring.
        Which also calls to question using the concept of spacetime, as the speed of intergalactic light would not be constant to intergalactic space, if space is expanding, but light speed remains stable.
        So either we are at the exact center of the universe, as defined by light speed, or there is an optical effect that’s not being taken into account, since we are at the enter of our point of view.
        One I came across some years ago, is that while single spectrum light will only redshift due to recession, multi-spectrum light “packets” do redshift over distance, as the higher frequencies dissipate faster;
        h ttps://fqxi.org/data/forum-attachments/2008CChristov_WaveMotion_45_154_EvolutionWavePackets.pdf (that link has a space to keep the whole thing from downloading)
        Though this would seem to mean we are sampling a wave front, not observing photons traveling billions of lightyears

      • telescoper Says:

        “My point is the theory still assumes the universe is expanding in comparison to the speed of light.”

        The speed of light is not expanding.

      • Ack. You can delete that here it is again;

      • “The speed of light is not expanding.”

        At least we are in agreement there.

      • Brodix: “My point is the theory still assumes the universe is expanding in comparison to the speed of light.”
        I cannot understand the question you are asking because the universe (space) with a distance dimension cannot be compared to the speed of light (dimensions of speed) which is a constant.

        I also don’t know if you are asking a question about (a) what the current theories describe or predict or (b) how observations are used to come up with the theory (with other assumptions). Without independent learning, the former can be somewhat easier to follow, while the latter is likely harder.

        I will make one honest guess as to what you may be asking (assuming you are asking what happens in the current theory), but of course the guess could be wrong:

        If there were two friends A and B ‘at rest’ turning on and off their (super powerful) flashlight pointing at each other, and counting the time intervals at which they could see their friend’s flashlight with a stopwatch, would this time interval increase with time or not ?

        The answer is it would.

        And in answer to your:
        `How could we measure that velocity/redshift, if there is nothing being used as comparison`

        The redshift is simply defined to be the wavelength of light observed to the wavelength of light emitted – 1. Since we measure such wavelengths from emission/absorption spectra of astrophysical sources (stars/galaxies etc.) this is directly measured with the assumption that the atoms in these sources are the same kind that exist in our earth.

        If you want to understand how observations explain models, you will have to do some studying like the source mentioned in the replies.

  7. rgb,

    So you are saying that it’s about four lightyears to Alpha Centauri isn’t a distance dimension?
    According to wikipedia, the universe is about 93 billion lightyears in diameter.
    A lightyear is about a trillion miles.
    Am I missing something?
    Why is the measure of the universe stated in lightyears, if that is not the normal measure of space?
    Presumably it grew from a point, to the current size, as measured in lightyears.
    What is this other “distance dimension” you speak of?

    • We don‘t understand “expanding in comparison to the speed of light”.

      • It’s called, “Doppler effect.” As the source moves away, aka, increased distance, the wave appears stretched. This is because the speed of the light is a constant, so as the distance between source and receiver increases, it takes longer to cross, so the wave appears stretched to the receiver. The overall space, as defined by the speed of light, doesn’t expand, only the distance in that space. So the expansion is increasing distance, not an expanding metric of space. The space, as defined by the speed of light, amounts to the denominator, while the expansion, based on the redshift, is the numerator. It doesn’t expand the units used as the denominator, only the number of those units. More lightyears, as the universe expands.
        Which gets back to why it was proposed as an expansion of space, rather than an expansion in space. Since redshift increases proportional to distance in all directions, it makes us appear to be at the exact center of the universe.

      • What is the problem if we appear to be at the exact center of the Universe because of the uniform expansion? Note that any observer would have the same perception.

        As to whether or not space expands, what matters is that your calculations come out right. I prefer the expanding-space paradigm, because it is more intuitive and one doesn’t have to worry about faster-than-light expansion (which exists) and so on.

  8. Look, if that’s how you like to see things, I’m not going to argue. We are all at the center of our view of the entire universe and with enough math, it would be possible to construct a Philcentric model of the entire universe. Though would you have titans pushing everything the other way, if you happen to walk across the room?

    When redshift was first discovered, there were considerable efforts to figure out where we were, in relation to the overall expansion and where the center of it was. When it appeared that we are at the center, the argument simply became that space itself must be expanding.
    Consider that according to Relativity, gravity causes space to contract, curve inward. To which Einstein amended the cosmological constant, to explain why the entire universe doesn’t collapse to a point. Yet when Hubble discovered redshift and the assumption became the entire universe expanded, Einstein famously dropped the CC. Yet what if Hubble actually discovered the CC? The balance to gravity.
    Presumably they do balance out, to where overall space does appear flat. Which is supposedly explained by Inflation.
    Yet what if the argument is simply that what curves inward, into galaxies as gravitational vortices, is matched by what curves outward, between galaxies? Then given that the only distant sources we can observe are the ones where the light isn’t interrupted, it would have to travel over that outward curved space, creating the effect of redshift. It would match what we actually see and there would be no need for dark energy, as this effect is compounding on itself, creating that parabolic increase in the rate of redshift.
    So basically the effect would be something akin to a cosmic convection cycle, between contracting mass and expanding light.
    Or the next several generations can explore the logical implications of the multiverse, with no evidence to build on it.

    • The fact that we seem to be in the centre has nothing to do whether one thinks of space expanding or objects expanding through space; it follows from a homogeneous and isotropic expansion, as discussed in essentially every introductory cosmology book.

      • Which gets back to the fact we rely on a stable speed of light as the metric of that expansion. What is the basis of light speed, if it’s not the metric of that space?
        It doesn’t matter how many millions of believers a system has, or how many thousands of years it’s been around, if it’s logically contradictory, it’s logically contradictory.

      • telescoper Says:

        The speed of light is not a “metric of space” nor anything else. You are using words in a way that suggests you have no understanding of what they mean.

  9. So how is interstellar and intergalactic space measured, other than in terms of the speed of light, aka, lightyears?

  10. Brodix,
    Yes, lightyears are units of dimensions of length (so spatial distance can be measured with it). But as you implied by comparing it to miles, it is simply a constant distance that is used as a unit. So any length can be measured in it, or in miles if you so prefer. The part of your previous statements that did not make sense were that you were talking about the speed of light not lightyears. That settled, sure, you can measure any distance whether that is from your home to your workplace, or the distance from the earth to a distant galaxy in units of lightyears or miles. So, what is objectionable about this?
    A few comments on the answers to others (Phillip Helbig) since:
    – Doppler effect : Sure, that exists. But your description and explanations are not correct. And for a uniformly expanding model one could formulate an understanding without invoking the Doppler Effect at all. So perhaps the discussion should steer clear of a new concept.
    – Perhaps the relevant lines are : “The overall space, as defined by the speed of light, doesn’t expand, only the distance in that space. So the expansion is increasing distance, not an expanding metric of space. The space, as defined by the speed of light, amounts to the denominator, while the expansion, based on the redshift, is the numerator. It doesn’t expand the units used as the denominator, only the number of those units. More lightyears, as the universe expands.”
    The ‘overall space, as defined by the speed of light’ is a non-existent concept and plays no part in the standard model of cosmology. I am pretty sure you can drop this idea from your head, and the rest of the stuff above goes away. Do you still have a problem?

    • rgb,

      Thank you for taking the time to respond, though you haven’t quite cleared the concept up, in my mind.
      Classic doppler shift is due to “recession” in an otherwise stable frame. When the train moves down the tracks and the tone of the whistle drops, it is because there is a relatively stable speed of sound and as it takes longer to cross, the wave is stretched to the receiver. The tracks are not stretched by this, only the distance on them is increasing.
      Similarly, the reason given for cosmic redshift is because the sources are referred to as “receding” and so the light waves are stretched, to the observer. More lightyears, as they recede.
      So the same basic mechanism seems to be at work. The cause of the redshift requires a stable speed of light and the distances referred to are described in terms of lightyears. What is this other “distance dimension?” It doesn’t seem to be anywhere in the equation.
      If the concept of “spacetime” is being invoked, wouldn’t the speed of light have to increase, as space expands, in order to remain “constant?” Yet that would negate the reason given for redshift.
      Einstein said, “Space is what you measure with a ruler.” The only ruler I can see anywhere in this theory is the speed of light.
      As for “overall space,” I see space as infinite and the cosmic background radiation as light from ever further sources, shifted off the visible spectrum.

  11. Ok.

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