Multiverses and physical cosmology

Classified as probably not a substantial claim.

The probability distribution for the existence of galaxies as a function of the cosmological constant can be approximated by P_gal = N(ρ)P(ρ), where N(ρ) is the fraction of baryons that form galaxies.

“It has been suggested (Vilenkin 1995;Weinberg 1997) that the way the probability distribution for the existence of galaxies depends on the cosmological constant can be approximated by P gal = N (ρ )P(ρ ) (24 ) where N(ρ ) is the fraction of baryons that form galaxies.”

• cites Vilenkin 1995 sourcePartly supported

  In “Predictions from Quantum Cosmology” (page unavailable), Vilenkin describes a probability distribution weighted by N(α) and discusses how the cosmological constant can affect galaxy formation. But N(α) is defined as the average number of civilizations in a universe, not the fraction of baryons that form galaxies; our copy does not give the claimed P_gal = N(ρ)P(ρ) approximation. (LLM, conf=0.87)

  Experimental — accuracy not yet measured
• cites Weinberg 1997Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The 'small universe' situation is observationally testable, and the cosmic background radiation power spectrum might already be giving evidence for it because of its lack of power on the largest angular scales.

“This 'small universe' situation is observationally testable, and indeed it has been suggested that the cosmic background radiation power spectrum might already be giving us evidence that this is indeed so, because of its lack of power on the largest angular scales (Luminet et al. 2003).”

• cites Luminet et al. 2003 sourceSupported

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

A proper measure on the space of all really existing universes or universe domains is needed so that probabilities can be calculated.

“A proper measure on the space of all really existing universes or universe domains is needed, so that probabilities can be calculated”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

The astrophysical issues expressed in the product are the easier ones to investigate.

“The astrophysical issues expressed in the product are the easier ones to investigate.”

Classified as probably not a substantial claim.

It has not been demonstrated that a generic well-defined ensemble will admit life.

“nor has it been demonstrated that a generic well-defined ensemble will admit life.”

Probably not a substantial claim: may not pass S2 (checkable).

The full space M must be large enough to represent all possibilities, along with many others we cannot even conceive of, but which can nevertheless in principle also be described by such parameters.

“The full space M must be large enough to represent all of these possibilities, along with many others we cannot even conceive of, but which can nevertheless in principle also be described by such parameters.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Infinity cannot be arrived at or realized.

“However, if that is the case, then 'infinity' cannot be arrived at, or realized.”

Probably not a substantial claim: may not pass S2 (checkable).

For providing an explanation of existence, simply having a conceptually possible ensemble is not adequate; a link to objects or things that actually exist, or to mechanisms that make them exist, is needed.

“For the purposes of providing an explanation of existence, simply having a conceptually possible ensemble is not adequate -we need a link to objects or things that actually exist, or to mechanisms that make them exist.”

Probably not a substantial claim: may not pass S4 (based).

Universes in a multiverse should be able to differ in at least some properties from each other.

“It is clear that universes in a multiverse should be able to differ in at least some properties from each other.”

Probably not a substantial claim: may not pass S2 (checkable).

It is not at all clear that we shall ever be able to accurately delineate the class of all possible universes.

“Furthermore, it is not at all clear that we shall ever be able to accurately delineate the class of all possible universes.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

We can, in principle, make a cut between those consistent with the eventual emergence of life and those incompatible with it.

“We can, in principle, make a cut between those consistent with the eventual emergence of life and those incompatible with it”

May combine two claims.

The relevant integrals may diverge, making assignment of mean values or averages for physical quantities in an ensemble problematic.

“Finally, the relevant integrals may diverge.In that case, assigning mean values or averages for physical quantities in an ensemble of universes is problematic”

• cites Kirchner & Ellis 2003 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

In an ensemble in which all that is possible happens, all parameters will be member parameters.

“In an ensemble in which all that is possible happens, all parameters will be member parameters”

Probably not a substantial claim: may not pass S3 (load-bearing).

The existence of the actually infinite inevitably leads to unresolvable contradictions in set theory and in definitions and deductive foundations of mathematics.

“As he points out, following many others, the existence of the actually infinite inevitably leads to well-recognized unresolvable contradictions in set theory, and thus in definitions and deductive foundations of mathematics itself”

• cites Hilbert 1964Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

No proof has been given that the physics that maximizes black hole production also favours life.

“no proof has been given of the last step, that the physics that maximizes black hole production also favours life.”

• cites Smolin's (1999)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

If the set of realized models is finite or countably infinite, then almost all possible models are not realized and the ensemble represents a set of measure zero in the set of possible universes.

“However, on the other hand, if the set of realized models is either finite or countably infinite, then almost all possible models are not realized -the ensemble represents a set of measure zero in the set of possible universes.”

May combine two claims.

There are infinitely many distribution functions that realize all possible universes, so a really existing 'ensemble of all possible universes' is not unique.

“However, there are an infinite number of distribution functions which would fulfil this condition, and so a really existing 'ensemble of all possible universes' is not unique.”

Probably not a substantial claim: may not pass S3 (load-bearing).

There is still considerable uncertainty as to the nature of an ensemble even within the restricted FLRW context.

“There is still considerable uncertainty as to the nature of an ensemble even within this restricted context.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

Problems arise when it is claimed that there is an actually existing ensemble containing an infinite number of universes or of expanding universe regimes.

“the problems arising when it is claimed that there is an actually existing ensemble containing an infinite number of universes or of expanding universe regimes.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The structures defined so far are uniform across the class of models in the possibility space, characterized by laws of physics and a restricted class of geometries.

“The structures defined so far are the uniform structures across the class of models in this possibility space, characterized both by laws of physics (in particular, general relativity) and by a restricted class of geometries.”

May combine two claims.

The assumption that the product N_S * f_S * f_p * n_e * f_l * f_i > 0 might be acceptable in our physically realized Universe but there is no reason to believe it holds generally in an ensemble.

“This assumption might be acceptable in our physically realized Universe, but there is no reason to believe it would hold generally in an ensemble because these parameters will depend on other ensemble parameters, which will vary.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

Because the parameters P determine the dynamics, the set of paths in S characterizing individual universes m are determined by this prescription.

“Because the parameters P determine the dynamics, the set of paths in S characterizing individual universes m are determined by this prescription.”

May combine two claims.

The existence of multiverses or ensembles is in principle untestable by any direct observations, and the same applies to any hypothesized properties we may suppose for them.

“the existence of multiverses or ensembles is in principle untestable by any direct observations, and the same applies to any hypothesized properties we may suppose for them.”

• cites Leslie 1996Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Gardner 2003Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

There is no conceptual problem with an infinite set of possible or conceivable universes.

“There is no conceptual problem with an infinite set -countable or uncountable -of possible or conceivable universes.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.

The arguments against an infinite past time are strong; it is not constructible in terms of events or instants of time.

“The arguments against an infinite past time are strong -it is simply not constructible in terms of events or instants of time, besides being conceptually indefinite.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

Realizing probabilities for points of M implies a causal mechanism relating created members of the multiverse; otherwise there is no reason any probability law should be obeyed.

“Realizing such probabilities seems to imply a causal mechanism relating the created members of the multiverse to one another so they are not, in fact, causally disjoint.Otherwise, there is no reason why any probability law (Gaussian normal, for example) should be obeyed.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

The regularities which must underlie any systematic description of truly disjoint multiverses must imply some kind of common generating mechanism.

“the regularities which must underlie any systematic description of truly disjoint multiverses must imply some kind of common generating mechanism.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

Specifying the set of possible parameters determines a uniform high-level structure that is obeyed by all universes in M.

“specifying the set of possible parameters determines a uniform high-level structure that is obeyed by all universes in M.”

May combine two claims.

Some such structuring is necessary if we are to be able to describe a multiverse with specified properties; a coherent description is only possible through the existence of such regularities.

“Some such structuring is necessary if we are to be able to describe a multiverse with specified properties -a coherent description is only possible through the existence of such regularities.”

May combine two claims.

M anthropic does not intersect M FLRW, because realistic models of a life-bearing universe like ours cannot be exactly FLRW, for then there is no structure.

“but does not intersect M FLRW (realistic models of a life-bearing universe like ours cannot be exactly FLRW, for then there is no structure).”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

It is often convenient to use a set of parameters which are comoving in state space, i.e. constants of motion.

“For these reasons it is often convenient to use a set of parameters which are comoving in the state space, i.e. parameters which are constants of motion.”

Probably not a substantial claim: may not pass S3 (load-bearing).

There is vagueness about the proposed nature of multiverses.

“There is, however, a vagueness about the proposed nature of multiverses.”

May combine two claims.

The same universe may occur several times over in the space of possible universes; the equivalence problem determines when such multiple representations occur.

“Note that the same universe may occur several times over in this space; the equivalence problem determines when such multiple representations occur.”

Classified as probably not a substantial claim.

For a complete probabilistic description of an ensemble we need both a distribution function P and a measure π.

“For a complete probabilistic description of an ensemble we need not only a distribution function P, but also a measure π = µ(x) dx for each parameter space with parameter x”

Probably not a substantial claim: may not pass S4 (based).

In order to define a FLRW ensemble, we need a set of independent parameters which uniquely identify all possible FLRW models.

“In order to define a FLRW ensemble, we need a set of independent parameters which uniquely identify all possible FLRW models.”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

In any given ensemble, not all possible universes may be realized, and some may be realized many times.

“However, in any given ensemble, they may not all be realized, and some may be realized many times.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

It will be impossible at any stage to characterize that set of the multiverse in which all the conditions necessary for the emergence of self-conscious life and its maintenance have been met, because we do not know what those conditions are.

“It will be impossible at any stage to characterize that set of the multiverse in which all the conditions necessary for the emergence of self-conscious life and its maintenance have been met, for we do not know what those conditions are”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Realized infinite sets are not constructible; there is no procedure to complete such a set.

“Others (see Spitzer 2000;Stoeger 2003, and references therein) have further pointed out that realized infinite sets are not constructible -there is no procedure we can in principle implement to complete such a set -they are simply incompletable.”

• cites Spitzer 2000 sourceNot checked — no full text of the source
• cites Stoeger 2003Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

M Observational is a subset of M anthropic because we need observers to make observations.

“Precisely because we need observers to make observations, this is a subset of M anthropic .”

Classified as probably not a substantial claim.

Life demands unique combinations of many different parameter values that must be realized simultaneously.

“life demands unique combinations of many different parameter values that must be realized simultaneously.”

• cites Davies 2003Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Tegmark 2003 sourceNot checked — no full text of the source

May combine two claims.

We can provide necessary sets of parameter values but cannot guarantee completeness or independence.

“This means we can provide necessary sets of parameter values but cannot guarantee completeness or independence.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The detailed characterization of the space M and its relationship to S depends on the matter description used and its behaviour.

“The detailed characterization of this space, and its relationship to S, will depend on the matter description used and its behaviour.”

May combine two claims.

Future infinite time is never realized; whatever time we reach, there is always more time available.

“Future infinite time also is never realized; rather, the situation is that whatever time we reach, there is always more time available.”

Probably not a substantial claim: may not pass S2 (checkable).

Genuine existence of an uncountable infinitude of models is highly problematic.

“Because of the real number continuum, this is an uncountably infinite set of models -and genuine existence of such an uncountable infinitude is highly problematic.”

Probably not a substantial claim: may not pass S3 (load-bearing).

A really existing infinite set is not possible.

“However, as stressed by Hilbert (1964), it can be argued that a really existing infinite set is not possible.”

• cites Hilbert 1964Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Many inflaton potentials may yield ensembles uninteresting for life, but some will be bio-friendly.

“Many of these potentials may yield ensembles which are uninteresting as far as the emergence of life is concerned, but some will be bio-friendly.”

May combine two claims.

Chaotic inflation proposals are not directly observationally testable, and there is no astronomical evidence that the supposed other FLRW-like regions exist.

“Also, these proposals are not directly observationally testable -we have no astronomical evidence the supposed other FLRW-like regions exist.”

Probably not a substantial claim: may not pass S2 (checkable).

Overarching physics, or a 'law of laws' represented by the inflaton field and its potential, can lead to a really existing ensemble of many very different FLRW-like regions of a larger universe.

“This type of scenario suggests how overarching physics, or a 'law of laws' (represented by the inflaton field and its potential), can lead to a really existing ensemble of many very different FLRW-like regions of a larger universe.”

Probably not a substantial claim: may not pass S3 (load-bearing).

If a multiverse contains a finite or infinite countable number of universes, the distribution function contains Dirac δ-functions.

“A multiverse might contain a finite or infinite countable number of universes.In these cases, the distribution function contains Dirac δ-functions”

May combine two claims.

There is no evidence that the postulated physics is true in this universe, much less in some pre-existing metaspace that might generate a multiverse.

“There is no evidence that the postulated physics is true in this universe, much less in some pre-existing metaspace that might generate a multiverse.”

May combine two claims.

We seem to face an infinite regress when following the logic of explaining meta-laws, and it is not clear how to end it except by arbitrarily calling a stop.

“We seem to face an infinite regress as we follow this logic to its conclusion, and it is not clear how to end it except by arbitrarily calling a stop to this process.”

• AssumptionThe authors state this as an assumption: Some relevant meta-laws pre-exist.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.

If a multiverse is 'tested' by its prediction that our universe is a likely member, then an ensemble with many copies should be the most satisfying one, but one copy (just our universe) might be just as well.

“If a multiverse is 'tested' by its prediction that our universe is a likely member, then such an ensemble should be the most satisfying one -but then we might just as well be happy with one copy, i.e. just our universe.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Different distribution functions are needed for different possibility spaces.

“While distribution functions can be parametrized by any set of coordinates over the possibility space, we need different distribution functions for different possibility spaces.”

May combine two claims.

If we live in a 'small universe' where we have already seen right round the universe, then the universe closes up on itself in a single FLRW-like domain and no further causally connected such domains can exist.

“These are when we live in a 'small universe' where we have already seen right round the universe (Ellis & Schrieber 1986;Lachieze-Rey & Luminet 1995) for then the universe closes up on itself in a single FLRW-like domain and so no further such domains that are causally connected to us in a single connected space-time can exist.”

• cites Ellis & Schrieber 1986 sourceNot checked — no full text of the source
• cites Lachieze-Rey & Luminet 1995 sourceNot checked — no full text of the source

May combine two claims.

These transformations are not unique, and hence it is possible to find many different measures.

“These transformations are not unique, and hence it is possible to find many different measures.”

Probably not a substantial claim: may not pass S2 (checkable).

Philosophical argumentation is unavoidable if one is to seriously argue the claim for existence of a multiverse.

“Thus, philosophical argumentation is unavoidable if one is to seriously argue the claim for existence of a multiverse.”

May combine two claims.

The measure is in general non-normalizable and hence there is no normalizable maximum-entropy distribution; without additional information we cannot calculate definite probabilities.

“Secondly, the measure is in general non-normalizable and hence there is no normalizable maximum-entropy distribution.Without additional information we are not able to calculate definite probabilities.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

A particular distribution function can be expressed in any set of coordinates.

“It is clear that a particular distribution function can be expressed in any set of coordinates.”

Probably not a substantial claim: may not pass S2 (checkable).

In order to establish distributions in a non-arbitrary way, we need a theory of how this particular ensemble is selected for from all other possible ones.

“However, in order to establish these in a non-arbitrary way, we need a theory of how this particular ensemble is selected for from all the other possible ones.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

There is a vast set of possible distribution functions.

“Obviously there is a vast set of possible distribution functions.”

May combine two claims.

The individual universes making up an ensemble with regularities are not actually independent of each other; they are products of a single process.

“This in turn means that the individual universes making up the ensemble are not actually independent of each other.They are, instead, products of a single process, as in the case of chaotic inflation.”

May combine two claims.

For the 1/ρ distribution, the divergence is inside the anthropically allowed region and is non-integrable.

“In this case the divergence is located inside the anthropically allowed region and is non-integrable.”

Borderline on S4 (based): unclear from the text.

Ensembles resulting from a single causal process and ensembles consisting of discrete entities are ultimately not distinguishable from each other.

“We discuss these two cases in turn, and then show that they are ultimately not distinguishable from each other.”

May combine two claims.

If space-time is quantized at the Planck level, then all physical quantities are quantized and uncountable infinities become finite numbers in any finite interval.

“The problem would be allayed if space-time is quantized at the Planck level, as suggested for example by loop quantum gravity.In that case we can argue that all physical quantities also are quantized, and the uncountable infinities of the real line become transmuted into finite numbers in any finite interval”

May combine two claims.

The proposed underlying physics for chaotic inflation has not been tested and may be untestable.

“However, the problem is that the proposed underlying physics has not been tested, and indeed may be untestable.”

May combine two claims.

For the 1/ρ distribution, the expectation value of the cosmological constant vanishes, so we fail to explain the observed non-zero value.

“For this case, the expectation value vanishes, i.e. ρ = ρ max 0 ρ (1/ρ ) dρ ρ max 0 (1/ρ ) dρ = 0 and we fail to explain the observed non-zero value of the cosmological constant.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

Observational probabilities are never conclusive.

“In any case, in the end those papers all deal just with observational probabilities, which are never conclusive.”

May combine two claims.

In scalar-field models P(ρ) is directly related to the a priori distribution of scalar-field fluctuations, and for a wide class of potentials the variations of P(ρ) over the anthropically allowed range should be negligible.

“In scalar-field models P(ρ ) is in direct relation to the a priori distribution of the scalar-field fluctuations and it has been argued (Weinberg 2000a,b) that for a wide class of potentials the variations of P(ρ ) over the anthropically allowed range (where N(ρ ) = 0) should be negligible.”

• cites Weinberg 2000a,bNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

We cannot link the distribution of the cosmological constant to that of the scalar field in a unique way, and there is a vast choice for possible a priori probability distributions for the cosmological constant.

“Hence, we cannot link the distribution of the cosmological constant to that of the scalar field in a unique way, and there is a vast choice for possible a priori probability distributions for the cosmological constant.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

In the ensemble of all possible universes, all possible inflaton potentials and all solutions to those potentials should exist, including stationary and non-stationary chaotic inflationary models.

“Finally, from the point of view of the ensemble of all possible universes often invoked in discussions of multiverses, all possible inflaton potentials should be considered, as well as all solutions to all those potentials.They should all exist in such a multiverse, which will include chaotic inflationary models which are stationary as well as those which are non-stationary.”

May combine two claims.

For the 1/√ρ distribution, there is a divergence in the anthropically allowed region, but it is integrable.

“Again, there is a divergence in the anthropically allowed region, but this time it is integrable.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

There is a philosophical problem surrounding a realized infinite set of any kind.

“As we have pointed out above, there is a philosophical problem surrounding a realized infinite set of any kind.”

May combine two claims.

The infinities of really existent FLRW-like domains derive from the assumed initial infinite flat or open space sections, and there are problems in assuming such space sections are actually realized.

“In this case, the infinities of really existent FLRW-like domains derive from the assumed initial infinite flat (or open) space sections -and we have pointed out above the problems in assuming such space sections are actually realized.”

• AssumptionThe authors state this as an assumption: The initial space sections are infinite flat or open.

Probably not a substantial claim: may not pass S4 (based).

The only known method for constructing such a measure is Jaynes' principle.

“The only known method for constructing such a measure is Jaynes' principle.”

Probably not a substantial claim: may not pass S2 (checkable).

If you cannot show which particular multiverse exists, it is doubtful you have shown any one exists.

“Indeed, if you cannot show which particular one exists, it is doubtful you have shown any one exists.”

Classified as probably not a substantial claim.

Anthropic FLRW universes are those in which the necessary cosmological conditions for life are fulfilled, allowing galaxies, stars and planets if the universe is perturbed, so allowing a non-zero factor N_g * N_S.

“We can identify those FLRW universes in which the emergence and sustenance of life is possible at a broad levelfoot_8 -the necessary cosmological conditions have been fulfilled allowing the existence of galaxies, stars and planets if the universe is perturbed, so allowing a non-zero factor N g * N S * as discussed above.”

May combine two claims.

In the state of minimum information we do not know the natural parametrization, and different measures correspond to different guesses.

“Nevertheless, in the state of minimum information we do not know what the natural parametrization is for the possibility space and different measures correspond to different guesses.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

A similar relation to equation (24) should hold for multiverses in the wider sense.

“It is clear that a similar relation to equation ( 24) should hold for multiverses in the wider sense.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

In a true multiverse, there is no possibility of any indirect causal connection of any kind; the universes are completely disjoint.

“In the case of a true multiverse, there is not even any possibility of any indirect causal connection of any kind -the universes are then completely disjoint and nothing that happens in any one of them is causally linked to what happens in any other one.”

May combine two claims.

There is no direct evidence of existence of the claimed other universe regions in an ensemble, nor can there be any, because they lie beyond the visual horizon and most beyond the particle horizon.

“There is no direct evidence of existence of the claimed other universe regions in an ensemble, nor can there be any, for they lie beyond the visual horizon; most will even be beyond the particle horizon, so there is no causal connection with them.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

The one way we might make a reasonable claim for the existence of a multiverse would be if we could show its existence was a more or less inevitable consequence of well-established physical laws and processes.

“The one way we might make a reasonable claim for the existence of a multiverse would be if we could show its existence was a more or less inevitable consequence of well-established physical laws and processes.”

Probably not a substantial claim: may not pass S4 (based).

Without knowledge of the creation mechanism, it is impossible to determine the measure with certainty.

“Without knowledge of the creation mechanism, it is impossible to determine this measure with certainty.”

May combine two claims.

The measure is derived from the chosen set of parameters; generally a different choice of parameters yields a different minimum-information measure, predicting another maximum-entropy distribution function.

“First, the measure is derived from the chosen set of parameters.Generally a different choice of parameters yields a different minimum-information measure, predicting another maximum-entropy distribution function.”

May combine two claims.

If the existence of a multiverse is a scientific proposition, we need to be able to show which specific multiverse exists, but there is no observational way to do this.

“The point is that there is not just an issue of showing a multiverse exists -if this is a scientific proposition we need to be able to show which specific multiverse exists; but there is no observational way to do this.”

May combine two claims.

The requirement of structure formation as a prerequisite for life places strong anthropic constraints on the domains in which observers could exist, and these constraints must be satisfied in the really existing universe.

“The requirement of structure formation as a prerequisite for life places strong anthropic constraints on the domains in which observers could exist; these constraints must be satisfied in the really existing universe.”

May combine two claims.

Really existing multiverses that can be defined as candidates for the one to which our Universe belongs are not unique, and neither their properties nor their existence are directly testable.

“It is, however, abundantly clear that 'really existing multiverses' which can be defined as candidates for the one to which our Universe belongs are not unique, and neither their properties nor their existence are directly testable.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

If all that can exist exists, then there are universe models occupying the biophilic subspace.

“The issue of fine-tuning is the statement that the biophilic set of universes is a very small subset of the set of possible universes; but if all that can exist exists then there are universe models occupying this biophilic subspace.”

May combine two claims.

A small universe would disprove the usual chaotic inflationary scenario, but not a true multiverse proposal, for that cannot be shown false by any observation, nor shown true.

“This would disprove the usual chaotic inflationary scenario, but not a true multiverse proposal, for that cannot be shown to be false by any observation.Neither can it be shown to be true.”

May combine two claims.

Perturbations of exact FLRW models can allow life, but exact FLRW models themselves cannot.

“More accurately, perturbations of these models can allow life -the exact FLRW models themselves cannot do so.”

Probably not a substantial claim: may not pass S1 (asserted), S4 (based).

Even if inflation works just once, that is sufficient to give a model close enough to standard FLRW cosmological models to be friendly to life.

“The counter response is that this does not matter; however small the chances are, if it works just once then that is sufficient to give a model close enough to the standard FLRW cosmological models to be friendly to life.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

The multiverse idea has problems: realized infinities; inability to describe such ensembles because we do not know all possibilities; and it is not testable or provable in the usual scientific sense, remaining a matter of faith rather than proof.

“However, there are the following problems: (i) the issue of realized infinities discussed above; (ii) the problem of our inability to describe such ensembles because we do not know what all the possibilities are, so our solution is in terms of a category we cannot fully describe; (iii) the multiverse idea is not testable or provable in the usual scientific sense -existence of the hypothesized”

May combine two claims.

A really existing ensemble or multiverse is not a priori unique, nor uniquely defined; it must somehow be selected for.

“Our fundamental starting point is the recognition that there is an important distinction to be made between possible universes and realized universes, and our main conclusion is that a really existing ensemble or multiverse is not a priori unique, nor uniquely defined.It must somehow be selected for.”

May combine two claims.

It is very likely that the simultaneous realization of all the conditions for life will pick out only a very small sector of the parameter space of all possibilities; anthropic universes are fine-tuned.

“It is very likely that the simultaneous realization of all the conditions for life will pick out only a very small sector of the parameter space of all possibilities; anthropic universes are fine-tuned.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

Previous discussions have not made clear what is required in order to define a multiverse, although some specific physical calculations have been given based on restricted low-dimensional multiverses.

“However, previous discussions have not made clear what is required in order to define a multiverse, although some specific physical calculations have been given based on restricted low-dimensional multiverses.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

The ultimate questions about why this multiverse and its order cannot be answered scientifically because of the lack of any possibility of verification of any proposed underlying theory, and must be argued in philosophical terms.

“In our view these questions -Issues 1 and 2 discussed in this paper -cannot be answered scientifically because of the lack of any possibility of verification of any proposed underlying theory.They will of necessity have to be argued in philosophical terms.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

The existence of life is quite unlike anything else in the physical world and requires explanation beyond chance.

“The counter response is that the existence of life is quite unlike anything else in the physical world -its coming into being is not just like choosing one out of numerous essentially identical hands of cards.It is like being transformed into an entirely different higher level game, and so does indeed require explanation.”

May combine two claims.

The claim that inflation explains the current state of the universe is only partially successful, because very anisotropic or inhomogeneous models may never inflate.

“However, this move is only partially successful, because very anisotropic or inhomogeneous models may never inflate.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

At present, uniqueness eludes us.

“At present, uniqueness eludes us.”

May combine two claims.

The evolution of life should only be possible in sufficiently flat models, at not too early and not too late times.

“The evolution of life should only be possible in sufficiently flat models -otherwise the universes either recollapse too early or are too empty -at not too early and not too late times.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

The primordial process or overarching cosmic principle effectively selects a really existing multiverse from the possibilities in M and defines a distribution function over M.

“These effectively select a really existing multiverse from the possibilities in M, and, as such, effectively define a distribution function over M.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

The multiverse idea in the end represents a regress of causation.

“Furthermore, in the end it simply represents a regress of causation.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

Almost-FLRW universes that are good models of our observable Universe are a small subset of all possible universes, and it is conceivable they are part of a multiverse or ensemble.

“They are a small subset of all possible universes, and it is conceivable they are part of a multiverse or ensemble of universes.”