arXiv subjects
Publications and source records attributed to Brett McInnes.
The familiar Bang/Crunch singularities of classical cosmology have recently been augmented by new varieties: rips, sudden singularities, and so on. These tend to be associated with final states. Here we consider an alternative possibility for the initial state: a singularity which has the novel property of being inaccessible to physically well-defined probes. These singularities arise naturally in cosmologies with toral spatial sections.
Recently it has been suggested that non-gaussian inflationary perturbations can be usefully analysed in terms of a putative dual gauge theory defined on the future conformal infinity generated by an accelerating cosmology. The problem is that unitarity of this gauge theory implies a strong constraint [the "Strominger bound"] on the matter fields in the bulk. We argue that the bound is just a reflection of the equation of state of cosmological matter. The details motivate a discussion of the possible relevance of the ``dS/CFT correspondence" to the resolution of the Big Bang singularity. It is argued that the correspondence may require the Universe to come into existence along a non-singular spacelike hypersurface, as in the theories of ``creation from nothing" discussed by Firouzjahi, Sarangi, and Tye, and also by Ooguri et al. The argument makes use of the unusual properties of gauge theories defined on topologically non-trivial spaces.
Ooguri, Vafa, and Verlinde have outlined an approach to two-dimensional accelerating string cosmology which is based on topological string theory, the ultimate objective being to develop a string-theoretic understanding of "creating the Universe from nothing". The key technical idea here is to assign *two different* Lorentzian spacetimes to a certain Euclidean space. Here we give a simple framework which allows this to be done in a systematic way. This framework allows us to extend the construction to higher dimensions. We find then that the general shape of the spatial sections of the newly created Universe is constrained by the OVV formalism: the sections have to be flat and compact.
Seiberg and Witten have shown that the non-perturbative stability of string physics on conformally compactified spacetimes is related to the behaviour of the areas and volumes of certain branes as the brane is moved towards infinity. If, as is particularly natural in quantum cosmology, the spatial sections of an accelerating cosmological model are flat and compact, then the spacetime is on the brink of disaster: it turns out that the version of inflationary spacetime geometry with toral spatial sections is marginally stable in the Seiberg-Witten sense. The question is whether the system remains stable before and after Inflation, when the spacetime geometry is distorted away from the inflationary form but still has flat spatial sections. We show that it is indeed possible to avoid disaster, but that requiring stability at all times imposes non-trivial conditions on the spacetime geometry of the early Universe in string cosmology. This in turn allows us to suggest a candidate for the structure which, in the earliest Universe, forbids cosmological singularities.
It has recently been suggested, by Firouzjahi, Sarangi, and Tye, that string-motivated modifications of the Hartle-Hawking wave function predict that our Universe came into existence from "nothing" with a de Sitter-like spacetime geometry and a spacetime curvature similar to that of "low-scale" models of Inflation. This means, however, that the Universe was quite large at birth. It would be preferable for the initial scale to be close to the string scale, or perhaps the Planck scale. The problem with this, however, is to explain how any initial homogeneity is preserved during the pre-inflationary era, so that Inflation can indeed begin. Here we modify a suggestion due to Linde and assume that the Universe was born with the topology of a torus; however, we propose that the size of the torus is to be predicted by the FST wave function. The latter does predict an initial size for the torus at about the string scale, and it also predicts a pre-inflationary spacetime geometry such that chaotic mixing preserves any initial homogeneity until Inflation can begin at a relatively low scale.
Ooguri, Vafa, and Verlinde have recently proposed an approach to string cosmology which is based on the idea that cosmological string moduli should be selected by a Hartle-Hawking wave function. They are led to consider a certain Euclidean space which has *two different Lorentzian interpretations*, one of which is a model of an *accelerating cosmology*. We describe in detail how to implement this idea without resorting to a "complex metric". We show that the four-dimensional version of the OVV cosmology is null geodesically incomplete but has no curvature singularity; also that it is [barely] stable against the Seiberg-Witten process [nucleation of brane pairs]. The introduction of matter satisfying the Null Energy Condition has the paradoxical effect of both stabilizing the spacetime and rendering it genuinely singular. We show however that it is possible to arrange for an effective violation of the NEC in such a way that the singularity is avoided and yet the spacetime remains stable. The possible implications for the early history of these cosmologies are discussed.
One of the main virtues of string gas cosmology is that it resolves cosmological singularities. Since the Universe can be approximated by a locally asymptotically de Sitter spacetime by the end of the inflationary era, a singularity theorem implies that these cosmologies effectively violate the Null Energy Condition [not just the Strong Energy Condition]. We stress that this is an extremely robust result, which does not depend on assuming that the spatial sections remain precisely flat in the early Universe. This means, however, that it must be possible for string cosmologies to cross the recently much-discussed "phantom divide" [from w < -1 to w > -1, where w is the equation-of-state parameter]. This naturally raises the question as to whether the phantom divide can be crossed again, to account for recent observations suggesting that w < -1 at the present time. We argue that non-perturbative string effects rule out this possibility, even if the NEC violation in question is only "effective".
Linde has recently argued that compact flat or negatively curved spatial sections should, in many circumstances, be considered typical in Inflationary cosmologies. We suggest that the "large brane instability" of Seiberg and Witten eliminates the negative candidates in the context of string theory. That leaves the flat, compact, three-dimensional manifolds -- Conway's *platycosms*. We show that deep theorems of Schoen, Yau, Gromov and Lawson imply that, even in this case, Seiberg-Witten instability can be avoided only with difficulty. Using a specific cosmological model of the Maldacena-Maoz type, we explain how to do this, and we also show how the list of platycosmic candidates can be reduced to three. This leads to an extension of the basic idea: the conformal compactification of the entire Euclidean spacetime also has the topology of a flat, compact, four-dimensional space.
The current cosmic acceleration does not imply that our Universe is basically de Sitter-like: in the first part of this work we argue that, by introducing matter into *anti-de Sitter* spacetime in a natural way, one may be able to account for the acceleration just as well. However, this leads to a Big Crunch, and the Euclidean versions of Bang/Crunch cosmologies have [apparently] disconnected conformal boundaries. As Maldacena and Maoz have recently stressed, this seems to contradict the holographic principle. In the second part we argue that this "double boundary problem" is a matter not of geometry but rather of how one chooses a conformal compactification: if one chooses to compactify in an unorthodox way, then the appearance of disconnectedness can be regarded as a *coordinate effect*. With the kind of matter we have introduced here, namely a Euclidean axion, the underlying compact Euclidean manifold has an unexpectedly non-trivial topology: it is in fact one of the 75 possible underlying manifolds of flat compact four-dimensional Euclidean spaces.
It is generally believed the way to resolve the black hole information paradox in string theory is to embed the black hole in anti-deSitter spacetime -- without of course claiming that Schwarzschild-AdS is a realistic spacetime. Here we propose that, similarly, the best way to study topologically non-trivial versions of de Sitter spacetime from a stringy point of view is to embed them in an anti-de Sitter orbifold bulk, again without claiming that this is literally how de Sitter arises in string theory. Our results indicate that string theory may rule out the more complex spacetime topologies which are compatible with local de Sitter geometry, while still allowing the simplest versions.
As is well known, classical General Relativity does not constrain the topology of the spatial sections of our Universe. However, the Brane-World approach to cosmology might be expected to do so, since in general any modification of the topology of the brane must be reflected in some modification of that of the bulk. Assuming the truth of the Adams-Polchinski-Silverstein conjecture on the instability of non-supersymmetric AdS orbifolds, evidence for which has recently been accumulating, we argue that indeed many possible topologies for accelerating universes can be ruled out because they lead to non-perturbative instabilities.
Maldacena and Maoz have proposed a new approach to holographic cosmology based on Euclidean manifolds with disconnected boundaries. This approach appears, however, to be in conflict with the known geometric results [the Witten-Yau theorem and its extensions] on spaces with boundaries of non-negative scalar curvature. We show precisely how the Maldacena-Maoz approach evades these theorems. We also exhibit Maldacena-Maoz cosmologies with [cosmologically] more natural matter content, namely quintessence instead of Yang-Mills fields, thereby demonstrating that these cosmologies do not depend on a special choice of matter to split the Euclidean boundary. We conclude that if our Universe is fundamentally anti-de Sitter-like [with the current acceleration being only temporary], then this may force us to confront the holography of spaces with a connected bulk but a disconnected boundary.
When de Sitter first introduced his celebrated spacetime, he claimed, following Schwarzschild, that its spatial sections have the topology of the real projective space RP^3 (that is, the topology of the group manifold SO(3)) rather than, as is almost universally assumed today, that of the sphere S^3. (In modern language, Schwarzschild was disturbed by the non-local correlations enforced by S^3 geometry.) Thus, what we today call "de Sitter space" would not have been accepted as such by de Sitter. There is no real basis within classical cosmology for preferring S^3 to RP^3, but the general feeling appears to be that the distinction is in any case of little importance. We wish to argue that, in the light of current concerns about the nature of de Sitter space, this is a mistake. In particular, we argue that the difference between "dS(S^3)" and "dS(RP^3)" may be very important in attacking the problem of understanding horizon entropies. In the approach to de Sitter entropy via Schwarzschild-de Sitter spacetime, we find that the apparently trivial difference between RP^3 and S^3 actually leads to very different perspectives on this major question of quantum cosmology.
Recently it has been argued that, because tachyonic matter satisfies the Strong Energy Condition [SEC], there is little hope of avoiding the singularities which plague S-Brane spacetimes. Meanwhile, however, Townsend and Wohlfarth have suggested an ingenious way of circumventing the SEC in such situations, and other suggestions for actually violating it in the S-Brane context have recently been proposed. Of course, the natural context for discussions of [effective or actual] violations of the SEC is the theory of asymptotically deSitter spacetimes, which tend to be less singular than ordinary FRW spacetimes. However, while violating or circumventing the SEC is necessary if singularities are to be avoided, it is not at all clear that it is sufficient. That is, we can ask: would an asymptotically deSitter S-brane spacetime be non-singular? We show that this is difficult to achieve; this result is in the spirit of the recently proved "S-brane singularity theorem". Essentially our results suggest that circumventing or violating the SEC may not suffice to solve the S-Brane singularity problem, though we do propose two ways of avoiding this conclusion.
Seiberg and Witten have discussed a specifically "stringy" kind of instability which arises in connection with "large" branes in asymptotically AdS spacetimes. It is easy to see that this instability actually arises in most five-dimensional asymptotically AdS black hole string spacetimes with non-trivial horizon topologies. We point out that this is a more serious problem than it may at first seem, for it cannot be resolved even by taking into account the effect of the branes on the geometry of spacetime. [It is ultimately due to the {\em topology} of spacetime, not its geometry.] Next, assuming the validity of some kind of dS/CFT correspondence, we argue that asymptotically deSitter versions of the Hull-Strominger-Gutperle S-brane spacetimes are also unstable in this "topological" sense, at least in the case where the R-symmetries are preserved. We conjecture that this is due to the unrestrained creation of "late" branes, the spacelike analogue of large branes, at very late cosmological times.
In discussions of Bousso's Covariant Entropy Bound, the Null Energy Condition is always assumed, as a sufficient {\em but not necessary} condition which helps to ensure that the entropy on any lightsheet shall necessarily be finite. The spectacular failure of the Strong Energy Condition in cosmology has, however, led many astrophysicists and cosmologists to consider models of dark energy which violate {\em all} of the energy conditions, and indeed the current data do not completely rule out such models. The NEC also has a questionable status in brane cosmology: it is probably necessary to violate the NEC in the bulk in order to obtain a "self-tuning" theory of the cosmological constant. In order to investigate these proposals, we modify the Karch-Randall model by introducing NEC-violating matter into $AdS_5$ in such a way that the brane cosmological constant relaxes to zero. The entropy on lightsheets remains finite. However, we still find that the spacetime is fundamentally incompatible with the Covariant Entropy Bound machinery, in the sense that it fails the Bousso-Randall consistency condition. We argue that holography probably forbids all {\em cosmological} violations of the NEC, and that holography is in fact the fundamental physical principle underlying the cosmological version of the NEC.
The cosmological "equation of state parameter", w, is equal to -1 for a true cosmological constant, and is greater than -1 for quintessence. There is a widespread reluctance to consider the remaining possibility, w < -1, though in fact there is a variety of theoretical and observational evidence in favour of this range. We briefly discuss some of the objections to w < -1 and show that each of them can readily be circumvented. We also briefly consider what string theory has to say about this.