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Superstrings,
Black Holes, Branes, and Cosmology
Superstring theory is one of the most promising candidates for the ultimate theory of the
quantum gravitational field, incorporating the hope that quantum gravity is unified with
the other fundamental interactions [1,2].
The essence of string theories is based on the hypothesis that fundamental objects are not
pointlike particles but one-dimensional entities whose structure becomes evident only at
very short distances (around 10-33 cm). Superstrings, which exist in a spacetime with ten
dimensions, six of which are believed to be compactified to an unobservable small size.
Elementary particles are identified by the vibrational modes of the strings. Supergravity
theories can arise from string theories as effective field theories in the long-wavelength
limit.
Five distinct mathematically consistent string theories are known. However, it has
become clear that these theories are actually related by duality relations. Possibly, they
can be interpreted as different realisations of a deeper new theory called M-theory. Mtheory is believed to be an eleven-dimensional theory whose fundamental objects are not
superstrings but, rather, higher dimensional entities such as two-dimensional and fivedimensional supermembranes.
The low-energy limit of M-theory is given by
supergravity in eleven dimensions [2]. Again, seven dimensions are thought to be curled
up to an unobservable small size.
A natural arena where the ideas mentioned above can be tested, at least at a
phenomenological level, is given by early universe cosmology and black hole physics.
Indeed, both black hole theory and cosmology should be re-examined in the context of
Supergravity/Superstring theory [3-6]:
 The description of black holes in string theory points to very important results
because it may provide the answer to well-known problems, for instance the origin of
the black hole entropy and of the information paradox [2,7,8];
 Furthermore, string theories may constitute an important research program in early
cosmology since the corresponding field equations have obviously a different
structure from Einstein equations. Thus short-distance modifications of general
relativity due to superstring/supergravity theories would affect the dynamics of the
early universe [4-6,9-12] and be crucial in order to understand long standing
problems. More precisely, symmetries of string theory provide an alternative picture
with the aditional feature that superstrings and M-theory are naturally formulated in a
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higher dimensional spacetime. So it seems natural to query how extra dimensions are
affecting the physics of the four-dimensional world.
The aim of the research project to carry on at the Astrophysics and Cosmology Group of
the Physics Department of UBI (GATC-DF/UBI) is therefore to give a contribution to the
ongoing discussion of both superstring/supergravity theories. In particular, focusing on
black hole/early universe physics by investigating related issues in the context of
effective theories derived from M-theory, superstring and/or supergravity theories.
The underlying motivations for this specific research proposal rely in the mutual benefit
that may follow from the interplay of techniques and results peculiar of
superstring/supergravity and black hole/early cosmology research programs. Let us
illustrate in detail some ideas that we plan to realise in the framework of this research
project.
 Quantum Cosmological Implications of Supersymmetry and String Theory
The presence of a Quantum Gravity theory is mandatory if one wants to thoroughly address longstanding and fundamental questions such as ``Why is our Universe as it is’’ and ``How did it
evolve to its present form’’. En route towards a theory of quantum gravity many significant
results have been obtained in the last 15 years or so (see ref. [5,13,14,15] for a review).
Further advances in our understanding about the nature of quantum gravity can be explored
within a specific methodology that is directly based on two celebrated approaches to quantum
gravity: quantum cosmology and string theory [4-6,9-12]. This essential aspect brings about
innovative concepts and instruments, which are new in comparison with other approaches
regarding quantum gravity and cosmology. In more precise terms, we will therefore focus this
section of our research in quantum cosmological models derived from supergravity and string
theory inspired actions.
Regarding string theory, it basically describes particles and interactions by way of the oscillation
modes of different types of strings. It is now widely accepted that all five 10-dimensional
superstring theories are equivalent and related by a particular type of symmetry transformation
[2] designated as dualities. At a cosmological scenario, these may correspond to a  a 1 (for the
scale factor of a cosmological model) and     6 ln a (for the corresponding scalar field),
playing thereby an important role: it maps an expanding onto a contracting cosmological solution,
leaving the string action invariant [9-11]. Moreover, it provides a promising inflationary scenario
(driven by the dilaton field) in a quite natural way, in what as been designated as a Pre Big-Bang
scenario [10]. The basic assumption is that the Universe starts at a flat, empty, string vacuum
state and then evolves accelerating (kinetically driven by the inflation) towards a state of
increasing curvature and typically a non-perturbative regime. A transition (yet to be fully
clarified) should then occur, leading the universe to the Standard (Post Big Bang) phase of
evolution.
As far as quantum cosmological methods applied to the early universe are concerned, the physical
state,  , of the universe is identified as a wave function instead of a classical space-time
solution. The almost totally of models that have been considered [5,14,15] have all but a finite
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number of degrees of freedom ``frozen’’. This is achieved by restricting the fields to be
homogeneous and such models are known as (finite dimensional) minisuperpaces.
By combining the main features of the string and quantum cosmological approaches we get a
pertinent as well as active framework to analyse the very early stages of our universe. Some
advances have been recently achieved, where members of this project have played quite a
noteworthy role [4-6,9-12,16-22]. In particular, it has been suggested in recent years or so that the
presence of dualities in quantum cosmological models induce the existence of quantum states that
have invariance under Supersymmetry (SUSY) [9,11,22].
The presence of SUSY invariance in a description of the very early universe represents an
element of the uppermost value. In fact, SUSY plays a crucial role in Supergravity (that is, local
SUSY) and Superstring theory by inducing the cancellation of divergences that would otherwise
be present in plain quantum gravity theories. Moreover, some supergravity theories represent a
``square-root’’ of Einstein gravity: to determine physical states it is sufficient to employ the
Lorentz and Supersymmetry invariances. Instead of dealing with the second-order differential
equation H  = 0 we may just have to solve a system of coupled first-order differential equations
--- each one similar to a Dirac-like equation. This scenario is designated as Supersymmetric
Quantum Cosmology (SQC). Most of the previous research in SQC has been aimed at finding
quantum states and overcome consistency problems (see ref. [5]).
We thus propose to advance the current understanding of quantum cosmology by investigating
thoroughly the following issues within the framework of superstrings and supergravity applied to
cosmology:
(1) Quantum Cosmological Models in the presence of String Dualities
(1.1) Examine how the presence of duality transformations induces the existence of SUSY
invariance. Previous studies involving FRW models (that is, homogeneous and isotropic)
have suggested the existence of N=2 SUSY [9,22]. We will extend this assertion towards a
considerable larger range by analysing a broader class of homogeneous cosmologies (that
is, Bianchi models, which are not isotropic). If this could be proven it would point to
deeper structures of symmetry that could be present in a full quantum gravity theory.
(1.2) Investigate (specific) minisuperspace models arising from the bosonic sector of string
effective actions with potentials derived from the requirement of S and T duality [10]. Namely,
by employing inhomogenous perturbations of the metric and dilaton fields. In that context, new
quantum states, which would have a physical significance regarding (a) a period of evolution
from String (Pre Big Bang)/Supergravity cosmological physics towards a semi-classical stage,
together with (b) identifying the existence of any quantum state associated with dilaton driven
inflation and to structure formation, may be found.
(1.3) Quite recently, numerical simulations regarding inhomogenous cosmological models in
string cosmology [23] have been investigated. However, they have not provided a full
agreement or a consistent scenario. Our purpose is to further investigate these models but
within the more general scenario of scalar-tensor theories, where the dilaton kinetic term in the
action is multiplied by a constant factor  . These include low-energy string actions as a
particular case (  = -1), as well as a cosmological constant. Examining such a general scenario
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where string theory fits, will clearly assist us in identifying the reasons(s) for those apparent
differences. Moreover, it will provide a relevant picture of the dynamical processes that are
involved.
(1.4) Another line of research that we aim to analyse is the recent cosmological scenario within
the Horava-Witten formulation of M-theory [24]. This is an active and most innovative area of
research where a fundamental description for the origin and subsequent evolution of the very
early Universe ought to be addressed. In particular, when dealing with a framework where
cosmological solutions entail as a direct consequence precise models for particle physics.
(2) Supersymmetric Quantum Cosmology (SQC)
(2.1) Address the same Bianchi models indicated in (1.1) but derived directly from N=1
supergravity, where a fermionic matter sector is explicitly present, that is, in a SQC context
[4,5,20,21]. This an urgent and pertinent issue: previous results with other models and
different matter contents have pointed instead to N=4 SUSY [5,20,22]. Our purpose is then to
compare these results with (1.1), discussing the physical reasons for any possible differences.
In particular, regarding the level of SUSY and its relation with the existence of dualities: how
does duality relates to supersymmetry?
(2.2) Analyse the retrieval of semi-classical features and origin of structure formation in SQC
[5,6]. Is it possible to identify a consistent quantum to classical transitions in SQC? How does
this compare to plain gravitational theories with matter fields but no SUSY? That is, which
additional feature(s) does the presence of SUSY invariance brings about in a quantum
mechanical description of the very early universe? Is there an imprint of an early SUSY
quantum epoch into the observed universe?
(2.3) Examine very recent results concerning the possibility of quantum creation of open
FRW universes (i.e., with negative spatial curvature) [25]. Such theoretical scenarios could
provide a consistent justification regarding some cosmological observations, even though
the evidence that we live in a spatially open universe has become less strong. However,
there is no widely accepted theoretical quantum description for them. Furthermore, there
persist sharp confronting issues to be settled [25]. Our objective is to investigate quantum
open universes in the presence of complex scalar fields derived from N=1 supergravity
[5,16,19], since all quantum models studied so far have employed real scalar fields within
the theory of General Relativity.
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 Black Holes in Quantum Gravity Theories
The quantisation of black holes will provide a key to the construction of a full, nonperturbative,
theory of quantum gravity. Although still far from this final goal, recent years have seen
significant progress in this respect;


First, within canonical gravity, the quantisation of the eternal spherically symmetric black
hole has been understood, while the quantisation of black holes resulting from collapsing
stars was understood within a consistent semiclassical quantisation scheme[26-40];
Second, progress in superstring theory [1] led to a statistical mechanical description of
extremal and near-extremal black holes in terms of D-brane states [1,2].
In general terms, our purpose is to both understand more thoroughly the semiclassical expansion
scheme (derived from canonical quantisation) for black holes as well as connecting these results
with methods and results derived within a string framework.
More precisely, we will compare and examine contrasting features regarding canonical
quantization and string theory, as far as black hole thermodynamics is concerned. On the one
hand, results obtained within canonical quantum gravity (i.e., from a wave function for the black
hole system) have shown how thermodynamical quantities (entropy, temperature) can acquire a
geometrical interpretation from quantum black holes [26-40]. On the other hand, string theory has
given a novel statistical context to black hole thermodynamics. Namely, from such concepts as
supersymmetric (BPS) solitonic states and extended objects designated as D-branes [1,2]. One
particular urgent and issue we want to investigate is why and how some thermodynamical
quantities (e.g., temperature) differ if we employ a canonical gravity framework or string theory.
Other important challenging and actual problems comprise analysing the above issues within
black strings and infer if the mass of black holes can be quantified.
In addition, we shall study the so-called black strings [33] and try to apply recent results about the
interpretation of black hole entropy from the canonical approach to this case [26-40]. This should
yield a deeper understanding of the entropy as arising from counting string states [1,2].
Moreover, we shall study in detail the question whether the area of quantum black holes is
quantised in Planck units. We hope thereby to put earlier heuristic derivations of this quantisation
on a firmer footing. In essence, we want to get some insight into the final phase of black hole
evaporation from canonical gravity.
Finally, we will further investigate the quantisation of the Schwarzschild black-hole in the
apparent horizon 3,39,40. The relevant feature is that at the apparent horizon the Hamiltonian
and difeomorphism (momentum) constraints become proportional. Hence, the solution of the
problem may become substantially simple. This scenario is also most adequate to examine
dynamical evaporating black holes, where the mass is a function of a time coordinate and there is
as matter source flux of outgoing radiation. We thus plan to examine (a) which vacuum states are
preferred within this framework and (b) investigate which consequences it brings about for blackholes in Einstein-yang-Mills theories.
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The investigation programme thoroughly described above constitutes the intended sequel
regarding the last six or seven years of research work conducted by the Principal
Investigator. The overwhelming majority of this research has been conducted at the
DAMTP, University of Cambridge, where Post-Doctoral experience as well as scientific
research on SQC and string theory were acquired. Our research proposal thus represents
the resolute intention of young and newly graduated scientists to conduct and consolidate
these new areas of research work in Portugal. In particular, it will sustain previously
initiated lines of investigation, strengthening collaboration with other research centres as
well. Consequently, it will definitely contribute towards enlarging and promoting
innovative investigation issues in Portugal for future prospective researchers.
In order for the objectives previously described to be achieved, several stages are
therefore obligatory.
To begin with, it ought to be emphasised that our underlying working principle is full
collaboration. Hence, all the participating members will attempt to contribute as a whole
within teams, towards achieving publishable results. The members constituting this
research project will engage in a series of tasks according to their specific background
and the objectives In particular, they will participate and engage in research activities,
jointly with a Post-Doctoral fellow (starting at GATC UBI in October 1999) and some
research students. Furthermore, specific sections of the research problems comprised
within (1)-(2) have been employed as research programmes for Ph.D. graduate students.
We plan to disseminate and publish our research results as follows:
 On the one hand, we will prepare scientific reports that will be presented at major
scientific conferences. Our aim will be to present the reports as part of oral
communications and have them included in the proceedings. The obvious reason is
that is mandatory to make results readily available to the widest possible audience,
given that the communication of results at major international meetings is of vital
importance. Moreover, this will promote and invest in fundamental human working
relations and establishing future research work via direct exchange of ideas. In
addition, extended and more technical versions will be submitted for publication in
major scientific peer-reviewed high energy-physics journals;
 On the other hand, we plan to organise a series of regular seminars/workshops as
well as Introductory Lectures in Portugal, with emphasis on the objectives (1)-(2)
above outlined. Our purpose is twofold. First, we intend to promote research on the
subjects of string inspired cosmology and quantum black holes at a university level in
Portugal. Second, that series will constitute the appropriate setting to up-date and
introduce new concepts and techniques to all engaged in this project.
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The Principal Investigator also expects, during the time of execution required for this
project, to further make progress in writing a scientific textbook. This book-project (still
incomplete and in a draft version) was initiated recently (when the author was still a PostDoctoral fellow at the University of Cambridge) and focuses on the quantum cosmology
of the early universe. It constitutes an additional long-term design and an explicit
procedure to contemplate future research topics in SQC and string theory consequences.
Several international publishers/editors have already shown their interest and disposition
to evaluate a complete draft of the book.
The successful completion of this research project will surely benefit from an adequate
financial support. Notice that the Prime Contractor (Universidade da Beira Interior - UBI)
lacks enormously on high-energy physics bibliography. Besides the understandable
support for intrinsic research activities, the requested funding will likewise contemplate
other practical objectives. In fact, it will sustain an effort that will allow Portuguese
scientists to continue and promote their scientific activity in Portugal and in co-operation
with European partners, namely through missions and working visits from consultants.
Furthermore, the support of this proposal will strengthen existing research areas,
promoting research in the interior of Portugal, and contemplate long term, future
research activities. This will fundamentally correct a sharp and disproportionate
asymmetry between major research centres near the sea-coast (for example, Lisbon,
Coimbra or Porto) and those thriving in the interior. This is of cardinal importance to
consolidate science development in the interior of Portugal, and fostering potential
vacancies (e.g., lecturer) for recent Ph.D. graduates.
We thus request funds (outlined in more detail in the appropriate form) to enable:
 Subscription of scientific journals (High Energy Physics) and purchase of several
scientific textbooks and Conference Proceedings – 900 contos;
 Financial support for several missions (e.g., attendance of conferences/workshops
with 1 week's duration) per year or some mid-duration missions (e.g.,
participation in research visiting programmes/advanced schools with duration of 2
weeks ) per year – 1,500 contos;
 Financial support regarding travel and accommodation expenses (duration: from 2
weeks to 1 month) for consultancy visits per year – 1,000 contos.
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