http://arxiv.org/abs/gr-qc/0703044
de Sitter space and the equivalence between f(R) and scalar-tensor gravity
Valerio Faraoni (Bishop's University)
4 pages, to appear in Phys. Rev. D
"It is shown that, when f'' is non-vanishing, metric f(R) gravity is completely equivalent to a scalar-tensor theory (with zero Brans-Dicke parameter) with respect to perturbations of de Sitter space, contrary to previous expectations. Moreover, the stability conditions of de Sitter space with respect to homogeneous and inhomogeneous perturbations coincide in most scalar-tensor theories, as is the case in metric f(R) gravity."
http://arxiv.org/abs/gr-qc/0703050
Vacuum properties of nonsymmetric gravity in de Sitter space
Tomas Janssen, Tomislav Prokopec (ITP & Spinoza Institute, Utrecht University)
32 pages, 2 figures
ITP-UU-07/9, SPIN-07/9
"We consider quantum effects of a massive antisymmetric tensor field on the dynamics of de Sitter space-time. Our starting point is the most general, stable, linearized Lagrangian arising in nonsymmetric gravitational theories (NGTs), where part of the antisymmetric field mass is generated by the cosmological term. We construct a renormalization group (RG) improved effective action by integrating out one loop vacuum fluctuations of the antisymmetric tensor field and show that, in the limit when the RG scale goes to zero, the Hubble parameter -- and thus the effective cosmological constant -- relaxes rapidly to zero. We thus conclude that quantum loop effects in de Sitter space can dramatically change the infrared sector of the on-shell gravity, making the expansion rate insensitive to the original (bare) cosmological constant."
http://arxiv.org/abs/quant-ph/0703060
A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
A. Doering, C.J. Isham
36 pages
"This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper we discuss two different types of language that can be attached to a system, S. The first is a propositional language, PL(S); the second is a higher-order, typed language L(S). Both languages provide deductive systems with an intuitionistic logic. The reason for introducing PL(S) is that, as shown in paper II of the series, it is the easiest way of understanding, and expanding on, the earlier work on topos theory and quantum physics. However, the main thrust of our programme utilises the more powerful language L(S) and its representation in an appropriate topos."
http://arxiv.org/abs/quant-ph/0703062
A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
A. Doering, C.J. Isham
34 pages
"This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper, we study in depth the topos representation of the propositional language, PL(S), for the case of quantum theory. In doing so, we make a direct link with, and clarify, the earlier work on applying topos theory to quantum physics. The key step is a process we term `daseinisation' by which a projection operator is mapped to a sub-object of the spectral presheaf--the topos quantum analogue of a classical state space. In the second part of the paper we change gear with the introduction of the more sophisticated local language L(S). From this point forward, throughout the rest of the series of papers, our attention will be devoted almost entirely to this language. In the present paper, we use L(S) to study `truth objects' in the topos. These are objects in the topos that play the role of states: a necessary development as the spectral presheaf has no global elements, and hence there are no microstates in the sense of classical physics. Truth objects therefore play a crucial role in our formalism."
http://arxiv.org/abs/quant-ph/0703064
A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows
A. Doering, C.J. Isham
38 pages
"This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. In paper II, we studied the topos representations of the propositional language PL(S) for the case of quantum theory, and in the present paper we do the same thing for the, more extensive, local language L(S). One of the main achievements is to find a topos representation for self-adjoint operators. This involves showing that, for any physical quantity A, there is an arrow \breve{\delta}^o(A):\Sig\mapsymbol, where symbol is the quantity-value object for this theory. The construction of \breve{\delta}^o(A) is an extension of the daseinisation of projection operators that was discussed in paper II. The object symbol is a monoid-object only in the topos, \tau_\phi, of the theory, and to enhance the applicability of the formalism, we apply to symbol a topos analogue of the Grothendieck extension of a monoid to a group. The resulting object, symbol, is an abelian group-object in \tau_\phi. We also discuss another candidate, PR, for the quantity-value object. In this presheaf, both inner and outer daseinisation are used in a symmetric way. Finally, there is a brief discussion of the role of unitary operators in the quantum topos scheme."
[Comment: I couldn't get many of the symbols in this abstract to translate into LaTex and eventually left a substantial portion untranslated.]
http://arxiv.org/abs/quant-ph/0703066
A Topos Foundation for Theories of Physics: IV. Categories of Systems
A. Doering, C.J. Isham
38 pages
"This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. The previous papers in this series are concerned with implementing this programme for a single system. In the present paper, we turn to considering a collection of systems: in particular, we are interested in the relation between the topos representation for a composite system, and the representations for its constituents. We also study this problem for the disjoint sum of two systems. Our approach to these matters is to construct a category of systems and to find a topos representation of the entire category."
http://arxiv.org/abs/gr-qc/0703027
Conserved Quantities in Background Independent Theories
Fotini Markopoulou
11 pages, 3 figures
"We discuss the difficulties that background independent theories based on quantum geometry encounter in deriving general relativity as the low energy limit. We follow a geometrogenesis scenario of a phase transition from a pre-geometric theory to a geometric phase which suggests that a first step towards the low energy limit is searching for the effective collective excitations that will characterize it. Using the correspondence between the pre-geometric background independent theory and a quantum information processor, we are able to use the method of noiseless subsystems to extract such coherent collective excitations. We illustrate this in the case of locally evolving graphs."
http://arxiv.org/abs/gr-qc/0703052
Existence of generalized semiclassical Kodama states. I. The Ashtekar--Klein--Gordon model
Eyo Eyo Ita
32 pages
"This is the first in a series of papers aimed at outlining an algorithm to explicitly construct a finite quantum theory of gravity in Ashtekar variables. The algorithm is based upon extending some properties of a special state, the Kodama state for pure gravity, to more general models. In this paper we analyse a simple case, gravity coupled to a Klein-Gordon scalar field in the minisuperspace Ansatz, in order to derive a criterion for a new semiclassical state and its corresponding semiclassical orbits of spacetime. We then illustrate a presciption for nonperturbatively constructing the analog of the Kodama state for a general case, in preparation for subsequent works in this series."
http://arxiv.org/abs/gr-qc/0703056
Existence of generalized quantum Kodama states. II. The minisuperspace Ashtekar--Klein--Gordon model
Eyo Eyo Ita
41 pages
"This is the second in a series of papers outlining an algorithm to consistently construct a finite quantum theory of gravity in Ashtekar variables. In Part I we constructed a generalized semiclassical Kodama state by solving the classical Hamiltonian constraint under the condition of a broken semiclassical-quantum correspondence due to a Klein-Gordon scalar field. In Part II we will demonstrate a method of restoring this correspondence by generalizing the self-duality condition for the Ashtekar electromagnetic field. The end result will be to establish the existence of a generalized quantum Kodama state devoid of quantum corrections in the minisuperspace model. We also derive the equations needed to solve for the full theory of a finite theory of quantum gravity within the context of this new interpretation."
http://arxiv.org/abs/gr-qc/0703057
Existence of generalized Kodama quantum states. III. A new approach to finite, full quantum gravity
Eyo Eyo Ita
18 pages
"This is the third in a series of papers outlining an algorithm to consistently construct a finite quantum theory of gravity in Ashtekar variables. This paper is a first attempt at the quantization of the full theory coupled to matter, in this case to a spatially inhomogeneous Klein-Gordon scalar field. We delineate the conditions required to construct a solution to the quantum Hamiltonian constraint under the Ansatz of an isotropic, but spatially inhomogeneous, Ashtekar connection, and highlight some differences relative to the minisuperspace case."
briefly mentioned:
http://arxiv.org/abs/gr-qc/0703055
Hawking radiation as tunneling from Gravity's rainbow
Cheng-Zhou Liu, Jian-Yang Zhu
http://arxiv.org/abs/gr-qc/0703058
Asymptotic quasinormal modes of scalar field in a gravity's rainbow
Cheng-Zhou Liu, Jian-Yang Zhu
briefly mentioned:
http://arxiv.org/abs/hep-th/0703055
(reminder about Vaas new book "Beyond the big bang" Springer 2007)