Narrow Results

This paper studies an extension of inductive definitions in the context of a type-free theory. It is a kind of simultaneous inductive definition of two predicates where the defining formulas are monotone with respect to the first predicate, but not monotone with respect to the second predicate. We call this inductive definition half-monotone in analogy of Allen’s term half-positive.

We can regard this definition as a variant of monotone inductive definitions by introducing a refined order between tuples of predicates. We give a general theory for half-monotone inductive definitions in a type-free first-order logic. We then give a realizability interpretation to our theory, and prove its soundness by extending Tatsuta’s technique. The mechanism of half-monotone inductive definitions is shown to be useful in interpreting many theories, including the Logical Theory of Constructions, and Martin-Löf’s Type Theory. We can also formalize the provability relation “a term p is a proof of a proposition P” naturally. As an application of this formalization, several techniques of program/proof-improvement can be formalized in our theory, and we can make use of this fact to develop programs in the paradigm of Constructive Programming. A characteristic point of our approach is that we can extract an optimization program since our theory enjoys the program extraction theorem.

We consider an anti de Sitter universe filled by quantum CFT with classical phantom matter and perfect fluid. The model represents the combination of a trace-anomaly annihilated and a phantom driven anti de Sitter universes. The influence exerted by the quantum effects and phantom matter on the AdS space is discussed. Different energy conditions in this type of universe are investigated and compared with those for the corresponding model in a de Sitter universe.

For the Poincaré gauge theory of gravity we consider the dynamical scalar torsion mode in a cosmological context. We explore in particular the possibility of using dynamical torsion to explain the current state of the accelerating Universe. With certain suitable sets of chosen parameters, this model can give a (qualitatively) proper description of the current universe without a cosmological constant, and the universe described is oscillating with a period of the Hubble time.

We study the f(T) theory as an extension of teleparallel gravity and consider the Noether symmetry of Kantowski–Sachs (KS) anisotropic model for this theory. We specify the explicit teleparallel form of f(T) and find the corresponding exact cosmological solutions under the assumption that the Lagrangian admits the Noether symmetry. It is found that the universe experiences a power law expansion for the scale factors in the context of f(T) theory. By deriving equation of state (EOS) parameter, we show that the universe passes through the phantom and $\mathrm{\Lambda }$CDM theoretical scenarios. In this way, we estimate a lower limit age for the universe in excellent agreement with the value reported from recent observations. When KS model reduces to the flat Friedmann–Robertson–Walker (FRW) metric, our results are properly transformed into the corresponding values.

We consider a homogeneous and isotropic Universe, described by the minisuperspace Lagrangian with the scale factor as a generalized coordinate. We show that the energy of a closed Universe is zero. We apply the uncertainty principle to this Lagrangian and propose that the quantum uncertainty of the scale factor causes the primordial fluctuations of the matter density. We use the dynamics of the early Universe in the Einstein–Cartan theory of gravity with spin and torsion, which eliminates the big-bang singularity and replaces it with a nonsingular bounce. Quantum particle production in highly curved spacetime generates a finite period of cosmic inflation that is consistent with the Planck satellite data. From the inflated primordial fluctuations we determine the magnitude of the temperature fluctuations in the cosmic microwave background, as a function of the numbers of the thermal degrees of freedom of elementary particles and the particle production coefficient which is the only unknown parameter.

Recently, some authors have generalized the idea of mimetic gravity to a Randall–Sundrum II braneworld model [L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999); L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)] and introduced Braneworld Mimetic Cosmology. In this paper, we extend their new cosmological model to brane–anti-brane systems and obtain the explicit form of potential which appeared in their action. This potential depends on the tachyonic fields, the separation distance between two branes and time. On the other hand, our universe is located on one of the branes and its evolution is controlled by the potential between two branes. By passing time and decreasing the separation distance between branes, more energy dissolves into branes and the universe expands. In the following, we presented the physical applications such as late time accelerating phase, inflation model and behavior of perturbations, with respect to brane–anti-brane system. Finally, we briefly discussed the moduli stabilization of the model.

The present paper is a polemic which describes how Inflation came on the scene and suggests a possible alternative.

We find a physical state of a closed universe with the minimal excitation of the universe expansion energy in quantum gravity. It is an analog of the vacuum state of the ordinary quantum field theory in the Minkowsky space, but in our approach an energy of space of a closed universe together with the energy of its matter content are minimized. This ground state is chosen among an enlarged set of physical states, compared with the ordinary covariant quantum gravity. In our approach, physical states are determined by weak constraints: quantum mechanical averages of gravitational constraint operators equal zero. As a result, they appear to be non-static in such a modification of quantum gravity. Quantum dynamics of the universe is described by Schrödinger equation with a cosmic time determined by weak gravitational constraints. In order to obtain the observed megascopic universe with the inflation stage just after its quantum beginning, a lot of the energy in the form of the inflaton scalar field condensate is prescribed to the initial state. Parameters of the initial state for a homogeneous model of the universe are calculated.

The conditional principle of extremum in quantum cosmology is formulated for a positive functional of the energy density of space, in which gravitational constraints serve as additional conditions. The extremum conditions determine the discrete spectrum of the “stationary” state of the universe with the corresponding values of the energy density of space. A dynamic interpretation of solutions is proposed, in which the quantum number of the energy density plays the role of cosmic time. In the self-consistent harmonic approximation, the quantum dynamics of the anisotropic model of the Bianchi IX universe is considered.

Perturbative and nonperturbative terms of the cross-sections of ultraperipheral production of lepton pairs in ion collisions are taken into account. It is shown that production of low-mass $e^{+}{e}^{-}$ pairs is strongly enhanced (compared to perturbative estimates) due to the nonperturbative Sommerfeld–Gamow–Sakharov (SGS) factor. Coulomb attraction of the nonrelativistic components of those pairs leads to the finite value of their mass distribution at lowest masses. Their annihilation can result in an increased intensity of 511 keV photons. It can be recorded at the NICA collider and is especially crucial in astrophysical implications regarding the 511 keV line emitted from the Galactic center. The analogous effect can be observed in lepton pairs production at LHC. Energy spectra of lepton pairs created in ultraperipheral nuclear collisions and their transverse momenta are calculated.

The Einstein–Maxwell-dilaton field equations are considered for four-dimensional Bianchi type-V and VI₀ models. The general solutions are obtained and their properties are discussed.

By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time) that requires not only a universally constant invariant velocity but also an invariant length given by its constant curvature, Λ and spacetime is completely free of dynamics. Thus c and Λ are the only two true constants of the spacetime structure and no other physical constant could claim this degree of fundamentalness. When matter is introduced, the spacetime becomes inhomogeneous and dynamic, and its curvature then determines by the Bianchi differential identity, the equation of motion for the Einstein gravity. The homogeneity thus demands that the natural state of free spacetime is of constant curvature and the cosmological constant thus emerges as a clear prediction which seems to be borne out by the observations of accelerating expansion of the Universe. However it has no relation to the vacuum energy and it could be envisioned that in terms of the Planck area, the Universe measures 10¹²⁰ units!

The cosmological consequences of a slow-rolling scalar field with constant kinetic term in analogy to the vertical movement of a skydiver after reaching terminal velocity are investigated. In this approach, the scalar field potential is given by a quadratic function of the field. This model provides solutions in which the universe was dominated in the past by a mixture of baryons and dark matter, is currently accelerating (as indicated by type Ia supernovae data), but will be followed by a contraction phase. The theoretical predictions of this model are consistent with current observations, therefore, a terminal scalar field is a viable candidate to dark energy.

We study a classical, noncommutative (NC), Friedmann–Robertson–Walker (FRW) cosmological model. The spatial sections may have positive, negative or zero constant curvatures. The matter content is a generic perfect fluid. The initial noncommutativity between some canonical variables is rewritten, such that, we end up with commutative variables and a NC parameter. Initially, we derive the scale factor dynamic equations for the general situation, without specifying the perfect fluid or the curvature of the spatial sections. Next, we consider two concrete situations: a radiation perfect fluid and dust. We study all possible scale factor behaviors, for both cases. We compare them with the corresponding commutative cases and one with the other. We obtain, some cases, where the NC model predicts a scale factor expansion which may describe the present expansion of our universe. Those cases are not present in the corresponding commutative models. Finally, we compare our model with another NC model, where the noncommutativity is between different canonical variables. We show that, in general, it leads to a scale factor behavior that is different from our model.

In this paper, we discuss a cosmological model for a universe with self-regulating features. We set up the theoretical framework for the model and determine the time evolution of the scale-factor $a(t)$. It is shown that such a universe repeatedly goes through alternate periods of matter and dark energy domination. The resulting dynamics oscillates about the would-be ideal time-linear or coasting path, with monotonic expansion. When compared to dynamics of the observed physical universe, the model recovers the observationally established evolutionary features of the latter, from the big bang to the current acceleration, and farther. It suggests a universe that initially emerges from a nonsingular state, associated with a non-exponential acceleration, and which acceleration it exits naturally with matter–energy generation. The model does not have a horizon problem or a flatness problem. It reproduces the observed current values of standard cosmic parameters, including the age $t_0$, the current Hubble parameter $H_0$ and dark energy ${\mathrm{\Omega }}_{\mathrm{\text{de}}}$ and matter ${\mathrm{\Omega }}_m$ density parameters. The model is falsifiable. It makes predictions that can be tested, as suggested. Finally, we discuss the dimensionless age $(H_0{t}_0\simeq 1)$ paradox as an example of the model’s ability to address standing puzzles. The findings suggest that dynamics of the physical universe may be self-regulating and predictable.

In this paper, the formation of cylindrical wormhole during evolution of manifolds is studied. It is shown that this type of wormholes may be produced at two stages and then disappeared very fast at the third stage. First, one $N$-dimensional is formed by joining point-like manifolds. Then, this manifold is torn and two child manifolds plus one Chern–Simons manifold appeared. Our universe is born on one of the child manifolds and connected to the other one by Chern–Simons manifold. At the third stage, this Chern–Simons manifold-which plays the role of cylindrical wormhole, dissolves into universes and gives its energy to them and causes inflation. Thus, the Chern–Simons cylindrical wormhole is unstable and dissolves in our four-dimensional universes and another universe very fast.

Recently, the role of energy conditions in $f(R)$-cosmology has been investigated. We generalize these results to BIonic systems in accelerating systems and show that the energy conditions can be changed in this system. We show that $f(R)$-gravity produces a wormhole between two universes and forms a BIonic system. On the other hand, the acceleration creates two regions in the Rindler space-time which BIon in each region acts reverse to other in another region. This means that by the expansion of universes of the BIon in one region, universes of another BIon in other regions contract. Also, in this model, by increasing the order of curvatures in $f(R)$-gravity, the energy and the entropy of system in one region increases and in other region decreases. Amount of this growth or decrease in the energy depends on the acceleration of universes. Finally, by calculating the dark energy equation of state, we observe that one universe enters to phantom phase and goes toward the big rip singularity and another goes out of phantom state.

This article discusses cosmology, bimetric gravity and their possible interplay.

I report the results from the first comparison of the genuine one-way speed of light in two directions relative to an inertially moving observer. An anisotropy that is first order in v/c is detected. The implications of the result and its relation to clock comparison experiments are discussed.

After a brief review of some results pertaining to the equivalence principle in the context of gravity and quantum mechanics, I discuss the important relation between the equivalence principle and the matter filled universe. I show that the universality of free fall is surprisingly robust in this context even if the gravitational constant is material dependent.