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Abstract Cosmological solutions are studied in the context of the modified measure formulation of string theory , then the string tension is a dynamical variable and the string the tension is an additional dynamical degree of freedom and its value is dynamically generated. These tensions are then not universal, rather each string generates its own tension which can have a different value for each of the string world sheets and in an ensemble of strings. The values of the tensions can have a certain dispersion in the ensemble. We consider a new background field that can couple to these strings, the “tension scalar” which is capable of changing locally along the world sheet and then the value of the tension of the string changes accordingly. When many types of strings probing the same region of space are considered this tension scalar is constrained by the requirement of quantum conformal invariance. For the case of two types of strings probing the same region of space with different dynamically generated tensions, there are two different metrics, associated to the different strings. Each of these metrics have to satisfy vacuum Einstein’s equations and the consistency of these two Einstein’s equations determine the tension scalar. The universal metric, common to both strings generically does not satisfy Einstein’s equation . The two string dependent metrics considered here are flat space in Minkowski space and Minkowski space after a special conformal transformation. The limit where the two string tensions are the same is studied, it leads to a well defined solution. If the string tension difference between the two types of strings is very small but finite, the approximately homogeneous and isotropic cosmological solution lasts for a long time, inversely proportional to the string tension difference and then the homogeneity and and isotropy of the cosmological disappears and the solution turns into an expanding braneworld where the strings are confined between two expanding bubbles separated by a very small distance at large times. The same principle is applied to the static end of the universe wall solution that lasts a time inversely proportional to the dispersion of string tensions. This suggest a scenario where quantum fluctuations of the cosmological or static solutions induce the evolution towards braneworld scenarios and decoherence between the different string tension states.

Abstract There is great interest in the construction of brane worlds, where matter and gravity are forced to be effective only in a lower dimensional surface, the brane . How these could appear as a consequence of string theory is a crucial question and this has been widely discussed. Here we will examine a distinct scenario that appears in dynamical tension theories and where string tension is positive between two surfaces separated by a short distance and at the two surfaces themselves the string tensions become infinite, therefore producing an effective confinement of the strings and therefore of all matter and gravity to the space between these to surfaces, which is in fact a new type of stringy brane world scenario. The basic formulation for obtaining this scenario consist of assuming two types of strings characterized by a different constant of integration related to the spontaneous string tension generation. These string tension multiplied by the embedding metric define conformally related metrics that both satisfy Einsteins equation. The braneworlds appear very naturally when these two metrics are both flat spaces related by a special conformal transformation. The two types of string tensions are determined and they blow up at two close expanding surfaces. A puzzling aspect appears then: the construction is based on flat spaces, but then there are also strings with very large tension near the boundaries of the braneworld,so can the back reaction from the infinite tension strings destroy the flat space background? Fortunatelly that can be resolved using the mechanism Universe creation from almost flat (or empty) spaces, which incorporates a gas of very large string tensions in a membrane, studied before in 1+1 membranes in a 2+1 embedding space and now is generalized for a 1+(D-2) membrane moving in a 1+(D-1) space.

Abstract An extension to the Einstein–Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, represented by a time-like axial vector $$S^\mu $$ S μ . The dynamics of torsion is invoked by a novel kinetic term. Here we show that this kinetic term gives rise to dark energy, while the quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing cosmology solution. A constraint on the bouncing solution is calculated using cosmological data from different epochs.

Abstract There is great interest in the construction of brane worlds, where matter and gravity are forced to be effective only in a lower dimensional surface, the brane . How these could appear as a consequence of string theory is a crucial question and this has been widely discussed. Here we will examine a distinct scenario that appears in dynamical string tension theories and where string tension is positive between two surfaces separated by a short distance and at the two surfaces themselves the string tensions become infinite, therefore producing an effective confinement of the strings and therefore of all matter and gravity to the space between these to surfaces, which is in fact a new type of stringy brane world scenario. The specific model studied is in the context of the modified measure formulation the string where tension appear as an additional dynamical degree of freedom and these tensions are not universal, but rather each string generates its own tension, which can have a different value for each string. We consider a new background field that can couple to these strings, the tension scalar is capable then of changing locally along the world sheet and then the value of the tension of the extended object changes accordingly. When many types of strings probing the same region of space are considered this tension scalar is constrained by the requirement of quantum conformal invariance. For the case of two types of strings probing the same region of space with different dynamically generated tensions, there are two different metrics, associated to the different strings, that have to satisfy vacuum Einsteins equations and the consistency of these two Einsteins equations determine the tension scalar. The universal metric, common to both strings generically does not satisfy Einsteins equation . The two metrics considered here are flat space in Minkowshi space and flat space after a special conformal transformation and the tension field behaves in such a way that strings are confined inside a light like Segment or alternatively as expanding Braneworlds where the strings are confined between two expanding bubbles separated by a very small distance at large times.

Abstract From the assumption that the slow-roll parameter $$\varepsilon $$ ε has a Lorentzian form as a function of the e-fold number N, a successful model of a quintessential inflation is obtained, as succinctly studied in [1]. The form corresponds to the vacuum energy both in the inflationary and in the dark-energy epochs and satisfies the condition to climb from small values of $$\varepsilon $$ ε to 1 at the end of the inflationary epoch. We find the corresponding scalar quintessential inflationary potential with two flat regions. Moreover, a reheating mechanism is suggested with numerical estimation for the homogeneous evolution of the universe. The suggested mechanism is consistent with the BBN bound.

Abstract We propose a simple modified gravity model without any initial matter fields in terms of several alternative non-Riemannian spacetime volume elements within the metric (second order) formalism. We show how the non-Riemannian volume-elements, when passing to the physical Einstein frame, create a canonical scalar field and produce dynamically a non-trivial inflationary-type potential for the latter with a large flat region and a stable low-lying minimum. We study the evolution of the cosmological solutions from the point of view of theory of dynamical systems. The theory predicts the spectral index $$n_s \approx 0.96$$ ns≈0.96 and the tensor-to-scalar ratio $$r \approx 0.002$$ r≈0.002 for 60 e-folds, which is in accordance with the observational data. In the future Euclid and SPHEREx missions or the BICEP3 experiment are expected to provide experimental evidence to test those predictions.

Abstract Here we generalize ideas of unified dark matter–dark energy in the context of two measure theories and of dynamical space time theories. In two measure theories one uses metric independent volume elements and this allows one to construct unified dark matter–dark energy, where the cosmological constant appears as an integration constant associated with the equation of motion of the measure fields. The dynamical space-time theories generalize the two measure theories by introducing a vector field whose equation of motion guarantees the conservation of a certain Energy Momentum tensor, which may be related, but in general is not the same as the gravitational Energy Momentum tensor. We propose two formulations of this idea: (I) by demanding that this vector field be the gradient of a scalar, (II) by considering the dynamical space field appearing in another part of the action. Then the dynamical space time theory becomes a theory of Diffusive Unified dark energy and dark matter. These generalizations produce non-conserved energy momentum tensors instead of conserved energy momentum tensors which leads at the end to a formulation of interacting DE–DM dust models in the form of a diffusive type interacting Unified dark energy and dark matter scenario. We solved analytically the theories for perturbative solution and asymptotic solution, and we show that the $$\Lambda $$ Λ CDM is a fixed point of these theories at large times. Also a preliminary argument as regards the good behavior of the theory at the quantum level is proposed for both theories.

The main conclusion of long-standing discussions concerning the role of solutions with degenerate metric (g [?] det(gmn) = 0 and even with gmn = 0) was that in the first-order formalism they are physically acceptable and must be included in the path integral. In particular, they may describe topology changes and reduction of the ''metrical dimension'' of spacetime. The latter implies disappearance of the volume element \sqrt{-g}d^4x of a 4D spacetime in a neighborhood of the point with g = 0. We pay attention to the fact that besides \sqrt{-g} , the 4D spacetime differentiable manifold also possesses a ''manifold volume measure'' (MVM) described by a 4-form which is sign indefinite and generically independent of the metric. The first-order formalism proceeds with an originally independent connection and metric structures of the spacetime manifold. In this paper we bring up the question of whether the first-order formalism should be supplemented with degrees of freedom of the spacetime differentiable manifold itself, e.g. by means of the MVM. It turns out that adding the MVM degrees of freedom to the action principle in the first-order formalism one can realize very interesting dynamics. Such a two measures field theory (TMT) enables radically new approaches to the resolution of the cosmological constant problem. We show that fine tuning free solutions describing a transition to the L = 0 state involve oscillations of gmn and MVM around zero. The latter can be treated as a dynamics involving changes of orientation of the spacetime manifold. As we have shown earlier, in realistic scale invariant models (SIM), solutions formulated in the Einstein frame satisfy all existing tests of general relativity (GR). Here we reveal surprisingly that in SIM, all ground-state solutions with L [?] 0 appear to be degenerate either in g00 or in MVM. Sign indefiniteness of MVM in a natural way yields a dynamical realization of a phantom cosmology (w < [?]1). It is very important that for all solutions, the metric tensor rewritten in the Einstein frame has regularity properties exactly as in GR. We discuss new physical effects which arise from this theory and in particular the strong gravity effect in high energy physics experiments. [ABSTRACT FROM AUTHOR]

Generally accepted explanation of the observed accelerated expansion of the present day universe is based on the idea of the existence of a new entity called dark energy. Resolution of the 'cosmic coincidence' problem implies that dark energy and dark matter follow the same scaling solution during a significant period of evolution. This becomes possible only if there exists a coupling of the dark energy (modeled by a light scalar field) to dark matter. This conclusion following from the observed cosmological data serves for an additional evidence of well-known theoretical predictions of a light scalar coupled to matter. However, according to the results of the fifth force experiments, a similar coupling of the light scalar field to visible (baryonic) matter is strongly suppressed. After a brief review of some models intended for resolution of this 'fifth force problem', we present a model with spontaneously broken scale invariance where the strength of the dilaton-to-matter coupling appears to be dependent on the matter density. This is realized without any special assumptions in the underlying action intended for obtaining such a dependence. As a result the dilaton-to-matter coupling constant measured under conditions of all known fifth force experiments turns out automatically (without any sort of fine tuning) to be so small that, at least in the near future, experiments will not be able to reveal it. On the other hand, if the matter is very diluted (such as galaxy halo dark matter) then its coupling to the dilaton may not be weak. However, the latter situation is realized under conditions not compatible with the design of the fifth force experiments. [ABSTRACT FROM AUTHOR]