CPTM symmetry, closed time paths and cosmological constant problem in the formalism of extended manifold

Abstract

The problem of the cosmological constant is considered in the formalism of an extended space-time consisting of the extended classical solution of Einstein equations. The different regions of the extended manifold are proposed to be related by the charge, parity, time and mass (CPTM) reversal symmetry applied with respect to the metric fields of the manifolds. There are interactions between the points of the extended manifold provided by scalar fields present separately in the different patches of the extended solution. The value of the constant is obtained equal to zero at the classical level due the mutual contribution of the fields in the vacuum energy, it’s non-zero value is due the quantum interactions between the fields. There are few possible scenario for the actions of the fields are discussed. Each from the obtained variants is similar to the closed time path approach of non-equilibrium condensed matter physics and among these possibilities for the closed paths, there is a variant of the action equivalent to the formalism of Keldysh. Accordingly, we consider and shortly discuss the application of the proposed formalism to the problem of smallness of the cosmological constant and singularities problem.

Spinor fields, CPTM symmetry and smallness of cosmological constant in framework of extended manifold

“…similarly to scalar field results obtained in [2,3], an additional minus here is due the Eq. ( 15) commutation relations.…”

“…Assuming the cancellation of the large one-loop contributions, therefore, to the leading order the constant is proportional to the trace of the energy-momentum tensor if gravity fields are different, or to the difference of A and B tensors traces if we operate with the same gravity field. In the later case we have two possibilities: it can be precisely zero if the values of the different spinor fields are the same at the same value of their arguments or it can be non-zero value if the values are different, see discussion in [3]. In the case of the first possibility, the value of the constant is suppressed even more in comparison to the represented result.…”

“…The present article is devoted to an exploration of a model intended to explain the smallness of the cosmological constant and, at the same time, the absence of unwanted contributions from the one-loop effective action of spinor field. The framework is based on an application of the CPTM discrete symmetry, introduced in [1][2][3], to fermion fields. As an additional result, it is also demonstrated that dark matter appears in the approach in the form of a modified graviton propagator inevitably, the propagator's modification appears due to the second portion of the matter introduced in the form of B-spinors.…”

The Grand Canonical Multiverse and the Small Cosmological Constant

“…As is well known from statistical physics, tracing over one of two systems is enough for the untraced system to behave as a thermal system. This opens up interpreting our Universe as coupled to other universes in other ways such as Braneworld scenarios, globally or locally interacting, for example [16][17][18][19][20]40]. It would be interesting to try and work out such a model, and test our analysis.…”

Spinor fields, CPTM symmetry and smallness of cosmological constant in framework of extended manifold

“…In the present paper we continue an investigation of the model of an extended manifold introduced in [1][2][3]. There we discussed a model of manifold which consists two, at least, parts related by the classical symmetry which reverse charge, parity, time and mass (CPTM symmetry) preserving a form of the metric g at the case of the zero cosmological constant: q → − q , r → −r , t → − t , m grav → − mgrav ; q , r , t , mgrav > 0 ;…”