Emergent cosmological constant from colliding electromagnetic waves

Abstract

In this study we advocate the view that the cosmological constant is of electromagnetic (em) origin, which can be generated from the collision of em shock waves coupled with gravitational shock waves. The wave profiles that participate in the collision have different amplitudes. It is shown that, circular polarization with equal amplitude waves does not generate cosmological constant. We also prove that the generation of the cosmological constant is related to the linear polarization. The addition of cross polarization generates no cosmological constant. Depending on the value of the wave amplitudes, the generated cosmological constant can be positive or negative. We show additionally that, the collision of nonlinear em waves in a particular class of Born-Infeld theory also yields a cosmological constant.

Colliding waves in a model of nonlinear electrodynamics

“…It is observed from (41) and (45) that for B 0 < 1/B 0 > 1 we have Λ > 0/Λ < 0, so that B 0 = 1, i.e., the linear Maxwell limit acts as a turning point in the sign of Λ. Our result is in agreement with the previous works [10,11], in which the emergent Λ was proportional to the product of amplitudes of colliding waves. Here our amplitudes are same (∼ B 0 ) so that Λ ∼ B 2 0 .…”

“…From physics stand point this is not an unexpected result since in the Lagrangian (2) the scale invariance, i.e., the symmetry under x µ → λx µ , A µ → 1 λ A µ , (for λ =constant) is broken, and as a result null currents arise. We may comment that the emergent currents at the boundaries (u = v = 0) is the price paid against production of the cosmological constant [9][10][11]. Let us add that since our incoming waves are both linearly polarized in the direction of x and the resulting wave after collision has the same polarization we don't expect the phenomenon of birefringence.…”

“…To see birefringence one must change the polarization directions of the incoming waves to be different, which may be the subject of a separate study. The emergence of both J on the null boundaries and Λ for (u > 0, v > 0) may be interpreted as a redistribution of the overall energy, or distortion of the vacuum [10,11]. Finally it is needless to state that since our spacetime is still BS, the null singularities of the Weyl tensor remain intact.…”

Some constraints for the extensions of the degenerate Ferrari and Ibanez solution

“…ψ 1 (t, p (1) )= p M κ1 e −p (1) e ip (1) t (28) ψ 2 (t, p (2) )= p Mκ1 e −p (2) e ip (2) t (29) 3) e ip (3) t (30) ... These wave function are orthogonal in time evolution.…”

“…The theme of colliding plane waves (CPWs) in general relativity has established one of the important topics that the effects of the nonlinearity of the Einsteins equations manifest itself explicitly. The work of CPWs is not only to find out exact solutions of CPWs but also make corresponding predictions, such as focusing effect and the emergence of cosmology constant [1]. In 1971, Khan, Penrose [2] have proved that the collision of two impulsive gravitational plane waves produces curvature; In 1974, Bell and Szekeres [3] have found out a solution of interacting electromagnetic shock waves which have no curvature singularities.…”