M. Heyl’s research while affiliated with German Aerospace Center (DLR) and other places

Context. The pressure equilibrium between the inner heliosheath and the outer heliosheath (referred to as the local interstellar medium) is an eminent theoretical and practical problem; theoretical, because the relevant pressure carriers have to be identified, and practical, because data must be gathered in order to confirm such a pressure equilibrium. The problem is closely connected with the stability of the heliopause, that is, of the tangential discontinuity between these two counterflowing media, and is of utmost importance for understanding the stability of the whole circumsolar plasma structure. Aims. In this paper we analyze the thermodynamic conditions of the multi-fluid plasma between the solar wind termination shock and the heliopause determining the total heliosheath pressure. We look into this problem from a theoretical standpoint and revisit theoretical descriptions of the solar wind plasma after its passage over the solar wind termination shock, thereafter forming the subsonic heliosheath region. Methods. Hereby we take into account the 3D magnetohydrodynamics shock conditions and the resulting 3D temperature structure of the downstream plasma flow. We use a kind of seismological procedure to probe the heliosheath plasma by inquiring into the propagation conditions of traveling shock wave perturbations in this predetermined 3D heliosheath plasma structure. We discuss the fact that the front geometry of such a traveling shock wave most probably does not remain spherical, if it was to begin with, due to asymmetric shock propagation conditions. In contrast, the wave front is likely to become strongly deformed into an upwind bulge. Results. Concerning the plasma pressure, in addition to solar wind and pick-up proton pressures, we have to take into account the solar wind electron pressure which as a surprise turns out to be of comparable magnitude. As a consequence, the characteristic propagation speed of the traveling shock wave in the weakly magnetized heliosheath plasma is given as a mixed speed expressed by the sound speeds of the protons and the electrons. We describe local low-energy proton density signatures that can be found in Voyager-2 proton data as a consequence of traveling shock wave passages and show that the total local plasma pressure can be directly derived from them.

In typical plasma physics scenarios, when treated on kinetic levels, distribution functions with suprathermal wings are obtained. This raises the question of how the associated typical velocity moments, which are needed to arrive at magnetohydrodynamic plasma descriptions, may appear. It has become evident that the higher velocity moments in particular, for example the pressure or heat transport, which are constructed as integrations of the distribution function, contain unphysical contributions from particles with velocities greater than the velocity of light. In what follows, we discuss two possibilities to overcome this problem. One is to calculate a maximal, physically permitted, upper velocity, which can be realized in view of the underlying energization processes, and to stop the integration there. The other is to modify the distribution function relativistically so that no particles with superluminal (v ≥ c) velocities appear. On the basis of a typical collision-free plasma scenario, like the plasma in the heliosheath, we obtain the corresponding expressions for electron and proton pressures and can show that in both cases the pressures are reduced compared with their classical values; however, electrons experience a stronger reduction than protons. When calculating pressure ratios, it turns out that these are of the same order of magnitude regardless of which of the two methods is used. The electron, as the low-mass particle, undergoes the more pronounced pressure reduction. It may turn out that electrons and protons constitute about equal pressures in the heliosheath, implying that no pressure deficit need be claimed here.

In the more recent literature on cosmological evolutions of the universe the cosmic vacuum energy has become a non-renouncable ingredient. The cosmological constant $\Lambda$, first invented by Einstein, but later also rejected by him, presently experiences an astonishing revival. Interestingly enough it acts, like a constant vacuum energy density would also do. Namely, it has an accelerating action on cosmic dynamics without which, as it appears, presently obtained cosmological data cannot be conciliated with theory. As we are going to show in this review, however, the concept of a constant vacuum energy density is unsatisfactory for very basic reasons, since it would claim for a physical reality that acts upon spacetime and matter dynamics without itself being acted upon by spacetime or matter.

According to present cosmological views the energy density of CMB (Cosmic Microwave Background) photons, freely propagating through the expanding cosmos, varies proportional to 1/S^4 with S being the scale factor of the universe. This behavior is expected, because General Theory of Relativity, in application to FLRW- (Friedmann-Lemaitre-Robertson-Walker) cosmological universes, leads to the conclusion that the photon wavelengths increase during their free passage through the spacetime metrics of the universe by the same factor as does the scale factor S. This appears to be a reasonable explanation for the presently observed Planckian CMB spectrum with its actual temperature of about 2.7 K, while at the time of its origin after the last scattering during the recombination phase its temperature should have been about 3000 K, at an epoch of about 380 ky after the Big Bang, when the scale of the universe S_r was smaller by roughly a factor of S/S_r = 1+z_r = 1100 compared to the present scale S = S_0 of the universe. In this paper we start from putting the question whether the scale-behavior of the CMB energy density that enters the energy-momentum tensor of the field equations describing the expanding universe is really falling off like 1/S^4 and, if in fact a deviation from a behavior according to 1/S^4 would occur, why do we nevertheless presently observe a CMB energy density which appears to be in accordance with such a 1/S^4-scaling? This question arises from another basic and fundamental question, namely: Can we really assume that the wavelength of the freely propagating photon during its travel all the way along its light geodetic is permanently affected by the expansion of the universe, i.e continuously recognizes the expansion of the cosmic scale S? With other words: Do freely propagating photons ........