The idea that the vacuum energy density $rho_{Lambda}$ could be time dependent is a most reasonable one in the expanding Universe; in fact, much more reasonable than just a rigid cosmological constant for the entire cosmic history. Being $rho_{Lambda
}=rho_{Lambda}(t)$ dynamical, it offers a possibility to tackle the cosmological constant problem in its various facets. Furthermore, for a long time (most prominently since Diracs first proposal on a time variable gravitational coupling) the possibility that the fundamental constants of Nature are slowly drifting with the cosmic expansion has been continuously investigated. In the last two decades, and specially in recent times, mounting experimental evidence attests that this could be the case. In this paper, we consider the possibility that these two groups of facts might be intimately connected, namely that the observed acceleration of the Universe and the possible time variation of the fundamental constants are two manifestations of the same underlying dynamics. We call it: the micro and macro connection, and on its basis we expect that the cosmological term in Einsteins equations, Newtons coupling and the masses of all the particles in the Universe, both the dark matter particles and the ordinary baryons and leptons, should all drift with the cosmic expansion. Here we discuss specific cosmological models realizing such possibility in a way that preserves the principle of covariance of General Relativity.
In an expanding universe the vacuum energy density rho_{Lambda} is expected to be a dynamical quantity. In quantum field theory in curved space-time rho_{Lambda} should exhibit a slow evolution, determined by the expansion rate of the universe H. Rec
ent measurements on the time variation of the fine structure constant and of the proton-electron mass ratio suggest that basic quantities of the Standard Model, such as the QCD scale parameter Lambda_{QCD}, may not be conserved in the course of the cosmological evolution. The masses of the nucleons m_N and of the atomic nuclei would also be affected. Matter is not conserved in such a universe. These measurements can be interpreted as a leakage of matter into vacuum or vice versa. We point out that the amount of leakage necessary to explain the measured value of dot{m}_N/m_N could be of the same order of magnitude as the observationally allowed value of dot{rho}_{Lambda}/rho_{Lambda}, with a possible contribution from the dark matter particles. The dark energy in our universe could be the dynamical vacuum energy in interaction with ordinary baryonic matter as well as with dark matter.
Inclusive Higgs boson pair production through the mechanism of gauge boson fusion e^{+} e^{-} -> V* V* -> h h + X (V=W,Z) in the general Two-Higgs-Doublet Model (2HDM), with h=h^0,H^0,A^0,H^{pm}, is analyzed at order alpha^4_{ew} in the linear collid
ers ILC and CLIC. This kind of processes is highly sensitive to the trilinear Higgs (3H) boson self-interactions and hence can be a true keystone in the reconstruction of the Higgs potential. For example, in the ILC at 1 TeV, the most favorable scenarios yield cross-sections up to roughly 1 pb, thus entailing 10^5 events per 100 fb^{-1} of integrated luminosity, whilst remaining fully consistent with the perturbativity and unitarity bounds on the 3H couplings, the electroweak precision data and the constraints from BR(b->sgamma). Comparing with other competing mechanisms, we conclude that the Higgs boson-pair events could be the dominant signature for Higgs-boson production in the TeV-class linear colliders for a wide region of the 2HDM parameter space, with no counterpart in the Minimal Supersymmetric Standard Model. Owing to the extremely clean environment of these colliders, inclusive 2H events should allow a comfortable tagging and might therefore open privileged new vistas into the structure of the Higgs potential.
