We study the value of cosmological constant in de Sitter brane embedded in five dimensions with positive, vanishing and negative bulk cosmological constant. In the case of negative bulk cosmological constant, we show that not zero but tiny four-dimensional cosmological constant can be realized by tiny deviation from bulk curvature of the Randall-Sundrum model. ∗E-mail address: [email protected]...

Unimodular relativity is a theory of gravity and space–time with a fixed absolute space–time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an arbitrary fixed measure can be imposed as a gauge condition, while in unimodular relativity it is determined by the events in the volume. Since this seems t...

A dynamical theory is studied in which a scalar field φ in Einstein-Minkowski space is coupled to the four-velocity Nμ of a preferred inertial observer in that space. As a consistent requirement on this coupling we study a principle of duality invariance of the dynamical mass-term of φ at some universal length in the smalldistance regime. In the large-distance regime duality breaking can be int...

Some issues of the cosmological constant or dark energy are briefly reviewed. There are an increasing number of observations that constrain the equation of state of dark energy more stringently and favor the time-independent cosmological constant. Then a plausible model of dark energy would be a theory with degenerate perturbative vacua in which its origin is explained by a nonperturbative effe...

The idea of quintessence originates from an attempt to understand the smallness of the “cosmological constant” or dark energy in terms of the large age of the universe [1]. As a characteristic consequence, the amount of dark energy may be of the same order of magnitude as radiation or dark matter during a long period of the cosmological history, including the present epoch. Today, the inhomogen...

To describe a massive graviton in 4D Minkowski space-time one introduces a quadratic term in the Lagrangian. This term, however, can lead to a readjustment or instability of the background instead of describing a massive graviton on flat space. We show that for all local Lorentz-invariant mass terms Minkowski space is unstable. We start with the Pauli-Fierz (PF) term that is the only local mass...