Cosmic gravitational background waves in the scenario of a deformed relativity with an invariant minimum speed

We show the need of the emergence of an invariant minimum speed in the space–time. So, we propose a deformed special relativity with two limits of speed so-called Symmetrical Special Relativity (SSR). It presents a universal minimum speed V that plays the role of a preferred reference frame [Formula: see text] associated with vacuum. This new paradigm of space–time allows us to understand the origin of the cosmological constant [Formula: see text] starting from first principles given by a new kinematic invariance at low energies, which leads us to build a space–time metric with the presence of a minimum speed, so that such metric is equivalent to a de Sitter metric. In order to do that, we use a model of spherical universe with Hubble radius [Formula: see text] filled by a low vacuum energy density [Formula: see text] that governs the accelerated expansion of the universe with negative pressure shown by the equation of state (EOS) of vacuum given by SSR-theory ([Formula: see text]). Thus, we realize that such spherical universe made up of dark energy works like a black body with adiabatic expansion thermalized with a kind of dark gas that plays the role of the dark energy. From this model of virtual particles of dark gas that fills the sphere with dark energy, we are able to derive the law of universal gravitation, allowing us to understand the cosmological anti-gravity according to the EOS of vacuum in the space–time with a minimum speed. So, we estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this model, as the dark universe can be thought of as a black body with Hubble radius, we obtain its power and frequency of emission of radiation for a low temperature. We conclude that such radiation is a gravitational wave with an extremely low frequency and power due to the slight stretching of the fabric of space–time, since [Formula: see text] is very small.