# A variable metric universe model

The idea that a mass is the source of a basic field $$\Xi$$ of the universe is introduced. It is called Space-Time Field because it builds both the Space-Time and the particles in it, using an original formulation of quantum oscillator (IQuO). This field is fed with energy flowing from a background (Θ) having the structure of no-field because it is composed by no-coupled IQuO. Note that the mass creation has a double consequence: gravity increase (curvature) and space increase (expansion). This allows to formulate a universe model with a variable metric (open in the past, flat in the present and closed in the future) and to explain some fundamental aspects of the universe: the Hubble’s law by creating the mass-space, the acceleration of galaxies as effect of a pressure of increasing Space-Mass $$\Lambda$$, the age of the universe as time needed to reach the flat metric phase.

# Introduction

In modern cosmology the expansion of space-time and its zero curvature are not derived from any fundamental principle of physics, but they are deﬁned as empirical properties of space and time in the universe.
In this study we will try to prove that the two physical realities are at­tributable to a single source in which particles and space-time (ST) are closely related. Then we formulate the hypothesis of the existence of a fundamental field on which the universe, deﬁned like a space-time with fields-particles, is built. In order to support this idea we begin (\ref{spacetimefield}) highlighting the strong connection between the fields-particles and empirical concepts of space and time, defined in any reference system, which induces us to use it as a field-object.
Some physical aspects as:

• the invariance of the light speed $$c$$, which value is set as a constant of structure for the spacetime;

• the relevant role of massive objects building a reference systems and defining their curvature;

• the universe expansion like stretching of a object-space;

lead us to conjecture the existence of a ST-Field.
As a first step for better the hypothesis of ST field we must introduce (\ref{iquo}) a new idea of quantum oscillator: the Intrinsic Quantum Oscillator (IQuO), composed by two sub-oscillators each endowed of two half-quanta.
One builds thus a scalar field $$\Xi$$ made by lattice of 1-dim. chains of IQuO reciprocally couplings.
Besides, the structure of an IQuO in vacuum eigenstate (one sub-oscillator with vacuum energy), leads us to admit the existence of a quantum vacuum that it is different than the standard vacuum: a set of IQuO elastically uncoupled without the structure of a field. We define this system ad quantum vacuum of no-field, and called it $$\Theta$$.
In (\ref{massive}), following the general relativity, where the mass takes the role of agent characteristic (gravitational charge, $$\Gamma$$), and considering the hypothesis of a connatural structure between agent (massive particles) and gravitational field, we can derive that the mass of a particle must be expressed by fundamental property of the ST field-object $$\Xi$$.
Then we conjecture that the mass is given by a particular transversal additional coupling (called massive coupling) between the oscillator chains of the field $$\Xi^0$$.
This additional coupling builds a field with lattice structure $$\Xi$$ where is given a time step and a space step, and which gives empirical sense to reference frame associated with a massive particle with Compton wave length $$\lambda_c$$.
In this way, the mass becomes an essential property to deﬁne the spacetime in the universe, which we will deﬁne (\ref{cosmos}) as Universe Space Time Field, where each particle could be identiﬁed by a distinct and articu­lated structure of the IQuOs of the field.
We denote by $$\Xi_U$$ the USTF having as components the base fields ($$\Xi^0_i, \Xi_i$$).
Moreover it becomes possible to assign to a set of identical massive particles, with mass $$m_i$$, a ﬁeld with a lattice structure which we will call lattice-Uni­verse, denoted by $$U_i$$. The universe $$U$$ will thus be expressed as a set of lattices $$U_i$$ associated to the respective basic massive particles $$m_i$$.
In (\ref{cosmos}) we underline the equivalence between the relativities and cosmological principles. Combining these hypothesis we obtain a universe in which the apparent relative motion of each reference system must be radial compared to any observator (isotropy) and this is compatible with an expansion or a future contraction of the universe. The fact that we are in a phase of expansion and not of contraction could not be derived from the relativities principles, but from a particular condition of the physical state of the universe that derives from a property of the spacetime field.
Because the space implies the existence of a space step, $$\lambda_C$$, it follows that the expansion is amenable to the mass, and in the same way the flow of the cosmic time is amenable to the time step.
Then, we note that when a massive particle is created with its spacetime lattice, we are forced to add space and time in universe $$\Xi_U$$ because every massive particle is itself space and time.
Also, we will show that the origin of the expansion of the universe is to be found in a sort of creation of space following the appearance of massive particles in the field $$\Xi_U$$.
We can say the same thing about the cosmic time.
We note that if the universe expansion is detected to be a mutual spacing between galaxies, then saying that this is caused by an increasing quantity of space interposed between them, could be equally acceptable to consider the idea of the expansion as a stretching of the space.
Rather we show that the expansion of the universe cannot be a consequence of any stretching of a certain spatial length $$L$$, which can be described by the parameter $$a(t)$$ (Friedmann 1922,