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The physical history of the Universe is completed by including the quantum Planckian and trans-Planckian phase before inflation in the Standard Model of the Universe in agreement with observations. In the absence of a complete quantum theory of gravity, we start from quantum physics and its foundational milestone. The universal classical-quantum (or wave-particle) duality, which we extend to gravity and the Planck domain. As a consequence, classical, quantum Planckian and super-Planckian regimes are covered, and the usual quantum domain as well. A new quantum precursor phase of the Universe appears beyond the Planck scale $(t_P)$: $10^{-61}{t}_P\le t\le t_P$; the known classical/semiclassical Universe being in the range: $t_P\le t\le 10^{+61}{t}_P$. We extend in this way the de Sitter Universe to the quantum domain: classical-quantum de Sitter duality. As a result: (i) The classical and quantum dual de Sitter temperatures and entropies are naturally included, and the different (classical, semiclassical, quantum Planckian and trans-Planckian) de Sitter regimes characterized in a precise and unifying way. (ii) We apply it to relevant cosmological examples as the CMB, inflation and dark energy. This allows us to find in a simple and consistent way. (iii) Full quantum inflationary spectra and their CMB observables, including in particular the classical known inflation spectra and the quantum corrections to them. (iv) A whole unifying picture for the Universe epochs and their quantum precursors emerges with the cosmological constant as the vacuum energy, entropy and temperature of the Universe, clarifying the so-called cosmological constant problem which once more in its rich history needed to be revised.

The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q) elementary particle domain: $O_Q=o_P^2{O}_G^{-1}$, $o_P$ being the Planck scale. This duality is universal. From the gravity (G) and quantum (Q) variables $(O_G,O_Q)$, we define new quantum gravity (QG) variables $O_{\mathrm{\text{QG}}}=(1/2)(O_G+O_Q)$ which include all (classical, semiclassical and QG) domains passing through the Planck scale and the elementary particle domain. The QG variables are more complete than the usual ($O_Q$, $O_G$) ones which cover only one domain (Q or G). Two$O_G$ or $O_Q$ values $(\pm )$ are needed for each value of $O_{\mathrm{\text{QG}}}$ (reflecting the two dual ways of reaching the Planck scale). We perform the complete analytic extension of the QG variables through analytic (holomorphic) mappings which preserve the light-cone structure. This allows us to reveal the classical-quantum duality of the Schwarzschild–Kruskal spacetime: exterior regions are classical or semiclassical while the interior is totally quantum: its boundaries being the Planck scale. Exterior and interior lose their difference near the horizon: four Planck scale hyperbolae border the horizons as a quantum dressing or width: “l’horizon habillé”. QG variables are naturally invariant under $O_G\to O_Q$. Spacetime reflections, antipodal symmetry and PT or CPT symmetry are contained in the QG symmetry, which also shed insight on the global properties of the Kruskal manifold and its present renewed interest.

In this study, a radical hypothesis concerning the wave-particle duality exhibited by extremely small objects in nature is explored by developing a Planck lattice model of space–time that grapples with the uncertain dynamic quantum structure of space–time at the Planck scale. Upon applying the Planck lattice model to two notable experiments that most clearly demonstrate the essence of wave-particle duality, one immediately finds that it successfully shows in a relatively straightforward and physically consistent manner how parcels of matter and energy, i.e., electrons and photons, respectively, can behave like waves. The heuristic concepts regarding the underlying structure of space–time contained herein are intended to show the classical particle description of matter and energy as fundamental, while at the same time doing away with the widely held notion of a continuous space–time.

The first step to complete physical theories is to contemplate on the axiomatic character of the principles. This principle of relativity was formulated by Galileo and used by Newton to derive the laws of motion, and later was placed by Einstein at the center of the Special Theory and the General Relativity. This work considers the general principle of relativity as an expression of the inherent characteristic of the most important quantity in physics - the energy - that states that the energy is constant and is independent of the type or speed of movement of an object. The energy of an object is expressed as one entity that equals the sum of two energy expressions with different character. One of these two terms is denoted as the exposed energy with a kinetic character and represents the magnitude of the field of an object. This new definition of the energy offers several perspectives that are valid for both the classical and relativistic physics and provides insights beyond these two as: i) it leads to a coherent and complete model that relates the energy with the momentum and the force, ii) enables to construct the lagrangian that can be used to derive the equations of motion without artifices, iii) offers an original viewpoint on the dark matter and dark energy that is coherent with recent developments. Einstein was the first to deny the separate existence of gravitation and electromagnetism and has implied that the goal of a unified theory would be to explain the existence and to calculate the properties of matter. He revolutionized the use of the principles of symmetry in deriving the physical laws. It is known that the classical and quantum domain do not overlap and one would not expect the same governing symmetry principles in both domains. To calculate the properties of matter we employ spatial parameters that are related with the energy state of an object and the force that it exhibits. The mechanism assumes the common origin of different forces at the highest energy level. These spacetime parameters can be used to derive the electric and gravitational forces through a single mechanism that respects the LT dimensional analysis using neither the electrical charge nor the gravitational constant.

A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated to a minimal uncertainty in position measurements, which is encoded in deformed commutation relations. Once applied in the Heisenberg dynamics, they give effects potentially detectable in low energy experiments. For instance, an isolated harmonic oscillator becomes intrinsically nonlinear and its dynamics shows a dependence of the oscillation frequency on the amplitude, as well as the appearance of higher harmonics. Here we analyze the free decay of micro and nano-oscillators, spanning a wide range of masses, and we place upper limits to the parameters quantifying the commutator deformation.