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Register a new userFoundations of a quantum gravity at large scales of length and its consequences for the dynamics of cosmological expansion
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Authors
Claudio Nassif
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We attempt to find new symmetries in the space-time structure, leading to a modified gravitation at large length scales, which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified model for electrodynamics and gravitation, so that the influence of the gravitational field on the electrodynamics at very large distances leads to a reformulation of our understanding about space-time through the elimination of the classical idea of rest at quantum level. This leads us to a modification of the relativistic theory by introducing the idea of a universal minimum speed related to Planck minimum length. Such a speed, unattainable by the particles, represents a privileged inertial reference frame associated with a universal background field. The structure of space-time becomes extended due to such a vacuum energy density, which leads to a cosmological anti-gravity, playing the role of the cosmological constant. The tiny values of the vacuum energy density and the cosmological constant are successfully obtained, being in agreement with current observational results. We estimate the very high value of vacuum energy density at Planck length scale. After we find the critical radius of the universe, beyond which the accelerated expansion takes place. We show that such a critical radius is $R_{uc}=r_g/2$, where $r_g=2GM/c^2$, being $r_g$ the Shwarzschild radius of a sphere with a mass $M$ representing the total attractive mass contained in our universe. And finally we obtain the radius $R_{u0}=3r_g/4(>R_{uc})$ where we find the maximum rate of accelerated expansion. For $R_u>R_{u0}$, the rate of acceleration decreases to zero at the infinite, avoiding Big Rip.
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Gravity stands apart from other fundamental interactions in that it is locally equivalent to an accelerated frame and can be transformed away. Again it is indistinguishable from the geometry of space-time (which is an arena for all other basic interactions), its strength being linked with the curvature. This is a major reason why it has so far not been amenable to quantisation like other interactions. It is also evident that new ideas are required to resolve several conundrums in areas like cosmology, black hole physics, and particles at high energies. That gravity can have strong coupling at microscales has also been suggested in several contexts earlier. Here we develop some of these ideas, especially in connection with the high accelerations experienced by particles at microscales, which would be interpreted as strong local gravitational fields. The consequences are developed for various situations and possible experimental manifestations are discussed.
I discuss the dark energy characterized by the violation of the null energy condition ($varrho + p geq 0$), dubbed phantom. Amazingly, it is admitted by the current astronomical data from supernovae. We discuss both classical and quantum cosmological models with phantom as a source of matter and present the phenomenon called phantom duality.
We propose a new model of gravity where the Ricci scalar (R) in Einstein-Hilbert action is replaced by an arbitrary function of R and of the norm of energy-momentum tensor i.e., $f(R,T_{mu u}T^{mu u})$. Field equations are derived in the metric formalism. We find that the equation of motion of massive test particles is non-geodesic and these test particles are acted upon by a force which is orthogonal to the four-velocity of the particles. We also find the Newtonian limit of the model to calculate the extra acceleration which can affect the perihelion of Mercury. There is a deviation from the general relativistic(GR) result unless the energy density of fluid is constant. Arranging $alpha$ parameter gives an opportunity to cure the inconsistency between the observational values for the abundance of light elements and the standard Big Bang Nucleosynthesis results. Even the dust dominated universe undergoes an accelerated expansion without using a cosmological constant in Model II. With this specific choice of $f(R,T_{mu u}T^{mu u})$, we get the a Cardassian-like expansion.
We derive a model of dark energy which evolves with time via the scale factor. The equation of state $omega=(1-2alpha)/(1+2alpha)$ is studied as a function of a parameter $alpha$ introduced in this model. In addition to the recent accelerated expansion, the model predicts another decelerated phase. The age of the universe is found to be almost consistent with observation. In the limiting case, the cosmological constant model, we find that vacuum energy gravitates with a gravitational strength, different than Newtons constant. This enables degravitation of the vacuum energy which in turn produces the tiny observed curvature, rather than a 120 orders of magnitude larger value.
A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter $n$. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of $n$. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyze their stability for a generic value of the parameter $n$. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the $R^n$ cosmology. When matter is present a transient almost-Friedman phase can also be present before the transition to an accelerated expansion.
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