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Register a new userInteracting quintessence in light of Generalized Uncertainty Principle: Cosmological perturbations and dynamics
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We consider a cosmological scenario endowed with an interaction between the universes dark components $-$ dark matter and dark energy. Specifically, we assume the dark matter component to be a pressure-less fluid, while the dark energy component is a quintessence scalar field with Lagrangian function modified by the quadratic Generalized Uncertainty Principle. The latter modification introduces new higher-order terms of fourth-derivative due to quantum corrections in the scalar fields equation of motion. Then we investigate asymptotic dynamics and general behaviour of solutions of the field equations for some interacting models of special interests in the literature. At the background level, the present interacting model exhibits the matter-dominated and de Sitter solutions which are absent in the corresponding quintessence model. Furthermore, to boost the background analysis, we study cosmological linear perturbations in the Newtonian gauge where we show how perturbations are modified by quantum corrected terms from the quadratic Generalized Uncertainty Principle. Depending on the coupling parameters, scalar perturbations show a wide range of behavior.
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The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies.In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein-Gordon, Schrodinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator.
We present a formalism which allows for the perturbative derivation of the Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and observers. Entering the realm of small position uncertainties, we derive a general asymptotic EUP. The leading 2nd order curvature induced correction is proportional to the Ricci scalar, while the 4th order correction features the 0th order Cartan invariant Psi^2 (a scalar quadratic in curvature tensors) and the curved space Laplacian of the Ricci scalar all of which are evaluated at the expectation value of the position operator, i.e. the expected position when performing a measurement. This result is first verified for previously derived homogeneous space models and then applied to other non-trivial curvature related effects such as inhomogeneities, rotation and an anisotropic stress fluid leading to black hole hair. Our main achievement combines the method we introduce with the Generalized Uncertainty Principle (GUP) by virtue of deformed commutators to formulate a generic form of what we call the Asymptotic Generalized Extended Uncertainty Principle (AGEUP).
In this work, we apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field, which has been previously investigated in the literature. For a coupling function $Q = -(alpha dot{rho}_m + beta dot{rho}_{phi} )$, we have found that it can be rewritten in the form $Q = 3H (alpha rho_m + beta dot{phi}^2)/(1-alpha +beta)$, so that its dependence on the dark matter density and on the kinetic term of the scalar field is linear and proportional to the Hubble parameter. We analyze the following scenarios $alpha=0$, $alpha = beta$ and $alpha = -beta$, separately and in order to describe the cosmological evolution for each solution we have calculated various observables. We find that there are not any new stable late-time solutions apart from those found of standard quintessence, nevertheless, the stability conditions are severely altered. A notable result found with respect to previous works is that in our case, with the exception of the matter dominated solution, the remaining critical points behave as scaling although the stiff matter solution and the dark energy dominated state can be recovered in the limit $beta rightarrow 0$ and $beta rightarrow 1$, respectively. Moreover, it is shown that for $alpha = beta $ and $alpha = - beta$ (in general for $alpha eq 0$), a separatrix arises modifying prominently the structure of the phase space. This represents a novel feature no mentioned before in the literature.
We find exact formulas for the Extended Uncertainty Principle (EUP) for the Rindler and Friedmann horizons and show that they can be expanded to obtain asymptotic forms known from the previous literature. We calculate the corrections to Hawking temperature and Bekenstein entropy of a black hole in the universe due to Rindler and Friedmann horizons. The effect of the EUP is similar to the canonical corrections of thermal fluctuations and so it rises the entropy signalling further loss of information.
The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out here that the two effects are mutually exclusive when compared with experimental bounds. Moreover, the former stems from modified Poisson brackets obtained from a wrong classical limit of the deformed canonical commutators.
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