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Register a new userPioneer Anomaly and Accelerating Universe as Effects of the Minkowski Space Conformal Symmetry
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Authors
L.M. Tomilchik
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On the basis of the nonisometric transformations subgroup of the SO(4.2) group, the nonlinear time inhomogeneity one-parameter conformal transformations are constructed. The connection between the group parameter and the Hubble constant H0 is established. It is shown that the existence of an anomalous blue-shifted frequency drift is a pure kinematic manifestation of the time inhomogeneity induced by the Universe expansion. This conclusion is confirmed via a generalization of the standard Special Relativity clock synchronization procedure to the space expanding case. The obtained formulae are in accordance with the observable Pioneer Anomaly effect. The anomalous blue-shifted drift is universal, does not depend on the presence of graviting centers and can be, in principle, observed on any frequencies under suitable experimental conditions. The explicit analytic expression for the speed of recession--intergalactic distance ratio is obtained in the form of a function of the red shift z valid in the whole range of its variation. In the small z limit this expression exactly reproduces the Hubble law. The maximum value of this function at z=0.475 quantitatively corresponds to the experimentally found value z(exp) = 0.46 +/- 0.13 of the transition from the decelerated to the accelerated expansion of the Universe.
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The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame to an uniformly accelerated one is given. The explicit form of the conformal time inhomogeneity is established. The expression defining the location cosmological distance in the form of simple function on the red shift is obtained. By coupling it with the relativistic formula for the longitudinal Doppler effect, the explicit expression for the Hubble law is obtained, which gives rise to the connection between acceleration and the Hubble constant. The expression generalizing the conventional Hubble law reproduces kinematically the experimentally observed phenomenon treated conventionally as a Dark Energy manifestation. The conformal time deformation in the small time limit leads to the quadratic time nonlinearity. Being applied to describe the location-type experiments, this predicts the existence of the universal uniformly changing blue-shifted frequency drift. The obtained formulae reproduce the Pioneer Anomaly experimental data.
The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame (RF) to an uniformly accelerated RF is given. The explicit form of the conformal deformation of time is established. The expression defining the location cosmological distance in the form of simple function on the red shift is obtained. By coupling it with the well known relativistic formula defining the relative velocity of the mutually moving apart source and receiver of the signal, the explicit analytic expression for the Hubble law is obtained. The connection between acceleration and the Hubble constant follows therefrom immediately. The expression for the conformal time deformation in the small time limit leads to the quadratic time nonlinearity. Being applied to describe the location-type experiments, this predicts the existence of the uniformly changing blue-shifted frequency drift. Phenomenon of the Pioneer Anomaly (PA) is treated as the first of such a kind of effects discovered experimentally. The obtained formulae reproduce the PA experimental data. The expression generalizing the conventional Hubble law reproduces the experimentally observed phenomenon which in the frame of the conventional cosmological paradigm is treated as the transition from the decelerated expansion of the Universe to the accelerated one.
From Doppler tracking data and data on circular motion of astronomical objects we obtain a metric of the Pioneer Anomaly. The metric resolves the issue of manifest absence of anomaly acceleration in orbits of the outer planets and extra-Pluto objects of the Solar system. However, it turns out that the energy-momentum tensor of matter, which generates such a gravitational field in GR, violates energy dominance conditions. At the same time the equation of state derived from the energy-momentum tensor is that of dark energy with $w=-1/3$. So the model proposed must be carefully studied by Grand-Fit investigations.
In this article, we clarify the link between the conformal (i.e. Weyl) correspondence from the Minkowski space to the de Sitter space and the conformal (i.e. SO(2,$d$)) invariance of the conformal scalar field on both spaces. We exhibit the realization on de Sitter space of the massless scalar representation of SO$(2,d)$. It is obtained from the corresponding representation in Minkowski space through an intertwining operator inherited from the Weyl relation between the two spaces. The de Sitter representation is written in a form which allows one to take the point of view of a Minkowskian observer who sees the effect of curvature through additional terms.
The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The equations of the model are reduced to the form which allows a direct comparison between them and the equations of the Einsteinian classical theory of gravity. It is shown that quantized scalar field has a form of a condensate which behaves as an antigravitating medium. The theory predicts an accelerating expansion of the universe even if the vacuum energy density vanishes. An antigravitating effect of a condensate has a purely quantum nature. It is shown that the universe with the parameters close to the Planck ones can go through the period of exponential expansion. The conditions under which in semi-classical approximation the universe looks effectively like spatially flat with negative deceleration parameter are determined. The reduction to the standard model of classical cosmology is discussed.
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