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Register a new userNon-minimally coupled varying constants quantum cosmologies
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Authors
Adam Balcerzak
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We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newtons Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singularity. We also investigate the quantum counterpart of the considered theory and find the probability of transition of the universe from the collapsing pre-big-bang phase to the expanding post-big-bang phase.
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In this paper we consider a third quantized cosmological model with varying speed of light $c$ and varying gravitational constant $G$ both represented by non-minimally coupled scalar fields. The third quantization of such a model leads to a scenario of the doubleverse with the two components being quantum mechanically entangled. We calculate the two parameters describing the entanglement, namely: the energy and the entropy of entanglement where the latter appears to be a proper measure of the entanglement. We consider a possibility that the entanglement can manifests itself as an effective perfect fluid characterized by the time dependent barotropic index $w_{eff}$, which for some specific case corresponds to the fluid of cosmic strings. It seems that such an entanglement induced effective perfect fluid may generate significant backreaction effect at early times.
We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $epsilon$ parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling $xi$ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small non-minimal couplings, $xisim -1/20$, and it changes sign (from negative to positive) at a recent epoch when inflation lasts not much longer than what is minimally required, $N gtrsim 66$. Since currently we do not have a way of treating the classical fluid and the quantum backreaction in a self-consistent manner, we cannot say decidely whether the backreaction from inflationary quantum fluctuations of a non-minimally coupled scalar can mimic dark energy.
In this paper we consider a specific type of the bimetric theory of gravitation with the two different metrics introduced in the cosmological frame. Both metrics respect all the symmetries of the standard FLRW solution and contain conformally related spatial parts. One of the metric is assumed to describe the causal structure for the matter. Another metric defines the causal structure for the gravitational interactions. A crucial point is that the spatial part of the metric describing gravity is given by the spatial part of the matter metric confromally rescaled by a time-dependent factor $alpha$ which, as it turns out, can be linked to the effective gravitational constant and the effective speed of light. In the context of such a bimetric framework we examine the strength of some singular cosmological scenarios in the sense of the criteria introduced by Tipler and Krolak. In particular, we show that for the nonsingular scale factor associated with the matter metric, both the vanishing or blowing up of the factor $alpha$ for some particular moment of the cosmic expansion may lead to a strong singularity with infinite value of the energy density and infinite value of the pressure.
We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models the inflationary stage of the Universe evolution changes into a quasi-cyclic stage of the Universe evolution with oscillation behaviour of the Hubble parameter from positive to negative values. Depending on the initial conditions the Hubble parameter can perform either one or several cycles before to become negative forever.
We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high friction limit. In particular, with the help of the non-minimally derivative coupling, the quartic power law potential is consistent with the observational constraint at 95% CL.
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