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Register a new userMaximum force and cosmic censorship
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Valerio Faraoni
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Although the idea that there is a maximum force in nature seems untenable, we explore whether this concept can make sense in the restricted context of black holes. We discuss uniformly accelerated and cosmological black holes and we find that, although a maximum force acting on these black holes can in principle be introduced, this concept is rather tautological.
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Three simple idealised models are studied in order to develop some intuition about the leading order effect of non-sphericity on the maximum turnaround size $R_{rm TA,max}$ of large scale bound cosmic structures. Two of them describe intrinsically axisymmetric static mass distributions whereas the other is the Kerr-de Sitter metric where the axisymmetry is generated due to the rotation of the structure. In all the cases the fractional change $delta R_{rm TA,max}(theta)/R^{(0)}_{rm TA,max}$ of $R_{rm TA,max}$ of a given structure, compared to a spherical one with the same mass $M$, depends on the polar angle $theta$ and is proportional to the product of the relevant eccentricity parameter, times the square of a small quantity. This quantity in the static examples is the ratio of two characteristic length scales, while in the spinning case it is the ratio $v_{rm out}/c$ of the azimuthal speed of the outmost members of the structure, over the speed of light. Furthermore, the angular average $langle delta R_{rm TA,max}(theta)/R^{(0)}_{rm TA,max}rangle$ is zero in the two static cases, while it is negative and proportional to ${cal O}(v^2_{rm out}/c^2)$ for the Kerr-de Sitter. Thus, $delta R_{rm TA,max}(theta)/R^{(0)}_{rm TA,max}$ for an axisymmetric structure is very small for practically any value of the eccentricity parameter. We speculate about some possible further implications of our result on the maximum turn around radius of realistic cosmic structures.
We explore the bound of the trans-Planckian censorship conjecture on an inflation model with multiple stages. We show that if the first inflationary stage is responsible for the primordial perturbations in the cosmic microwave background window, the $e$-folding number of each subsequent stage will be bounded by the energy scale of the first stage. This seems to imply that the lifetime of the current era of accelerated expansion (regarded as one of the multiple inflationary stages) might be a probe for distinguishing inflation from its alternatives. We also present a multistage inflation model in a landscape consisting of anti-de Sitter vacua separated by potential barriers.
We investigate the implication of Trans-Planckian Censorship Conjecture (TCC) for the initial state of primordial perturbations. It is possible to set the state of perturbation modes in the infinite past as the Minkowski vacuum, only if the pre-inflationary era is past-complete. We calculate the evolution of the perturbation modes in such a pre-inflationary era and show that at the beginning of inflation the perturbation modes with wavelengths much shorter than the Hubble scale (but still larger than the Planck length scale) will behave as they are in the Bunch-Davis state. Therefore, a past-complete pre-inflationary evolution may automatically prepare the initial state required for the inflationary perturbations at the CMB window while obeying the TCC.
In this paper, we discuss about the possibility to enhance the tensor-to-scalar ratio $r$ under the condition of Trans-Planckian censorship conjecture (TCC), thus $rsim O(10^{-3})$ could be observable within the sensitivity of future experiments. We make use of the scalar-tensor theory where inflaton is nonminimally coupled to gravity. After demonstrating that the TCC condition could be modified in scalar-tensor theory, we show that due to the effects of modified gravity at the end of inflation, a large $rsim O(10^{-3})$ could be allowed without violating the TCC. Moreover, the modification can give rise to a weak coupling of gravity to the inflation field. If such an effect has been present as early as inflation starts, it would imply that in our case, the Universe might have experienced an asymptotically safe period at its early time.
We find the series of example theories for which the relativistic limit of maximum tension $F_{max} = c^4/4G$ represented by the entropic force can be abolished. Among them the varying constants theories, some generalized entropy models applied both for cosmological and black hole horizons as well as some generalized uncertainty principle models.
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