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In any conformally invariant gravitational theory, the space of exact solutions is greatly enlarged. The Weyls conformal invariance can then be spontaneously broken to spherically symmetric vacuum solutions that exclude the spacetime region inside the black holes event horizon from our Universe. We baptize these solutions conformalons. It turns out that for all such spacetimes nothing can reach the Schwarzschild event horizon in a finite amount of proper time for conformally coupled ``massive particles, or finite values of the affine parameter for massless particles. Therefore, for such vacuum solutions the event horizon is an asymptotic region of the Universe. As a general feature, all conformalons show a gravitational blueshift instead of a gravitational redshift at the unattainable event horizon, hence avoiding the Trans-Planckian problem in the Hawking evaporation process. The latter happens as usual near the event horizon, but now the annihilation process between the matter and Hawkings negative energy particles takes place outside of the event horizon. Indeed, in these solutions the gravitational collapse consists of matter that falls down forever towards the horizon without ever reaching it. According to a previous work that has been faithfully adapted to the conformalons scenario, the information is not lost in the whole process of singularity-free collapse and evaporation, as evident from the Penrose diagram.
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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.
The aim of Quantum Fisher Cosmology is to use the quantum Fisher information about pure de Sitter states to derive model independent observational consequences of the existence of a primordial phase of the Universe of de Sitter accelerated expansion. These quantum features are encoded in a scale dependent quantum cosmological tilt that defines what we can call the de Sitter universality class. The experimental predictions are: i) A phase transition from red into blue tilt at a scale order $k= 1$ Mpc$^{-1}$ that naturally solves the cosmological trans-Planckian problem, ii) A spectral index for curvature fluctuations at CMB scales $k= 0.05$ Mpc$^{-1}$ equal to $0.0328$, iii) A tilt running at scale $k=0.002$ Mpc$^{-1}$ equal to $-0.0019$, iv) An enhancement of the amplitude of CMB peaks for extremely high multipoles ($l > 10^5$) that can provide a natural mechanism for primordial black hole formation as a source of dark matter, v) A lack of power at scales of $8$ Mpc with respect to the CMB scale that can explain the $sigma_8$ tension.
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 make a critical comparison between ultra-high energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time required for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years which is much shorter than the age of the Universe. Thus from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black hole counterparts.
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.
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