Session B15: Quantum Theory of Cosmology and Black Holes

Live

The Bekenstein-Hawking equation argues that entropy of a black hole is proportional to the area of its horizon. However, this equation leads to an inconsistency, if it is combined with the first law of black hole mechanics, the original pair-creation picture of Hawking radiation, and quantum mechanics. Here we show that this inconsistency is completely resolved if the simple entropy in the Bekenstein-Hawking equation is replaced with the coherent information from the outside of a black hole to the positive-energy particles inside it. The coherent information is ``minus'' the conditional entropy, which can be defined only in the purely quantum regime and is associated with distillable entanglement in quantum information theory. Therefore, our equation argues that the black hole stores quantum entanglement, whose size reflects the area of its horizon. Our equation reproduces not only the Bekenstein-Hawking equation in the case where the effect of Hawking radiation is small, but also known results, such as Hawking's area theorem and Bekenstein's generalized second law. Besides, our equation is free from the information loss paradox in contrast to the Bekenstein-Hawking equation, and from the firewall paradox in contrast to Page's model. This talk is based on arXiv:1807.06753.   

Live

The entropy of a de Sitter horizon was derived long ago by Gibbons and Hawking via a gravitational partition function, but the foundation of their method is obscure because there is no boundary at which to define the ensemble. We introduce an artificial "York" boundary inside the cosmological horizon, with either canonical or microcanonical boundary conditions. Path integrals over spherically symmetric geometries (with a possible black hole in the center) then define either the partition function or the density of states. We explore the stability of these ensembles and investigate the viability of negative temperature for the cosmological horizon. The stationary point of the microcanonical path integral yields the expected Bekenstein-Hawking entropy of the cosmological horizon, and defines a positive temperature (but we have not found a way to test stability in this case). The canonical ensemble path integral at negative temperature is indeed dominated by the stationary point, but yields a negative entropy, indicating an underlying inconsistency in the analysis. The positive temperature ensemble yields the expected positive entropy, however the stationary point is a maximum, indicating an instability. Perhaps this points to decay of the cosmological constant.   

Live

In the context of AdS/BCFT correspondence, certain high-energy holographic CFT states correspond to AdS black hole microstates with a geometrical behind-the-horizon region, modeled by a portion of a second asymptotic region terminating at a dynamical end-of-the-world (ETW) brane. The ETW boundary geometry takes the form of a closed FLRW spacetime. Under the right conditions, gravity is locally localized on the ETW brane similarly to the Randall-Sundrum II scenario for cosmology. In this case, the effective description of the brane physics is that of an expanding and contracting cosmological universe of the same dimensionality as the CFT, and the black hole microstate would give a precise, microscopic description of this cosmology. We show that such a braneworld scenario can be realized in a simple bottom up model consisting of a constant tension brane coupled to Einstein-Maxwell theory. If the bulk AdS-Reissner-Nordstr\"om black hole is near-extremal and the brane is near-critical, gravity can be locally localized on the brane and the bulk spacetime admits a holographic dual description. This result opens the door to a new description of cosmology in AdS/CFT correspondence.   

Live

A recent firewall solution in general relativity was constructed to solve the black hole information problem. This novel solution is equivalent to a Schwarzschild black hole outside of a Planck-density shell, and within the shell, it is equivalent to the interior of a Reissner-Nordstrom black hole. In so doing, the existence of an event horizon is avoided. Gravitational waves probe the whole structure of the firewall and so test the interior of the solution and not just the exterior spacetime. Further, they reveal the stability of the solution under perturbations. We examine the quasinormal mode spectra given non-radial polar perturbations and find limits on the model's parameters for which it is stable. Importantly, the spectra differ greatly from that of a Schwarzschild black hole for all values. This provides a clean test for the existence of such an object.   

Live

Leveraging the Kerr-Schild form of the metric, we show that a Schwarzschild black hole can be described as a particle-like defect in a family of spatial slices. This solution can be characterized by a system of gravitational charges that are locally conserved. This unusual perspective on black holes should help to identify their distinctive nature in quantum gravity.~   

Live

A complete ``consistent histories'' framework is given for a covariant "spin-foam" quantum cosmological model, a highly symmetry-reduced (FLRW) model of covariant loop quantum gravity. A decoherence functional is constructed through which probabilities may be consistently extracted from quantum amplitudes. Branch wave functions corresponding to different possible quantum histories of the universe are described, such as whether the universe ``bounces'' at small volume or becomes singular. We discuss the construction and calculation of such branch wave functions, with an emphasis on the crucial role played by the decoherence of histories in arriving at self-consistent quantum predictions for these closed quantum systems. [Based on joint work with Parampreet Singh]   

Live

In this talk, I will present the phenomenology of modified loop quantum cosmology when gravity is minimally coupled to a scalar field. Due to the quantization ambiguities, two different effective Hamiltonians other than the standard one in loop quantum cosmology (LQC) can be derived as candidate theories of loop cosmology in a spatially flat Friedmann-Lemaitre-Robertson-Walker universe. Although in these modified models, the big bang singularities are still replaced by the quantum bounce, there are both qualitative and quantitative differences as compared with the standard loop quantum cosmology. I will first focus on the distinctive features of the background evolution of the universe in modified loop cosmological models and then talk about the primordial scalar and tensor power spectra in these models.   

Live

We investigate different regularizations and ambiguities in loop cosmological models on the predictions in the scalar and tensor primordial spectra of the CMB using the dressed metric approach (DMA). Three models, standard loop quantum cosmology (LQC), and two modified LQCs (mLQC-I and mLQC-II) arising from different regularizations of the Lorentzian term in the classical Hamiltonian constraint are explored in spatially flat FLRW universe. In each model, two different treatments of the conjugate momentum of the scale factor are considered. The first one corresponds to the conventional treatment in DMA, and the second one is inspired from the hybrid approach. For these two choices, we find the power spectrum to be scale-invariant in the UV regime for all three models, but there is at least a 10% relative difference in amplitude in the IR and intermediate regimes. In mLQC-I, the magnitude of the power spectrum in the IR regime is of the order of Planck scale irrespective of the ambiguity in conjugate momentum of the scale factor. The relative difference in the amplitude of the power spectrum between LQC and mLQC-II can be as large as 50% throughout the IR and intermediate regimes. Differences in amplitude due to regularizations and ambiguities are small in the UV regime.   

Not Participating

Sixty-five years ago, John Wheeler suggested that Planck-scale quantum fluctuations of geometry and topology---``spacetime foam''---might be important for understanding the cosmological constant. Twenty years later, Stephen Hawking initiated an exploration of this proposal through Euclidean path integral techniques. Here, I report on further progress, based on a canonical approach to quantum gravity and recent advances in the initial value formalism, that suggests that spacetime foam may indeed be capable of ``hiding'' a large cosmological constant.