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Register a new userQuantum gravity, information theory and the CMB
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Achim Kempf
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We review connections between the metric of spacetime and the quantum fluctuations of fields. In particular, we discuss the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlators of the fluctuations of quantum fields. We also discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization would, therefore, have the benefit of not requiring the modding out of the diffeomorphism group. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background (CMB) that may become observable.
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We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.
The back reactions of Hawking radiation allow nontrivial correlations between consecutive Hawking quanta, which gives a possible way of resolving the paradox of black hole information loss known as the hidden messenger method. In a recent work of Ma {it et al} [arXiv:1711.10704], this method is enhanced by a general derivation using small deviations of the states of Hawking quanta off canonical typicality. In this paper, we use this typicality argument to study the effects of generic back reactions on the quantum geometries described by spin network states, and discuss the viability of entropy conservation in loop quantum gravity. We find that such back reactions lead to small area deformations of quantum geometries including those of quantum black holes. This shows that the hidden-messenger method is still viable in loop quantum gravity, which is a first step towards resolving the paradox of black hole information loss in quantum gravity.
In this semi-technical review we discuss string theory (and all that goes by that name) as a framework for a quantum theory of gravity. This is a new paradigm in theoretical physics that goes beyond relativistic quantum field theory. We provide concrete evidence for this proposal. It leads to the resolution of the ultra-violet catastrophe of Einsteins theory of general relativity and an explanation of the Bekenstein-Hawking entropy (of a class of black holes) in terms of Boltzmanns formula for entropy in statistical mechanics. We discuss `the holographic principle and its precise and consequential formulation in the AdS/CFT correspondence of Maldacena. One consequence of this correspondence is the ability to do strong coupling calculations in SU(N) gauge theories in terms of semi-classical gravity. In particular, we indicate a connection between dissipative fluid dynamics and the dynamics of black hole horizons. We end with a discussion of elementary particle physics and cosmology in the framework of string theory. We do not cover all aspects of string theory and its applications to diverse areas of physics and mathematics, but follow a few paths in a vast landscape of ideas. (This article has been prepared for the TWAS Silver Jubilee)
We show that if one starts with a Universe with some matter and a cosmological constant, then quantum mechanics naturally induces an attractive gravitational potential and an effective Newtons coupling. Thus gravity is an emergent phenomenon and what should be quantized are the fundamental degrees of freedom from which it emerges.
We present a description of CMB anisotropies generated by tensor perturbations in f(R) theories of gravity. The temperature power spectrum in the special case of $f(R)=R^n$ is computed using a modified version of CAMB package.
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