Antonin Coutant (AEI Potsdam)

Unitary and non-unitary transitions around a cosmological bounce

In this presentation, we will discuss the notion of time and unitarity in the vicinity of a bounce in quantum cosmology, that is, a turning point for the scale factor. This starts from the Vilenkin approach to the interpretation of the solutions of the Wheeler-DeWitt equation. In this approach, unitarity is defined through the conserved current and is by nature an approximate concept. In minisuperspace it amounts to using the scale factor as a time variable. A unitary evolution is recovered when the latter becomes semi-classical enough.

Unfortunately, WKB methods drastically fail near a turning point and the scale factor cannot play the role of time in scenarios with a bounce or a recollapsing phase for the universe. In this work, we extend the results of Vilenkin Massar and Parentani to momentum representation. For this, we investigate the dynamics of matter transitions when using its conjugate momentum as a time. In a first part, we describe the precise conditions so as to recover unitarity, and hence, a consistent notion of probability. In a second part, we discuss a concrete example in the vicinity of a bounce.

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Patrick Dürr (Tübingen)

Aspects of Alternative Theories of Gravity

Modifying standard theories of gravity is looking back upon a long history. In this talk, we shall examine the contemporary motivation behind and some exciting results and aspects of one of the most natural extensions of GR, Brans–Dicke-like theories, in which gravity is also mediated by a scalar (thus, rendering the gravitational coupling “constant” a dynamical variable).

After a brief review of the foundations and a few generic viability criteria, mainly concerning stability issues and constraints imposed by cosmological data, our discussion will focus upon weak field astrophysics, which turns out to have some surprises in store for us: How do such modifications fare with the Weak Equivalence Principle and classical tests, viz. in our solar system? Might they contribute to the solution of the Dark Matter mystery? What do they imply for gravitational wave phenomenology, perhaps even of observational relevance?

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Anne Franzen (Utrecht)

Boundedness of a massless scalar wave on Reissner–Nordström interior backgrounds

We consider solutions of the scalar wave equation ☐_g φ = 0, without symmetry, on fixed subextremal Reissner–Nordström backgrounds (M, g). Previously, it has been shown that for φ arising from sufficiently regular data on a two ended Cauchy hypersurface, the solution and its derivatives decay suitably fast on the event horizon H⁺. Using this, we show here that φ is in fact uniformly bounded, |φ| ≤ C, in the black hole interior up to and including the bifurcate Cauchy horizon CH⁺.

The proof depends on novel weighted energy estimates in the black hole interior which, in combination with commutation by angular momentum operators and Sobolev embedding, yield uniform pointwise estimates.

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