Research interests


Jump to:  Quantum-gravity effects in the CMB | Third quantization | Singularity avoidance | Entanglement

During my scientific career, I specialized on quantum cosmology and one of the main lines of my research was the search for effects of a theory of quantum gravity in the Cosmic Microwave Background anisotropy spectrum.

I focussed on using canonical quantum cosmology that leads to the Wheeler–DeWitt equation. Even though the Wheeler–DeWitt equation is probably not the final answer to the problem of quantum gravity and should be superseded at the most fundamental level by a theory like string theory that unifies all forces in nature, its conservative construction should give us insights into the quantum nature of the universe and allow us to study general properties of a theory of quantum gravity in cosmological models and for black holes. In particular, using the Wheeler–DeWitt equation to determine effects of quantum gravity should give us an estimate of their magnitude.

Quantum-gravitational effects in the CMB arising from a semiclassical approximation
[1] 1103.4967
[2] 1303.0531
[3] 1511.05545
[4] 1611.02932
[5] 1903.01234
[6] 2011.06426
The Wheeler–DeWitt equation is the result of a direct canonical quantization of general relativity. It is constructed in the same way as the Schrödinger equation by looking for a wave equation that gives back general relativity in the semiclassical limit. Therefore, we have a well-defined semiclassical approximation at hand.

At the beginning of my PhD studies, I worked on using the above-mentioned semiclassical approximation of the Wheeler–DeWitt equation, which leads to a Schrödinger equation with quantum-gravitational correction terms, to determine the effect of this correction onto the CMB spectrum. This first model was still simplified in the sense that we only used perturbations of the scalar field instead of gauge-invariant perturbations involving the metric. However, the resulting article published in PRL [1] has set the stage for a series of papers refining the model [2] and eventually using Mukhanov–Sasaki variables [3,4], which allowed us to explicitly compare the corrections we found to observations. We have also generalized our analysis in order to study excited states of inflationary perturbations [5]. Recently, we revisited the issue of the unitarity of the corrections [6].

These corrections, which are most prominent on large scales and show a specific behavior of k−3, are only of the order of 10−10 and as such cannot be seen in the CMB. However, galaxy–galaxy correlations, where cosmic variance is not present, are still a possibility to look for such effects. Given that the magnitude of these corrections is fundamentally limited by the energy scale of inflation, more sizable corrections could only come from scenarios where a pre-inflationary phase is present, which we will discuss below.

Third quantization, the multiverse picture and its observational consequences
[7] 1708.00025
[8] 1711.05138
[9] 1809.09133		 The so-called third quantization approach arises from a quantum-field-theoretical formulation of the Wheeler–DeWitt equation where universes described by a certain wave function are represented as “particles” that can be created and annihilated. Hence, it is a way to describe an ensemble of universes, i. e. a multiverse.

If one describes an (eternally) inflating universe in the third quantization picture, one ends up with an ensemble of sub-universes that exhibit a distinctive pre-inflationary phase which behaves like stiff matter with the equation of state p = ρ and appears as an a−6-term in the Friedmann equation. If the parent universe has positive curvature, this pre-inflationary phase corresponds to a baby-universe phase that is separated from the asymptotic de Sitter phase by a Euclidean region. We have thus analyzed the probability that a universe can tunnel from the baby-universe phase to the de Sitter phase [7].

Given that such a pre-inflationary phase can lead to effects in the CMB spectrum that are larger than the effects from a semiclassical approximation, we continued our studies using a flat parent universe without a Euclidean region to calculate the effects of the pre-inflationary phase onto the primordial scalar power spectrum in a sub-universe [8].

The result is that on the largest scales there is a suppression of power followed by a bump leading to an enhancement. As it turns out, in order to get a sizable effect for the suppression to explain the quadrupole anomaly in the CMB, the bump is enhanced that much that the model becomes incompatible with the CMB data.

Given that the model described above is in some tension with observations, we also studied a multiverse model where an explicit interaction between universes is implemented. It had already been shown that such an interaction leads to a different pre-inflationary phase and we found that such a model can indeed be compatible with observations and might even lead us towards an explanation of the CMB quadrupole discrepancy [9].

The fate of classical singularities in quantum cosmology
[10] 1312.5976 Another project of my PhD phase was the analysis of a cosmological model with a special type of matter that classically exhibits a specific type of mild singularity at late times [10]. Given that one expects that a theory of quantum gravity should remove classical singularities, we quantized this model using the Wheeler–DeWitt approach and found that this type of mild singularity is not always avoided in the quantized model, unlike earlier studies with stronger singularities which showed a divergence of energy density, pressure or even the scale factor itself leading to a big rip.

Entanglement in cyclic multiverse models
[11] 1701.04773 When I was a postdoc in the Szczecin Cosmology Group, its main research topic was to analyze universe models with varying fundamental couplings. In this context, I was involved in a project analyzing models with a varying gravitational coupling, which exhibit a cyclic evolution, in the third quantization approach [11].

We used the model of a multiverse consisting of cyclic universes going from a big bang to a big crunch, a(t) ∝ sin(t), or to a big rip, a(t) ∝ tan(t), which can both be inferred from a variation of the gravitational constant. We calculated the entropy and temperature of entanglement to see whether these quantities show a distinct behavior at the classical singularities and we concluded that the divergence of the entanglement temperature is a suitable measure of the “quantumness” of a point in the evolution of a universe.