
Christof WetterichHeidelberg University · Institute of Theoretical Physics
Christof Wetterich
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443
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Introduction
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October 1983 - March 1985
April 1981 - September 1985
August 1992 - present
Publications
Publications (443)
We propose that physical time is based on counting the oscillations of wave functions. The discrete counting of the ticks of these clocks does not depend on the metric frame. It remains well defined for the beginning epochs of the universe. The photon clock counts the oscillations of electromagnetic plane waves in the cosmic reference frame. It can...
If an ultraviolet fixed point renders quantum gravity renormalizable, the effective potential for a singlet scalar field -- the cosmon -- can be computed according to the corresponding scaling solution of the renormalization group equations. We associate the largest intrinsic mass scale generated by the flow away from the fixed point with the scale...
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial configurations. The properties of the deterministic updating are randomly distributed over space and time. We are in...
We compute the equation of state, the gap as well as the density fluctuations of a two-component superfluid Fermi gas over the whole range of BEC-BCS crossover at vanishing temperature within the functional renormalisation group approach. With an improved understanding of the relation between density and chemical potential, already a rather simple...
Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four dimensions. Local Lorentz symmetry is exact on the discrete level and diffeomorphism symmetry emerges in the naive cont...
A bstract
We compute scaling solutions of functional flow equations for quantum grav- ity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to perturbation theory, to the non-perturbative infrared region. The existence of such scaling solutions is nec...
The geometric concept of geodesic completeness depends on the choice of the metric field or “metric frame”. We develop a frame-invariant concept of “generalised geodesic completeness” or “time completeness”. It is based on the notion of physical time defined by counting oscillations for some physically allowed process. Oscillating solutions of wave...
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced by a probability distribution over initial conditions. The proposed automaton involves right- and left-movers,...
Some cosmological models with non-negligible dark energy fractions, in particular windows of the prerecombination epoch, are capable of alleviating the Hubble tension quite efficiently, while keeping the good description of the data that are used to build the cosmic inverse distance ladder. There has been an intensive discussion in the community on...
Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four dimensions. Local Lorentz symmetry is exact on the discrete level and diffeomorphism symmetry emerges in the naive cont...
We compute scaling solutions of functional flow equations for quantum gravity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to perturbation theory, to the non-perturbative infrared region. The existence of such scaling solutions is necessary for a...
We discuss predictions for cosmology which result from the scaling solution of functional flow equations for a quantum field theory of gravity. A scaling solution is necessary to render quantum gravity renormalizable. Our scaling solution is directly connected to the quantum effective action for the metric coupled to a scalar field. It includes all...
Quantum gravity can determine the dependence of gauge couplings in a scalar field, which is related to possible fifth forces and time varying fundamental “constants”. This prediction is based on the scaling solution of functional flow equations. For momenta below the field-dependent Planck mass the quantum scale invariant standard model emerges as...
Quantum computation builds on the use of correlations. Correlations could also play a central role for artificial intelligence, neuromorphic computing or “biological computing.” As a step toward a systematic exploration of “correlated computing” we demonstrate that neuromorphic computing can perform quantum operations. Spiking neurons in the active...
The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of physical time defined by counting oscillations for some physically allowed process. Oscillating solutions of wave...
Lattice simulations along with studies in continuum QCD indicate that non-perturbative quantum fluctuations lead to an infrared regularisation of the gluon propagator in covariant gauges in the form of an effective mass-like behaviour. In the present work we propose an analytic understanding of this phenomenon in terms of gluon condensation through...
Some cosmological models with non-negligible dark energy fractions in particular windows of the pre-recombination epoch are capable of alleviating the Hubble tension quite efficiently, while keeping the good description of the data that are used to build the cosmic inverse distance ladder. There has been an intensive discussion in the community on...
A bstract
In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of a model. For short distances we formulate our model as a Yang-Mills theory with fermions and vector...
Quantum gravity can determine the field-dependence of gauge couplings. This prediction is based on the scaling solution of functional flow equations. For momenta below the field-dependent Planck mass the quantum scale invariant standard model emerges as an effective low energy theory. For a small non-zero value of the infrared cutoff scale the fift...
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on a one-dimensional lattice are equivalent to two-dimensional quantum field theories for fermions. They can be v...
Many cellular automata admit an interpretation in terms of fermionic particles. Reversible automata on space-lattices with a local updating rule can be described by a partition function or Grassmann functional integral for interacting fermions moving in this space. We discuss large classes of automata that are equivalent to discretized fermionic qu...
Inflation and quintessence can both be described by a single scalar field. The cosmic time evolution of this cosmon field realizes a crossover from the region of an ultraviolet fixed point in the infinite past to an infrared fixed point in the infinite future. This amounts to a transition from early inflation to late dynamical dark energy, with int...
A bstract
We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract β -functions for all couplings. In our truncation we find two fixed points. One corresponds to asymptotically free higher derivat...
Inflation and quintessence can both be described by a single scalar field. The cosmic time evolution of this cosmon field realizes a crossover from the region of an ultraviolet fixed point in the infinite past to an infrared fixed point in the infinite future. This amounts to a transition from early inflation to late dynamical dark energy, with int...
Lattice simulations along with studies in continuum QCD indicate that non-perturbative quantum fluctuations lead to an infrared regularisation of the gluon propagator in covariant gauges in the form of an effective mass-like behaviour. In the present work we propose an analytic understanding of this phenomenon in terms of gluon condensation through...
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically on bit configurations. The genuinely probabilistic character of quantum physics is realized by probabilistic i...
We discuss cosmological solutions for a diffeomorphism invariant gauge theory of the noncompact Lorentz group SO(1,3). Besides the gauge bosons our model of pregeometry contains a vector field in the vector representation of SO(1,3) and a scalar singlet. General relativity and variable gravity emerge as effective theories for large distances and ti...
A class of fermionic quantum field theories with interactions can be described equivalently as probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on a one-dimensional lattice are equivalent to two - dimensional quantum field theories for fermions. They ca...
We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $\beta$-functions for all couplings. In our truncation we find two fixed points. One corresponds to asymptotically free higher derivative g...
Models of inflationary cosmology admit a choice of the metric for which the geometry of homogeneous isotropic solutions becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite past and quantum scale symmetry is realized. The cosmological evolution is dominantly described by the slow in...
A simple model for a scalar field and gravity admits homogeneous isotropic cosmological solutions which cross the Big Bang singularity. In the scaling frame with field dependent effective Planck mass these solutions are regular. They become singular in the Einstein frame with fixed Planck mass. This field singularity arises since the field transfor...
Einstein's general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a SO(4) - Yang-Mills theory. In addition to the gauge fields we include a vector field in the vector representation of the gauge group. The gauge - and diffeomorphism - invariant kinetic terms for the...
Dark energy could play a role at redshifts z≫O(1). Many quintessence models possess scaling or attractor solutions where the fraction of dark energy follows the dominant component in previous epochs of the Universe's expansion, or phase transitions may happen close to the time of matter-radiation equality. A non-negligible early dark energy (EDE) f...
Many quintessence models possess scaling or attractor solutions where the fraction of dark energy follows the dominant component in previous epochs of the expansion, or phase transitions may happen close to matter-radiation equality time. A non-negligible early dark energy (EDE) fraction around matter-radiation equality could contribute to alleviat...
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically on bit configurations. The genuinely probabilistic character of quantum physics is realized by probabilistic i...
The great emptiness is a possible beginning of the Universe in the infinite past of physical time. For the epoch of great emptiness particles are extremely rare and effectively massless. Only expectation values of fields and average fluctuations characterize the lightlike vacuum of this empty Universe. The physical content of the early stages of st...
We discuss cosmological solutions for a diffeomorphism invariant gauge theory of the non-compact Lorentz group $SO(1,3)$. Besides the gauge bosons our model of pregeometry contains a vector field in the vector representation of $SO(1,3)$ and a scalar singlet. General relativity and variable gravity emerge as effective theories for large distances a...
We investigate the dimensional crossover from three to two dimensions in an ultracold Fermi gas across the whole BCS-BEC crossover. Of particular interest is the strongly interacting regime as strong correlations and pair fluctuations are more pronounced in reduced dimensions. Our results are obtained from first principles within the framework of t...
A single paragraph of about 200 words maximum. For research articles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: des...
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling solutions of functional renormalization flow equ...
In pregeometry a metric arises as a composite object at large distances. For short distances we investigate a Yang-Mills theory with fermions and vector fields. The particular representation of the vector fields permits to formulate diffeomorphism invariant kinetic terms. Geometry and general relativity emerge at large distances by spontaneous symm...
A bstract
A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson M H and the top quark M t...
Einstein's general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a $SO(4)$ - Yang-Mills theory. In addition to the gauge fields we include a vector field in the vector representation. The gauge - and diffeomorphism - invariant kinetic terms for these fields permit...
We discuss aspects of non-perturbative unitarity in quantum field theory. The additional ghost degrees of freedom arising in “truncations” of an effective action at a finite order in derivatives could be fictitious degrees of freedom. Their contributions to the fully-dressed propagator – the residues of the corresponding ghost-like poles – vanish o...
A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic quantum field theory obeys a unitary time evolution and shows all properties of quantum mechanics. Classical...
This work attempts a fundamental formulation of physics based on probabilities. The basic assumptions are simple: One world exists. Humans can understand its properties by formulating laws based on probabilities. Our probabilistic setting only employs the notions of a probability distribution, observables and their expectation values, which are com...
We discuss aspects of non-perturbative unitarity in quantum field theory. The additional ghost degrees of freedom arising in "truncations" of an effective action at a finite order in derivatives could be fictitious degrees of freedom. Their contributions to the fully-dressed propagator -- the residues of the corresponding ghost-like poles -- vanish...
A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson $M_H$ and the top quark $M_t$. If on...
A bstract
If a grand-unified extension of the asymptotically safe Reuter fixed-point for quantum gravity exists, it determines free parameters of the grand-unified scalar potential. All quartic couplings take their fixed-point values in the trans-Planckian regime. They are irrelevant parameters that are, in principle, computable for a given particl...
Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling solutions of functional flow equations. Such theories are highly predictive since all relevant parameters for deviations from the exact scaling s...
A particular version of the Thirring model with imaginary coupling can be represented as a cellular automaton. This interacting fermionic quantum field theory obeys a unitary time evolution and shows all properties of quantum mechanics. Cellular automata with probabilistic initial conditions can take the form of quantum theories. Our model exhibits...
We propose that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and correlations of the Ising spins. As a step towards quantum computation we show for a two qubit system that quant...
Partial bosonization of the two-dimensional Hubbard model focuses the functional renormalization flow on channels in which interactions become strong and local order sets in. We compare the momentum structure of the four-fermion vertex, obtained on the basis of a patching approximation, to an effective bosonic description. For parameters in the ant...
A simple model for a scalar field and gravity admits cosmological solutions which cross the Big Bang singularity. In the scaling frame with field dependent effective Planck mass these solutions are regular. They become singular in the Einstein frame with fixed Planck mass. This field singularity arises since the field transformation of the metric t...
Models of inflationary cosmology admit a choice of the metric for which geometry becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite past and quantum scale symmetry is realized. The cosmological evolution is dominantly described by the slow increase of a scalar field which sets the...
In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice o...
In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric space-times with a non-trivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice...
We propose the great emptiness as a possible beginning of the Universe in the infinite past of physical time. In the beginning particles are very rare and effectively massless. Only expectation values of fields and average fluctuations characterize the lightlike vacuum of this empty Universe. Our observed inhomogeneous Universe can be extrapolated...
We investigate the shape of the effective potential for scalar fields at and near the ultraviolet fixed point of asymptotically safe quantum gravity. We find scaling solutions with a completely flat potential and vanishing gauge and Yukawa couplings. Nonvanishing gauge couplings can induce spontaneous symmetry breaking due to a potential minimum at...
Partial bosonisation of the two-dimensional Hubbard model focuses the functional renormalisation flow on channels in which interactions become strong and local order sets in. We compare the momentum structure of the four-fermion vertex, obtained on the basis of a patching approximation, to an effective bosonic description. For parameters in the ant...
We investigate the dimensional crossover from three to two dimensions in an ultracold Fermi gas across the whole BCS-BEC crossover. Of particular interest is the strongly interacting regime as strong correlations are more pronounced in reduced dimensions. Our results are obtained from first principles within the framework of the functional renormal...
We argue that primordial dark matter halos could be generated during radiation domination by long-range attractive forces stronger than gravity. In this paper, we derive the conditions under which these structures could dominate the dark matter content of the Universe while passing microlensing constraints and cosmic microwave background energy inj...
Using the gauge invariant flow equation for quantum gravity we compute how the strength of gravity depends on the length or energy scale. The fixed point value of the scale-dependent Planck mass in units of the momentum scale has an important impact on the question, which parameters of the Higgs potential can be predicted in the asymptotic safety s...
If a grand-unified extension of the asymptotically safe Reuter fixed-point for quantum gravity exists, it determines free parameters of the grand-unified scalar potential. All quartic couplings take their fixed-point values in the trans-Planckian regime. They are irrelevant parameters that are, in principle, computable for a given particle content...
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory m...
Am Anfang des Universums war fast nichts –Vakuum mit nur seltenen Elementarteilchen, die sich mit Lichtgeschwindigkeit bewegten. Erst später wurde das Plasma aus Elementarteilchen erzeugt, das unserem gängigen Urknallbild zugrunde liegt. Wie lange diese Anfangsperiode dauerte, hängt vom Konzept der Zeit ab. „Physikalische Uhren“ tickten unendlich o...
We argue that primordial dark matter halos could be generated during radiation domination by long range attractive forces stronger than gravity. In this paper we derive the conditions under which these structures could dominate the dark matter content of the Universe while passing microlensing constraints and cosmic microwave background energy inje...
Using the gauge invariant flow equation for quantum gravity we compute how the strength of gravity depends on the length or energy scale. The fixed point value of the scale-dependent Planck mass in units of the momentum scale has an important impact on the question which parameters of the Higgs-potential can be predicted in the asymptotic safety sc...
The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs boson, understanding the gauge hierarchy problem, and a possible explanation of an—asymptotically—vanishing cosmological constant. We find that the quartic self-interaction of the Higgs scalar fi...
Quantum scale symmetry is the realization of scale invariance in a quantum field theory. No parameters with dimension of length or mass are present in the quantum effective action. Quantum scale symmetry is generated by quantum fluctuations via the presence of fixed points for running couplings. As for any global symmetry, the ground state or cosmo...
The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs boson, understanding the gauge hierarchy problem and a possible explanation of an *asymptotically* vanishing cosmological constant. We find that the quartic self interaction of the Higgs scalar f...
We demonstrate, that artificial neural networks (ANN) can be trained to emulate single or multiple basic quantum operations. In order to realize a quantum state, we implement a novel "quantumness gate" that maps an arbitrary matrix to the real representation of a positive hermitean normalized density matrix. We train the CNOT gate, the Hadamard gat...
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. We discuss static memory materials based on Ising spins that realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical spins can account...
We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities oscillating with the distance from the boundary. The dependence of the local statistical information on this distance...
We explore the infrared limit of quantum gravity. For a positive cosmological constant or effective scalar potential, one-loop perturbation theory around flat space is divergent due to an instability of the graviton propagator. Functional renormalization solves this problem by a flow of couplings avoiding instabilities. This leads to a graviton bar...
We explore the infrared limit of quantum gravity in presence of a cosmological constant or effective potential for scalar fields. For a positive effective scalar potential, one-loop perturbation theory around flat space is divergent due to an instability of the graviton propagator. Functional renormalization solves this problem by a flow of couplin...
Primordial black holes can be produced by a long range attractive fifth force stronger than gravity, mediated by a light scalar field interacting with non-relativistic "heavy" particles. As soon as the energy fraction of heavy particles reaches a threshold, the fluctuations rapidly grow non-linear. The overdensities collapse into black holes or sim...
Primordial black holes can be produced by a long range attractive fifth force stronger than gravity, mediated by a light scalar field interacting with nonrelativistic "heavy" particles. As soon as the energy fraction of heavy particles reaches a threshold, the fluctuations rapidly become nonlinear. The overdensities collapse into black holes or sim...
Asymptotically safe quantum fluctuations of gravity can uniquely determine the value of the gauge coupling for a large class of grand unified models. In turn, this makes the electromagnetic fine-structure constant calculable. The balance of gravity and matter fluctuations results in a fixed point for the running of the gauge coupling. It is approac...
Asymptotically safe quantum fluctuations of gravity can uniquely determine the value of the gauge coupling for a large class of grand unified models. In turn, this makes the electromagnetic fine-structure constant calculable. The balance of gravity and matter fluctuations results in a fixed point for the running of the gauge coupling. It is approac...
We discuss the concept of gauge-invariant fields for non-abelian gauge theories. Infinitesimal fluctuations around a given gauge field can be split into physical and gauge fluctuations. Starting from some reference field the gauge-invariant fields are constructed by consecutively adding physical fluctuations. An effective action that depends on gau...
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schr\"odinger picture that keeps track of the local p...
In a variable gravity scenario containing an ultraviolet and an infrared fixed point quantum scale invariance emerges at both fixed points. We discuss a particular model for the crossover between the fixed points which can naturally account for inflation and dark energy using a single scalar field. In the Einstein-frame formulation the potential ca...
Quantum gravity computations suggest the existence of an ultraviolet and an infrared fixed point where quantum scale invariance emerges as an exact symmetry. We discuss a particular variable gravity model for the crossover between these fixed points which can naturally account for inflation and dark energy, using a single scalar field. In the Einst...
Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. In flat space the functional renormalization flow drives a positive cosmological constant to zero. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable...
We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We...
The gauge hierarchy problem could find a solution within the scenario of asymptotic safety for quantum gravity. We discuss a "resurgence mechanism" where the running dimensionless coupling responsible for the Higgs scalar mass first decreases in the ultraviolet regime and subsequently increases in the infrared regime. A gravity induced large anomal...
In many materials or equilibrium statistical systems the information of boundary conditions is lost inside the bulk of the material. In contrast, we describe here static classical statistical probability distributions for which bulk properties depend on boundary conditions. Such "static memory materials" can be realized if no unique equilibrium sta...
We investigate the formation and dissipation of large scale neutrino structures in cosmologies where the time evolution of dynamical dark energy is stopped by a growing neutrino mass. In models where the coupling between neutrinos and dark energy grows with the value of the scalar cosmon field, the evolution of neutrino lumps depends on the neutrin...
We investigate the formation and dissipation of large scale neutrino structures in cosmologies where the time evolution of dynamical dark energy is stopped by a growing neutrino mass. In models where the coupling between neutrinos and dark energy grows with the value of the scalar cosmon field, the evolution of neutrino lumps depends on the neutrin...
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetrie...
We propose a gauge invariant flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations, corresponding to a particular gauge fixing. The freedom in the precise choice of the macroscopic field can be exploited in order to keep the...
The observation of primordial cosmic fluctuations does not need a geometric
horizon $H^{-1}$, which is exceeded temporarily by the wavelength of
fluctuations. The primordial information can be protected against later thermal
washout even if all relevant wavelengths remain smaller than $H^{-1}$. This is
demonstrated by formulating the equations gove...
Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale k is varied. In the Einstein frame the quantum effective action corres...
Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale $k$ is varied. In the Einstein frame the quantum effective action corr...
We discuss the correlation function for the metric for homogeneous and isotropic cosmologies. The exact propagator equation determines the correlation function as the inverse of the second functional derivative of the quantum effective action, for which we take the Einstein-Hilbert approximation. This formulation relates the metric correlation func...