Search

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 whether these models enhance the power of matter fluctuations, leading {\it de facto} to a worsening of the tension with the large-scale structure measurements. We address this pivotal question in the context of several early dark energy (EDE) models, considering also in some cases a coupling between dark energy and dark matter, and the effect of massive neutrinos. We fit them using the Planck 2018 likelihoods, the supernovae of Type Ia from the Pantheon compilation and data on baryon acoustic oscillations. We find that ultra-light axion-like (ULA) EDE can actually alleviate the $H_0$ tension without increasing the values of $\sigma_{12}$ with respect to those found in the $\Lambda$CDM, whereas EDE with an exponential potential does not have any impact on the tensions. A coupling in the dark sector tends to enhance the clustering of matter, and the data limit a lot the influence of massive neutrinos, since the upper bounds on the sum of their masses are too close to those obtained in the standard model. We find that in the best case, namely ULA, the Hubble tension is reduced to $\sim 2\sigma$., Comment: 27 pages, 16 figures, 8 tables. Version accepted for publication in Phys. Rev. D

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 viewed as generalized Ising models on a square lattice and therefore as classical statistical systems. As quantum field theories they are quantum systems. Thus quantum mechanics emerges from classical statistics. As an explicit example for an interacting fermionic quantum field theory we describe a type of discretized Thirring model as a cellular automaton. The updating rule of the automaton is encoded in the step evolution operator that can be expressed in terms of fermionic annihilation and creation operators. The complex structure of quantum mechanics is associated to particle -- hole transformations. The naive continuum limit exhibits Lorentz symmetry. We exploit the equivalence to quantum field theory in order to show how quantum concepts as wave functions, density matrix, non-commuting operators for observables and similarity transformations are convenient and useful concepts for the description of probabilistic cellular automata., Comment: Clearer structure with focus on key points and appendices, 46 pages, 4 figures

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 renormalizable quantum field theory of gravity. If the proposed scaling solution is confirmed beyond our approximations asymptotic freedom is a viable alternative to asymptotic safety for quantum gravity., Comment: 19 pages, 10 figures, version published in JHEP

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 initial conditions. In turn, the probabilistic automaton is equivalent to the classical statistical system of a generalized Ising model. For a description of the probabilistic information at any given time quantum concepts as wave functions and non-commuting operators for observables emerge naturally. Quantum mechanics can be understood as a particular case of classical statistics. This offers prospects to realize aspects of quantum computing in the form of probabilistic classical computing., 15 pages, 1 figure

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 increase of a scalar field which sets the scale of all masses. We construct the primordial flat frame for standard models of inflation as Starobinsky inflation or chaotic inflation. In particular, we discuss the evolution of inhomogeneous solutions in the neighborhood of the homogeneous isotropic background solution and their relation to the observable primordial fluctuation spectrum. If the propagators for the graviton and scalar field remain regular, our observed inhomogeneous Universe can be extrapolated back to the infinite past in physical time. In this case there is no physical big-bang singularity -- the latter reflects only a singular choice of ``field coordinates". Independently of the issue of singularity the primordial flat frame offers a new view on the physical properties of the inflationary universe, which can be characterized as a very slowly evolving almost empty vacuum state with approximate scale symmetry., additional discussion of inhomogeneous cosmological solutions and big bang singularity , 31 pages

International audience; Cosmological data still allow for the presence of a non-negligible amount of dark energy at very high redshifts, namely during the matter- and radiation-dominated epochs. This is the so-called early dark energy (EDE), which could help to mitigate the tensions that affect the standard model of cosmology since (i) it reduces the sound horizon at the baryon-drag epoch, hence giving room to higher values of H0 than those found in the ΛCDM; and (ii) it could potentially decrease the number of large-scale structures in the Universe due its negative pressure and its inability to cluster efficiently for large enough values of its sound speed. Here we put constraints on the fraction of EDE using two methods: first, we use a perfect fluid parameterization that produces plateaux in Ωede(z) during the relativistic and non-relativistic matter-dominated eras. Second, we apply a tomographic approach to constrain the EDE density in redshift bins, which allows us to reconstruct the evolution of the EDE fraction before and after the decoupling of the Cosmic Microwave Background (CMB) photons. We have employed Planck data 2018, the Pantheon compilation of supernovae of Type Ia (SNIa), data on galaxy clustering, the prior on the absolute magnitude of SNIa by SH0ES, and weak lensing data from KiDS+VIKING-450 and DES-Y1. Using our minimal parameterization we find that EDE is not able to loosen the cosmological tensions, and show that the constraints on the EDE fraction weaken considerably when its sound speed takes lower values. Thanks to our binned analysis we are able to put tight constraints on the EDE fraction around the CMB decoupling time, ≲ 0.4% at 2σ c.l. We confirm previous results that a significant EDE fraction in the radiation-dominated epoch loosens the H0 tension, but tends to worsen the tension for σ8. A subsequent presence of EDE in the matter-dominated era helps to alleviate this problem. When both the SH0ES prior and weak lensing data are considered in the fitting analysis in combination with data from CMB, SNIa and baryon acoustic oscillations, the EDE fractions are constrained to be ≲ 2.6% in the radiation-dominated epoch and ≲ 1.5% in the redshift range z ∈ (100, 1000) at 2σ c.l. The two tensions remain with a statistical significance of ∽ 2 − 3σ c.l. This contribution to the proceedings of the CM3 parallel session of the MG16 Marcel Grossmann virtual Conference: “Status of the H0 and σ8 tensions: theoretical models and model-independent constraints” is based on the paper arXiv:2107.11065, which appeared in the arXiv shortly after my talk of July 6th 2021.

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 standard inflationary cosmological models is the lightlike vacuum. Towards the beginning, the Universe is almost scale invariant. This is best seen by an appropriate choice of the metric field -- the primordial flat frame -- for which the beginning of a homogeneous metric is flat Minkowski space. We suggest that our observed inhomogeneous Universe can evolve from the lightlike vacuum in the infinite past, and therefore can have lasted eternally. Then no physical big bang singularity is present., Comment: Additional remarks on inhomogeneities, 8 pages

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 alleviate the $H_0$ tension. We constrain the EDE fraction using two approaches: first, we use a fluid parameterization that mimics the plateaux of the dominant components in the past. An alternative tomographic approach constrains the EDE density in binned redshift intervals. This allows us to reconstruct $\Omega_{de}(z)$ before and after the decoupling of the CMB photons. We have employed Planck data 2018, the Pantheon supernovae of Type Ia (SNIa), galaxy clustering data, the prior on the absolute magnitude of SNIa by SH0ES, and weak lensing (WL) data from KiDS+VIKING-450 and DES-Y1. When we use a minimal parameterization mimicking the background plateaux, EDE has only a small impact on current cosmological tensions. The constraints on the EDE fraction weaken considerably when its sound speed is allowed to vary. By means of our binned analysis we put very tight constraints on the EDE fraction around the CMB decoupling time, $\lesssim 0.4\%$ at $2\sigma$ c.l. We confirm previous results that a significant EDE fraction in the radiation-dominated epoch (RDE) loosens the $H_0$ tension, but tends to worsen the $\sigma_8$ one. The presence of EDE in the matter-dominated era helps to alleviate this issue. When the SH0ES prior and WL data are considered in the fitting analysis in combination with data from CMB, SNIa and baryon acoustic oscillations, the EDE fractions are constrained to be $\lesssim 2.6\%$ in the RDE epoch and $\lesssim 1.5\%$ in the redshift range $z\in (100,1000)$ at $2\sigma$ c.l. The tensions remain at $\sim 2-3\sigma$ c.l., Comment: 17 pages, 5 figures, 5 tables. Version accepted for publication in PRD

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 and times in Planck units. We propose an approximation to the effective action with up to two derivatives. For a suitable range of parameters the universe approaches for large times stable Minkowski space. For late cosmology the model predicts dynamical dark energy and provides for a candidate for dark matter. Early cosmology is characterized by an inflationary epoch. The beginning of the universe in the infinite past is great emptiness, corresponding to an ultraviolet fixed point with the associated quantum scale symmetry. The beginning universe is a vacuum state with vanishing expectation values and finite non-vanishing correlation functions for the fluctuations of all fields. There is no physical big bang singularity., Comment: Further explanations, new references, 63 pages, 9 figures

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 fields. For the local gauge symmetry we take the non-compact group SO(4,\,$\mathbb{C}$). The particular representation of the vector field permits us to implement diffeomorphism invariant kinetic terms. Geometry and general relativity emerge at large distances due to a spontaneous breaking of the gauge symmetry which induces masses for the gauge bosons. The difference between time and space arises directly from this spontaneous symmetry breaking. For a euclidean metric all fields have a standard propagator at high momenta. Analytic continuation to a Minkowski-metric is achieved by a change of field values. We conjecture that this type of model could be consistent with unitarity and well behaved in the short distance limit., Comment: Extended discussion of the role of quantum fluctuations, 28 pages

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 equations. Such theories are highly predictive since all relevant parameters for deviations from the exact scaling solution vanish. Realistic particle physics and quantum gravity are compatible with this setting. The non-linear restrictions for scaling solutions can explain properties as an asymptotically vanishing cosmological constant or dynamical dark energy that would seem to need fine tuning of parameters from a perturbative viewpoint. As an example we discuss a pregeometry based on a diffeomorphism invariant Yang-Mills theory. It is a candidate for an ultraviolet completion of quantum gravity with a well behaved graviton propagator at short distances., Extended material, more concise discussion, 12 pages

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 cellular automata with probabilistic initial conditions admit a description in the formalism of quantum mechanics. Our model exhibits interesting features as spontaneous symmetry breaking or solitons. The same model can be formulated as a generalized Ising model. This euclidean lattice model can be investigated by standard techniques of statistical physics as Monte Carlo simulations. Our model is an example how quantum mechanics emerges from classical statistics., Additional clarifications, 14 pages, 5 figures

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 antiferromagnetic phase near the onset of local antiferromagnetic order, the interaction of the electrons is indeed well described by the exchange of collective bosonic degrees of freedom. The residual four-fermion vertex after the subtraction of the bosonic-exchange contribution is small. We propose that similar partial bosonization techniques can improve the accuracy of renormalization flow studies also for the case of competing order.

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 transformation of the metric to the Einstein frame is singular at the crossing point of a vanishing scalar field. No physical singularity is present for these solutions. Within general models with no more than two derivatives we find that the possibility of a crossing of the "Big Bang singularity" is not generic. It needs a tuning of model parameters. The present models are not a realistic description of the Universe since they fail to render acceptable inhomogeneities., further precisions on inhomogeneous cosmologies, 11 pages

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 quantum gates can be learned as a change of parameters for neural network dynamics. Our proposal for probabilistic computing goes beyond Markov chains, which are based on transition probabilities. Constraints on classical probability distributions relate changes made in one part of the system to other parts, similar to entangled quantum systems., Comment: 9 pages, 8 figures

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 only the standard model particles contribute to the running of couplings below the Planck mass, the observed $M_H\sim125\,{\rm GeV}$ results in the prediction for the top quark mass $M_t\sim 171\,{\rm GeV}$, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of a $SU(2)$ triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to $M_t\sim 172.5\,{\rm GeV}$ for a triplet mass of $M_\Delta\sim 10^8{\rm GeV}$. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of $M_t$ due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability., Comment: 18 pages, 16 figures

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 arbitrary gauge field can be mapped to an associated gauge invariant field. An effective action that depends on gauge-invariant fields becomes a gauge-invariant functional of arbitrary gauge fields by associating to every gauge field the corresponding gauge-invariant field. The gauge-invariant effective action can be obtained from an implicit functional integral with a suitable "physical gauge fixing". We generalize this concept to the gauge-invariant effective average action or flowing action, which involves an infrared cutoff. It obeys a gauge-invariant functional flow equation. We demonstrate the use of this flow equation by a simple computation of the running gauge coupling and propagator in pure $SU(N)$-Yang-Mills theory., Comment: new references, 28 pages

We propose a closed gauge-invariant functional 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. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schr\"odinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space., Comment: additional material and references, 38 pages

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 corresponding to the scaling solutions becomes independent of $k$. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity., 7 pages, 4 figures

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 scenario for quantum gravity? For the standard model and a large class of theories with additional particles the quartic Higgs coupling is an irrelevant parameter at the ultraviolet fixed point. This makes the ratio between the Higgs boson and the top-quark mass predictable., 43 pages, 11 figures, version published in PRD

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 injection bounds. The dark matter particles would be clumped in objects in the solar mass range with typical sizes of the order of the solar system. Consequences for direct dark matter searches are important., 14 pages, 10 figures, published version, added clarifications and references, corrected typos

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 of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

Am Anfang des Universums war fast nichts –Vakuum mit nur seltenen Elementarteilchen, die sich mit Lichtgeschwindigkeit bewegten. Erst spater wurde das Plasma aus Elementarteilchen erzeugt, das unserem gangigen Urknallbild zugrunde liegt. Wie lange diese Anfangsperiode dauerte, hangt vom Konzept der Zeit ab. „Physikalische Uhren“ tickten unendlich oft, das Universum gab es schon immer. Nur in der unphysikalischen „Eigenzeit“ schrumpft die Anfangsperiode auf winzige Bruchteile von Sekunden zusammen.

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: describe briefly the main methods or treatments applied, (3) Results: summarize the article’s main findings, (4) Conclusion: indicate the main conclusions or interpretations. The abstract should be an objective representation of the article, it must not contain results which are not presented and substantiated in the main text and should not exaggerate the main conclusions.

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 renormalisation group (FRG). Here, the confinement of the transverse direction is imposed by means of periodic boundary conditions. We calculate the equation of state, the gap parameter at zero temperature and the superfluid transition temperature across a wide range of transversal confinement length scales. Particular emphasis is put on the determination of the finite temperature phase diagram for different confinement length scales. In the end, our results are compared with recent experimental observations and we discuss them in the context of other theoretical works., Comment: 23 pages, 12 figures; additional explanations and comments, corrected typos, new and updated references; very close to published version

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 couplings avoiding instabilities. This leads to a graviton barrier limiting the maximal growth of the effective potential for large values of scalar fields. In the presence of this barrier, variable gravity with a field dependent Planck mass can solve the cosmological constant problem by a cosmological runaway solution. We discuss the naturalness of tiny values of the cosmological constant and cosmon mass due to a strong attraction towards an infrared fixed point., Comment: new references, 9 pages , 3 figures

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 similar screened objects, without the need for any particular feature in the spectrum of primordial density fluctuations generated during inflation. We discuss whether such primordial black holes can constitute the total dark matter component in the Universe., Comment: 6 pages, 1 figure, published version, added clarifications and references, corrected typos

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 materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins which may, in turn, correspond to continuous variables or fields. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases., Comment: New discussion of Bells inequalities and no cloning theorem for classical probabilistic systems, 51 pages, 3 figures

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 field is an irrelevant coupling at the asymptotically safe ultraviolet fixed point of quantum gravity. This renders the ratio between the masses of the Higgs boson and top quark predictable. If the flow of couplings below the Planck scale is approximated by the Standard Model, this prediction is consistent with the observed value. The quadratic term in the Higgs potential is irrelevant if the strength of gravity at short distances exceeds a bound that is determined here as a function of the particle content. In this event, a tiny value of the ratio between the Fermi scale and the Planck scale is predicted., Comment: 18 pages, 5 figures, Version published in PRD

We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a non-trivial minimum. For theories with dilatation anomaly one needs as a non-trivial "cosmon condition" that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short-distance renormalization group behavior of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible., Original preprint from 1987, 15 pages

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 Einstein-frame formulation the potential can be expressed in terms of Lambert functions, interpolating between a power-law inflationary potential and a mixed-quintessence potential. For two natural heating scenarios, the transition between inflation and radiation domination proceeds through a "graceful reheating" stage. The radiation temperature significantly exceeds the temperature of big bang nucleosynthesis. For this type of model, the observable consequences of the heating process can be summarized in a single parameter, the heating efficiency. Our quantitative analysis of compatibility with cosmological observations reveals the existence of realistic models able to describe the whole history of the Universe using only a single metric and scalar field and involving just a small number of order one parameters., 22 pages, 13 figures, matches the version published in PRD, added clarifications and references, corrected typos

Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. The functional renormalization flow drives a positive cosmological constant towards zero, solving the cosmological constant problem without the need to tune parameters. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable gravity we find that the potential increases asymptotically at most quadratically with the scalar field. With effective Planck mass proportional to the scalar field, the solutions of the derived cosmological equations lead to an asymptotically vanishing cosmological "constant" in the infinite future, providing for dynamical dark energy in the present cosmological epoch. Beyond a solution of the cosmological constant problem, our simplified computation also entails a sizeable positive graviton-induced anomalous dimension for the quartic Higgs coupling in the ultraviolet regime, substantiating the successful prediction of the Higgs boson mass within the asymptotic safety scenario for quantum gravity., extended discussion, new references, 14 pages, 2 figures

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 present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice., small changes, 17 pages

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 probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity., Comment: New section with example of three-spin chain realising quantum gates, 53 pages. arXiv admin note: text overlap with arXiv:1611.04820

We derive a new exact evolution equation for the scale dependence of an effective action. The corresponding equation for the effective potential permits a useful truncation. This allows one to deal with the infrared problems of theories with massless modes in less than four dimensions which are relevant for the high temperature phase transition in particle physics or the computation of critical exponents in statistical mechanics., Comment: Original manuscript from 1992, 5 pages

Linear lattice gauge theory is based on link variables that are arbitrary complex or real $N\times N$ matrices, in distinction to the usual (non-linear) formulation with unitary or orthogonal matrices. For a large region in parameter space both formulations belong to the same universality class, such that the continuum limits of linear and non-linear lattice gauge theory are identical. We explore if the linear formulation can help to find a non-perturbative continuum limit formulated in terms of continuum fields. Linear lattice gauge theory exhibits excitations beyond the gauge fields. In the linear formulation the running gauge coupling corresponds to the flow of the minimum of a ``link potential''. This minimum occurs for a nonzero value of the link variable $l_0$ in the perturbative regime, while $l_0$ vanishes in the confinement regime. We discuss a flow equation for the scale dependent location of the minimum $l_0(k)$., Comment: extended discussion of relation to standard gauge theories, 13 pages. arXiv admin note: substantial text overlap with arXiv:1212.3507

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 anomalous dimension plays a crucial role for the required "self-tuned criticality" in the ultraviolet regime beyond the Planck scale., Version published in Phys.Lett. B; 5 pages, 1 figure

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 neutrino mass. For small masses the lumps form and dissolve periodically, leaving only a small backreaction of the neutrino structures on the cosmic evolution. This process heats the neutrinos to temperatures much above the photon temperature such that neutrinos acquire again an almost relativistic equation of state. The present equation of state of the combined cosmon-neutrino fluid is very close to -1. In contrast, for larger neutrino masses the lumps become stable. The highly concentrated neutrino structures entail a large backreaction similar to the case of a constant neutrino-cosmon coupling. A present average neutrino mass of around 0.5 eV seems so far compatible with observation. For masses lower than this value, neutrino induced gravitational potentials remain small, making the lumps difficult to detect., 19 pages, 10 figures, 3 tables