# Quantum Vacuum: Renormalization Group and Anomalies in Cosmology

Europe/Berlin
02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

### 02.430

#### Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Staudingerweg 9 / 2nd floor, 55128 Mainz
Description

The standard cosmological model is ΛCDM, in which the dominant dark energy component of the energy density of the universe is assumed to be a cosmological constant term, which is of the same form as quantum vacuum energy. This suggests that quantum effects may be relevant at cosmological scales, and leads to possible viable alternative models, which may soon be testable with increasingly more detailed data. At the same time the direct detection of gravitational waves by LIGO has ushered in the era of gravitational wave and multi-messenger astronomy, which allow Einstein’s classical General Relativity to be put through more stringent tests in strong gravitational fields and finally probe possible quantum effects in extreme compact stars and black holes.The subject of the one-week topical workshop will be quantum effects in gravitation and cosmology, in particular, focusing on the following issues:

• Conformal Invariance, the Conformal Anomaly, and Applications of the Effective Action of the Trace Anomaly to Cosmology;
• The a and c Theorems and Application of Renormalization Group Methods to Gravity and Cosmology;
• Gravitational Condensates, Dynamical Vacuum Energy and Tests of the ΛCDM Model;
• Quantum Effects in Black Holes, Quantum Information, and Prospects for Observational Tests of Black Hole Physics with Gravitational Waves by aLIGO;
• Gravitational Stability of the Standard Model Higgs Field at High Energies and in Inflation.

The following are Confirmed Participants at the Workshop:

• Bartelmann, Matthias
• Barvinsky, Andrei
• Coriano, Claudio
• Dvali, Giorgi
• Emelyanov, Slava
• Glavan, Drazen
• Ketov, Sergey
• Lopez Nacir, Diana
• Maglio, Matteo Maria
• Modesto, Leonardo
• Oshita, Naritaka
• Peter, Patrick
• Pirozhenko, Irina
• Popov, Fedor
• Prokopec, Tomislav
• Rachwal, Leslaw
• Ramos, Rudnei
• Reuter, Martin
• Skenderis, Kostas
• Starobinsky, Alexei
• Stergiou, Andreas
• Theisen, Stefan
• Turok, Neil
• Zanusso, Omar
Contact @ MITP : Kerstin Massmann
• Monday, 23 September
• 08:30 09:15
Registration 45m
• 09:15 09:30
Opening/Welcome 15m
• 09:30 10:45
Inflation and pre-inflation: present status and the simplest models 1h 15m

At the present state-of-the-art, the simplest inflationary models, based either on scalar fields in General Relativity or on modified f(R) gravity, which produce the best fit to all existing astronomical data require one, maximum two dimensionless parameters taken from observations only. The main discoveries expected for these models in future are discussed. Among them the most fundamental are primordial quantum gravitational waves generated during inflation. In one parametric models, including the original R+R^2 one, the definite prediction for the tensor-to-scalar ratio r=3(1-n_s)^2=0.004 follows. The role of one-loop quantum gravitational corrections to these models is considered. Inflation, as a metastable quantum state, had finite life-time, and differences in its duration in terms of the number of e-folds between various points of space can be determined with remarkable accuracy. In the models considered, the most generic predecessor of inflation is an anisotropic and inhomogeneous space-time near a generic space-like singularity. Since the transition from such space-time to the generalized quasi-de Sitter regime is generic, too, for inflation to begin inside a patch including the observable part of the Universe, causal connection inside the whole patch is not necessary. However, it becomes obligatory for a graceful exit from inflation in order to have practically the same number of e-folds during inflation inside this patch.

Speaker: Prof. Alexei Starobinsky
• 10:45 11:15
Coffee break 30m
• 11:15 12:05
A simple method for singularity avoidance and some consequences 50m

In a simple model (FLRW or Bianchi I minisuperspace and Wheeler De Witt), I discuss how the singularity can be avoided by defining quantum trajectories. This permits to classify clocks and could thus be related to the issue of time. Applying similar procedures to perturbations, the primordial power spectrum can be affected, leading to possibly detectable consequences in the cosmic microwave background or large scale structure data.

Speaker: Prof. Patrick Peter
• 12:05 12:20
Discussion Session 15m
• 14:00 14:50
Structure formation in standard and non-standard cosmology 50m

Non-linear cosmic structure formation can be described by a kinetic field theory for classical particle ensembles out of equilibrium. Building upon the path-integral formalism for classical mechanics, this theory structurally resembles a statistical quantum field theory. Its generating functional encapsulates the statistical properties of an initial state of the ensemble and the equation of motion of its particles. Interactions between the particles are described by an interaction operator, which can either be Taylor expanded into a perturbation series of Feynman diagrams, or approximated in a mean-field approach. For cosmology, the mean-field approach has proven to be quite successful, allowing to calculate non-linear power spectra for cosmic structures analytically quite deeply into the non-linear regime even at late times and small scales.

The conceptual simplicity and the flexibility of this kinetic field theory allow to apply it quite easily to different models for the dark matter, and to generalisations of gravity theory. Extended model or theory spaces can now be studied with little effort for their effects on non-linear cosmic structure formation. In the talk, I intend to (i) review kinetic field theory, (2) summarise some results for standard cosmology, and (iii) describe extensions towards axionic or axion-like dark-matter models and some generalisations of general relativity.

Speaker: Prof. Matthias Bartelmann
• 14:50 15:40
Dissipative dynamics of Inflation and the swampland models in gravity and supergravity 50m

Much has been discussed recently about the swampland and inflation. An effective field theory able to describe inflation for instance, should satisfy some very restrict set of conjectures, the swampland conjectures, such to have a consistent ultraviolet completion and to be described as an effective field theory, in particular, coming from string theory. It is shown here a recent construction of such an effective field theory from fully renormalizable quantum field theory that is able to describe inflation in a strong dissipative regime, evading all the swampland conjectures. This construction naturally leads to a super-Hubble inflaton mass and sub-Planckian field excursions, which is thus technically natural and consistent with a high-energy completion within a theory of quantum gravity.

Speaker: Rudnei Ramos
• 15:40 16:10
Coffee break 30m
• 16:10 17:00
On the equivalence between Higgs and Starobinsky inflationary models in gravity and supergravity 50m
Speaker: Sergei Ketov
• 17:00 17:50
Cosmological phase transitions with cosmic impurities 50m
Speaker: Naritaka Oshita
• Tuesday, 24 September
• 09:30 10:45
Unitarity and area-law entropy bound: Black holes, Solitons and Instantons 1h 15m
Speaker: Georgi Dvali
• 10:45 11:15
Coffee break 30m
• 11:15 12:05
Background Independent Quantum Field Theory and Gravitating Vacuum Fluctuations 50m

The cosmological constant induced by quantum  vacuum fluctuations is reconsidered within a manifestly Background Independent approach to quantum field theory and quantum gravity. It is shown that in absence of any distinguished rigid spacetime they do not give rise to the notorious “cosmological constant problem”. The  nonperturbative functional renormalization group for gravity plays a central role, but no specific UV behavior (e. g. Asymptotic Safety) is required.

Speaker: Martin Reuter
• 12:05 12:20
Discussion Session 15m
• 14:00 14:50
Macroscopic Effects of the Conformal Anomaly 50m

Classical General Relativity receives an infrared relevant modification from the conformal anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective action associated with the conformal anomaly is expressible in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. This leads to the prediction of scalar gravitational wave solutions—a spin-0 breather mode— in addition to the transversely polarized tensor waves of the classical Einstein theory. It also implies generically large quantum back reaction effects and conformal correlators in the vicinity of black hole horizons which are relevant to the formation of a non-singular interior, as well as an additional scalar degree of freedom in cosmology, coupling to dynamical dark energy.

Speaker: Emil Mottola
• 14:50 15:40
Some aspects of the Weyl anomaly 50m
Speaker: Tomislav Prokopec
• 15:40 16:10
Coffee break 30m
• 16:10 17:00
Quantum Field Theory in the static patch of de Sitter 50m
Speaker: Fedor Popov
• 17:00 17:30
Discussion
• Wednesday, 25 September
• 09:30 10:45
Quantum Universe 1h 15m
Speaker: Neil Turok
• 10:45 11:15
Coffee break 30m
• 11:15 12:05
Anomaly-induced effective action of gravity: some new results 50m

The effective action of gravity is supposed to contain the main information about quantum corrections to gravity. However, in many cases it cannot be calculated exactly. A remarkable and important exception is the effective action of vacuum for massless and conformal-invariant matter fields. In this case the effective action can be easily derived by integrating the trace anomaly. The integration constant is an unknown conformal functional of the background metric, but for zero-order cosmology this functional is irrelevant and the solution becomes exact. Until recently the integrated anomaly was known only in dimensions d=2 and d=4, but recently we achieved the explicit result for d=6, which confirms the universal functional
structure of the effective action.

Speaker: Ilya Shapiro
• 12:05 12:20
Discussion Session 15m
• 14:00 14:50
Soft photon theorems and infrared divergences in QED 50m

One of the striking features of QED is the appearance of infrared divergences in the presence of charged particles. We analyze the effect of infrared divergences in the derivation of soft photon theorems. The infrared pathologies may be very relevant for understanding the black hole information paradox, but also raise some questions about the consistency of the whole theory.
But if the schedule is too tight I wouldn't mind to cancel it.

Speaker: Manuel Asorey
• 14:50 15:40
Nonlocal Quantum Gravity 50m

Starting from the general class of super-renormalizable theories studied by M. Asorey, J.L. Lopetz, and I.L. Shapiro in 1996, we present a weakly nonlocal gravitational theory unitary and finite at quantum level in the quantum field theory framework (the theory is also compatible with causality because a Shapiro's time advance never occurs.) As a consequence of finiteness, the Weyl's anomaly is not present and the theory turns out to be conformal invariant at classical as well at quantum level. Therefore, nonlocal quantum gravity is a conformal invariant theory in the spontaneously broken phase of the Weyl symmetry. As a result, Weyl conformal symmetry solves the black hole's singularity issue and cosmological singularity problem, otherwise unavoidable in any local or non-local gravitational theory. At classical level, all Einstein manifolds are stable at linear and non linear level if they are stable in General relativity. The generalization of the theory in presence of matter is the topic of the current research, hence it will be discussed only briefly.

Speaker: Leonardo Modesto
• 15:40 16:10
Coffee break 30m
• 16:10 17:00
Classical/Quantum Boundary Conditions at the Beginning/End of Time 50m

I will motivate and discuss certain boundary conditions at the beginning and/or end of time, and some of their theoretical and observational consequences (particularly for evaluating the effect of the conformal anomaly in cosmology).

Speaker: Latham Boyle
• 17:00 17:30
Discussion
• Thursday, 26 September
• 09:30 10:45
Holographic cosmology and the puzzles of Hot Big Bang cosmology 1h 15m
Speaker: Kostas Skenderis
• 10:45 11:15
Coffee break 30m
• 11:15 12:05
Modified gravity models: renormalization and cosmological implications 50m

We consider two classes of modified gravity models characterized by violation of Lorentz symmetry. One class of models is motivated by the search for a local renormalizable quantum gravity perturbatively consistent in UV domain. It consists of projectable Horava-Lifshitz models for which we show perturbative renormalizability in arbitrary dimension and prove their asymptotic freedom in the toy-model case of (2+1)-dimensional spacetime. Renormalization group flow is also built in (3+1)-dimensional Horava gravity for two of its coupling constants, indicating a potential domain of its asymptotic freedom for all seven couplings of this theory. Another class of models is motivated by the search for a possible mechanism of inflation and cosmological acceleration. This is the generalized unimodular gravity sharing in common with Horava models a peculiar kinematical restriction on the ADM lapse function, which manifests itself in the form of a special type of dark perfect fluid composed entirely from the metric sector of the theory and having a time dependent equation of state. Extra degree of freedom in this model -- scalar graviton -- has a nontrivial domain of unitarity and can drive inflationary scenario with scalar and tensor power spectra fitting observations. Quite remarkably, this model satisfies naturalness criterion -- O(1) magnitude of all theory parameters. This is because a typically accepted exponentially big e-folding factor, $e^{N}$, $N\sim 60$, for this model enters a special expression for tensor to scalar ratio $r\sim e^{-N(1-n_s)}\simeq 10^{-3}$, $n_s\simeq 0.96$ being the scalar red tilt, and easily satisfies known phenomenological bounds.

Speaker: Andrei Barvinsky
• 12:05 12:20
Discussion Session 15m
• 14:00 14:50
Conformal Invariance and Quantization of Conformal Gravity 50m
Speaker: Leslaw Rachwal
• 14:50 15:40
Anomaly Actions with axions and dilatons 50m

We review the structure of the local and nonlocal anomaly actions introduced in several scenarios where chiral and conformal anomalies play a key role.

Speaker: Claudio Coriano
• 15:40 16:10
Coffee break 30m
• 16:10 17:00
Matching CFT tensor correlators to perturbation theory 50m

We review a recent analysis of the solutions of the Conformal Ward Identities in general CFTs and their matching to free field theories. We compare these results with those predicted by the Conformal Anomaly Action.

Speaker: Matteo Maria Maglio
• 17:00 17:30
Discussion
• Friday, 27 September
• 09:30 10:45
The Weyl anomaly and some of its uses 1h 15m
Speaker: Stefan Theisen
• 10:45 11:15
Coffee break 30m
• 11:15 12:05
To the sphere and back again: de Sitter infrared correlators at NTLO in 1/N 50m
Speaker: Diana Lopez Nacir
• 12:05 12:20
Discussion Session 15m
• 13:50 14:40
The Minkowski quantum vacuum does not gravitate 50m
Speaker: Slava Emelyanov
• 14:40 15:30
Vacuum energy in the background of lower dimensional field or field living in half spaces 50m
Speaker: Irina Pirozhenko
• 15:30 16:00
Coffee break 30m
• 16:00 16:50
One-loop E&M correlators of SQED in power-law inflation 50m

Vector fields are insensitive to the rapid expansion of the primordial inflating universe due to their conformal coupling. However, they may couple to other light fields that are sensitive to the expansion and experience huge gravitational particle production, such as the complex scalar. In that case the vector field can develop large electric and magnetic field fluctuations induced by the gravitationaly enhanced charge fluctuations. I will present a computation of the one-loop corrections to the electric and magnetic field correlators of SQED in power-law inflation. One-loop corrections dwarf the tree-level result, and the slow-roll corrections very soon become large.

Speaker: Drazen Glavan
• 16:50 17:30
Unequal time correlator of scalar fields in de Sitter spacetime from the effective stochastic approach 40m

Applying the stochastic formalism to the test scalar field in de Sitter spacetime, we study in more details the effective theory of their infrared modes described by a Langevin equation. It corresponds to the well-known model A in statistical physics. We use the formulation in terms of a one dimensional supersymmetric field theory. We compute the unequal time field correlator at large (superhorizon) time separations in a 1/N expansion at NLO and compare with existing quantum field theory computation. We then attempt to get a result for finite N using the non perturbative renormalization group on this one dimensional theory, going beyond the local potential approximation.

Speaker: Gabriel Moreau (Université Paris Diderot)
• 17:30 18:00
Discussion: Closing