This paper initiates the systematic study of thermal field theory for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also of average angular momentum. The focus here is on scalar fields, although some results also apply to fields with arbitrary spins. A general technique to compute ensemble averages is provided. Moreover, path-integral methods are developed to study thermal Green’s functions (with an arbitrary number of points) in generic theories, which cover both the real-time and imaginary-time formalism. It is shown that, while the average angular momentum, like the chemical potentials, does not contribute positively to the Euclidean action, its negative contributions can be compensated by some other contributions that are instead positive, at least in some cases, e.g. when the chemical potentials vanish. As an application of the developed general formalism, it is shown that the production of particles weakly coupled to a rotating plasma can be significantly enhanced compared to the non-rotating case. The Higgs boson production through a portal coupling to a dark sector in the early universe is studied in some detail. The findings of this paper can also be useful, for example, to investigate the physics of rotating stars, ordinary and primordial black holes and more exotic compact objects.

Italy

Alberto Salvio

Scalar thermal field theory for a rotating plasma

It has been suggested that logarithmically enhanced infra-red loop corrections arising in theories with four derivatives correspond to a physical running of couplings, rendering quadratic gravity asymptotically free. We find that these effects depend on the gauge and on the field parameterisation. We compute physical on-shell amplitudes and find genuine infra-red log-enhanced loop corrections, that are process-dependent and cannot be absorbed into running couplings. As a byproduct, we show that the effective action of quadratic gravity at tree level and without matter fields is just Einstein gravity, so positivity bounds are satisfied despite the presence of ghosts.

Alessandro Strumia

Germany

Marco Vitti

Infra-red enhanced loops in quadratic gravity

<p>The Atacama Cosmology Telescope (ACT) has recently released new measurements and constraints on inflationary observables. In this paper, it is shown that a component of a dynamical affine connection, which is independent of the metric, can easily drive inflation in agreement with these observations. Such geometrical explanation of inflation is analyzed in detail here in the minimal model, including the predictions for the scalar spectral index <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> and its running <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math>, the amplitude of the scalar perturbations, and the tensor-to-scalar ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>r</mi></mrow></math>. Furthermore, this minimal model is shown to provide an inflationary attractor: arbitrary initial values of the kinetic energy density are dynamically attracted down to negligible values compared to the potential energy density in homogeneous and isotropic metrics. Also, the role of the Higgs boson during and after inflation is briefly discussed.</p>

Independent connection in action during inflation

Unimodular gravity addresses the old cosmological constant (CC) problem, explaining why such constant is not at least as large as the largest particle mass scale, but classically it is indistinguishable from ordinary gravity. Conversely, quantum physics may give us a way to distinguish the two theories. Thus, here the unimodular constraint is imposed on a non-perturbative and background-independent quantum version of quadratic gravity, which was recently formulated. It is shown that unimodularity does lead to different predictions for some inflationary quantum observables. Unimodular gravity per se does not solve the new CC problem (why the CC has the observed value?) even in this realization. To address this issue a multiverse made by different eras in a single big bang is considered and the observed scale of dark energy is explained anthropically.

Unimodular quadratic gravity and the cosmological constant

An explicit realistic model featuring a supercooled phase transition, which allows us to explain the background of gravitational waves recently detected by pulsar timing arrays, is constructed. In this model the phase transition corresponds to radiative symmetry breaking (and mass generation) in a dark sector featuring a dark photon associated with the broken symmetry. The completion of the transition is ensured by a non-minimal coupling between gravity and the order parameter and fast reheating occurs thanks to a preheating phase. Finally, it is also shown that the model leads to primordial black hole production.

Pulsar timing arrays and primordial black holes from a supercooled phase transition

It is shown that a component of the dynamical affine connection, which is independent of the metric, can drive inflation in agreement with observations. This provides a geometrical origin for the inflaton. It is also found that the decays of this field, which has spin 0 and odd parity, into Higgs bosons can reheat the Universe up to a sufficiently high temperature.

Inflating and reheating the Universe with an independent affine connection

In a geometrical approach to gravity the metric and the (gravitational) connection can be independent and one deals with metric-affine theories. We construct the most general action of metric-affine effective field theories, including a generic matter sector, where the connection does not carry additional dynamical fields. Among other things, this helps in identifying the complement set of effective field theories where there are other dynamical fields, which can have an interesting phenomenology. Within the latter set, we study in detail a vast class where the Holst invariant (the contraction of the curvature with the Levi-Civita antisymmetric tensor) is a dynamical pseudoscalar. In the Einstein–Cartan case (where the connection is metric compatible and fermions can be introduced) we also comment on the possible phenomenological role of dynamical dark photons from torsion and compute interactions of the above-mentioned pseudoscalar with a generic matter sector and the metric. Finally, we show that in an arbitrary realistic metric-affine theory featuring a generic matter sector the equivalence principle always emerges at low energies without the need to postulate it.

Gianfranco Pradisi

(In)equivalence of metric-affine and metric effective field theories

A totally asymptotically free QCD axion model, where all couplings flow to zero in the infinite energy limit, was recently formulated. A very interesting feature of this fundamental theory is the ability to predict some low-energy observables, like the masses of the extra fermions and scalars. Here we find and investigate a region of the parameter space where the Peccei-Quinn (PQ) symmetry is broken quantum mechanically through the Coleman-Weinberg mechanism. This results in an even more predictive framework: the axion sector features only two independent parameters (the PQ symmetry breaking scale and the QCD gauge coupling). In particular, we show that the PQ phase transition is strongly first order and can produce gravitational waves within the reach of future detectors. The predictivity of the model leads to a rigid dependence of the phase transition (like its duration and the nucleation temperature) and the gravitational wave spectrum on the PQ symmetry breaking scale and the QCD gauge coupling.

Anish Ghoshal

Gravitational waves from fundamental axion dynamics

We construct and study a fundamental field theory of the QCD axion: all couplings flow to zero in the infinite-energy limit realizing the totally asymptotically free (TAF) scenario. Some observable quantities (such as the masses of new quarks and scalars) are predicted at low energies by the TAF requirement in terms of gauge couplings and a vector-boson mass. Here the minimal model of this sort is explored; the axion sector is charged under an SU(2) gauge group and a dark photon appears at low energies. This model can be TAF and feature an absolutely stable vacuum at the same time.

A fundamental QCD axion model

Extensions of the Standard Model and general relativity featuring a UV fixed point can leave observable implications at accessible energies. Although mass parameters such as the Planck scale can appear through dimensional transmutation, all fundamental dimension-4 operators can (at least approximately) respect Weyl invariance at finite energy. An example is the Weyl-squared term, whose consistency and observational consequences are studied. This quasi-conformal scenario emerges from the UV complete quadratic gravity and is a possible framework for inflation. We find two realizations. In the first one the inflaton is a fundamental scalar with a quasi-conformal non-minimal coupling to the Ricci scalar. In this case the field excursion must not exceed the Planck mass by far. An example discussed in detail is hilltop inflation. In the second realization the inflaton is a pseudo-Goldstone boson (natural inflation). In this case we show how to obtain an elegant UV completion within an asymptotically free QCD-like theory, in which the inflaton is a composite scalar due to new strong dynamics. We also show how efficient reheating can occur. Unlike the natural inflation based on Einstein gravity, the tensor-to-scalar ratio is well below the current bound set by Planck. In both realizations mentioned above, the basic inflationary formulæ are computed analytically and, therefore, these possibilities can be used as simple benchmark models.