Large primordial lepton flavor asymmetries with almost vanishing total baryon-minus-lepton number can evade the usual BBN and CMB constraints if neutrino oscillations lead to perfect flavor equilibration. Solving the momentum averaged quantum kinetic equations (QKEs) describing neutrino oscillations and interactions, we perform the first systematic investigation of this scenario, uncovering a rich flavor structure in stark contradiction to the assumption of simple flavor equilibration. We find (i) a particular direction in flavor space, ∆$\textit{n}$ ≃ – 2/3 (– 1)∆$\textit{n}$ for normal (inverted) neutrino mass hierarchy, in which the flavor equilibration is efficient and primordial asymmetries are essentially unconstrained, (ii) a minimal washout factor, $$ {\left.\Delta {n}_e^2\right|}_{\textrm{BBN}} $$ $\textit{≤}$ 0.03 (0.016) ∑ $$ {\left.\Delta {n}_{\alpha}^2\right|}_{\textrm{ini}} $$ yielding a conservative estimate for the allowed primordial asymmetries in a generic flavor direction, and (iii) particularly strong or weak washout if one of the initial flavor asymmetries vanishes due to non-adiabatic muon- or electron-driven MSW transitions. These results open up the possibility of a first-order QCD phase transition facilitated by large lepton asymmetries as well as baryogenesis from large and compensated ∆$\textit{n}$ = ∆$\textit{n}$ asymmetries. Our systematic approach of deriving momentum averaged QKEs includes collision terms beyond the damping approximation, energy transfer between the neutrino and electron-photon plasma, and provides a fast and reliable way to investigate the impact of primordial lepton asymmetries at the time of BBN. We publicly release the Mathematica code COFLASY-M on https://github.com/mariofnavarro/COFLASY which solves the QKEs numerically.

Switzerland

Valerie Domcke

Miguel Escudero

United Kingdom

Mario Navarro

United States

Stefan Sandner

Lepton flavor asymmetries: from the early Universe to BBN

Sterile neutrinos with masses at the keV scale and mixing to the active neutrinos offer an elegant explanation of the observed dark matter (DM) density. However, the very same mixing inevitably leads to radiative photon emission and the non-observation of such peaked X-ray lines rules out this minimal sterile neutrino DM hypothesis. We show that in the context of the Standard Model effective field theory with sterile neutrinos (νSMEFT), higher dimensional operators can produce sterile neutrino DM in a broad range of parameter space. In particular, νSMEFT interactions can open the large mixing parameter space due to their destructive interference, through operator mixing or matching, in the X-ray emission. We also find that, even in the zero mixing limit, the DM density can always be explained by νSMEFT operators. The testability of the studied νSMEFT operators in searches for electric dipole moments, neutrinoless double beta decay, and pion decay measurements is discussed.

Kaori Fuyuto

Jacky Kumar

Emanuele Mereghetti

Chen Sun

Sterile neutrino dark matter within the νSMEFT

In this paper, the existence of a massive dark photon, associated with a new gauge group is considered. The dark photon can be kinetically mixed with the photon. To study some applications, the thermo field dynamics formalism is used. Exploring the topological structure of this approach, the influence of dark photons on the Stefan–Boltzmann law and the Casimir effect at zero and finite temperature is calculated.

Brazil

V. Prata

A. Santos

Canada

Faqir Khanna

Stefan–Boltzmann law and Casimir effect for dark photons

The cosmic microwave background (CMB) has proven to be an invaluable tool for studying the properties and interactions of neutrinos, providing insight not only into the sum of neutrino masses but also the free streaming nature of neutrinos prior to recombination. The CMB is a particularly powerful probe of new eV-scale bosons interacting with neutrinos, as these particles can thermalize with neutrinos via the inverse decay process,  $$\nu \bar{\nu } \rightarrow X$$  <math> <mrow> <mi>ν</mi> <mover> <mrow> <mi>ν</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>→</mo> <mi>X</mi> </mrow> </math>  , and suppress neutrino free streaming near recombination – even for couplings as small as  $$\lambda _{\nu } \sim {\mathcal {O}}(10^{-13})$$  <math> <mrow> <msub> <mi>λ</mi> <mi>ν</mi> </msub> <mo>∼</mo> <mi>O</mi> <mrow> <mo>(</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>13</mn> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </math>  . Here, we revisit CMB constraints on such bosons, improving upon a number of approximations previously adopted in the literature and generalizing the constraints to a broader class of models. This includes scenarios in which the boson is either spin-0 or spin-1, the number of interacting neutrinos is either  $$N_{\textrm{int}} = 1,2 $$  <math> <mrow> <msub> <mi>N</mi> <mtext>int</mtext> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </math>   or 3, and the case in which a primordial abundance of the species is present. We apply these bounds to well-motivated models, such as the singlet majoron model or a light  $$U(1)_{L_{\mu }-L_{\tau }}$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <msub> <mi>L</mi> <mi>μ</mi> </msub> <mo>-</mo> <msub> <mi>L</mi> <mi>τ</mi> </msub> </mrow> </msub> </mrow> </math>   gauge boson, and find that they represent the leading constraints for masses  $$m_X\sim 1\, {\textrm{eV}}$$  <math> <mrow> <msub> <mi>m</mi> <mi>X</mi> </msub> <mo>∼</mo> <mn>1</mn> <mspace width="0.166667em"></mspace> <mtext>eV</mtext> </mrow> </math>  . Finally, we revisit the extent to which neutrino-philic bosons can ameliorate the Hubble tension, and find that recent improvements in the understanding of how such bosons damp neutrino free streaming reduces the previously found success of this proposal.

Spain

CERN

Netherlands

Samuel Witte

Precision CMB constraints on eV-scale bosons coupled to neutrinos

At present, cosmological observations set the most stringent bound on the neutrino mass scale. Within the standard cosmological model (ΛCDM), the Planck collaboration reports ∑m  v  &lt; 0.12 eV at 95 % CL. This bound, taken at face value, excludes many neutrino mass models. However, unstable neutrinos, with lifetimes shorter than the age of the universe τ  ν  ≲ t  U , represent a particle physics avenue to relax this constraint. Motivated by this fact, we present a taxonomy of neutrino decay modes, categorizing them in terms of particle content and final decay products. Taking into account the relevant phenomenological bounds, our analysis shows that 2-body decaying neutrinos into BSM particles are a promising option to relax cosmological neutrino mass bounds. We then build a simple extension of the type I seesaw scenario by adding one sterile state ν 4 and a Goldstone boson ϕ, in which ν  i  → ν 4 ϕ decays can loosen the neutrino mass bounds up to ∑m  v  ∼ 1 eV, without spoiling the light neutrino mass generation mechanism. Remarkably, this is possible for a large range of the right-handed neutrino masses, from the electroweak up to the GUT scale. We successfully implement this idea in the context of minimal neutrino mass models based on a U(1) μ−τ  flavor symmetry, which are otherwise in tension with the current bound on ∑m  v .

Jacobo Lopez-Pavon

Nuria Rius

Relaxing cosmological neutrino mass bounds with unstable neutrinos

The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established, and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.

S.C. Ulhoa

R.G.G. Amorim

J.S. da Cruz Filho

A.F. Santos

F.C. Khanna

Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

Gravitons are described by the propagator in teleparallel gravity in nearly flat space-time. Finite temperature is introduced by using Thermofield Dynamics formalism. The gravitational Casimir effect and Stefan-Boltzmann law are calculated as a function of temperature. Then an equation of state for gravitons is determined.

T.F. Furtado

On Gravitational Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

We use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzmann law and Casimir effect, both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) formalism and the quantities are analyzed once projected in the space of coordinates. We show that using the framework of phase space it is possible to introduce a thermal energy which is related to temperature as it vanishes when the temperature tends to zero. In fact given such a correlation the formalism of TFD is equivalent when project is in momenta space when compared to coordinates space.

Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature

It has recently been suggested (S.B. Giddings (2016) [2] ) that the Hawking black-hole radiation spectrum originates from an effective quantum “atmosphere' which extends well outside the black-hole horizon. In particular, comparing the Hawking radiation power of a (3+1) -dimensional Schwarzschild black hole of horizon radius rH with the familiar Stefan–Boltzmann radiation power of a (3+1) -dimensional flat space perfect blackbody emitter, Giddings concluded that the source of the Hawking semi-classical black-hole radiation is a quantum region outside the Schwarzschild black-hole horizon whose effective radius rA is characterized by the relation Δr≡rA−rH∼rH . It is of considerable physical interest to test the general validity of Giddings's intriguing conclusion. To this end, we study the Hawking radiation of (D+1) -dimensional Schwarzschild black holes. We find that the dimensionless radii rA/rH which characterize the black-hole quantum atmospheres, as determined from the Hawking black-hole radiation power and the (D+1) -dimensional Stefan–Boltzmann radiation law, are a decreasing function of the number D+1 of spacetime dimensions. In particular, it is shown that radiating (D+1) -dimensional Schwarzschild black holes are characterized by the relation (rA−rH)/rH≪1 in the large D≫1 regime. Our results therefore suggest that, at least in some physical cases, the Hawking emission spectrum originates from quantum excitations very near the black-hole horizon.

Israel

Shahar Hod

Hawking radiation and the Stefan–Boltzmann law: The effective radius of the black-hole quantum atmosphere

Where does Hawking radiation originate? A common picture is that it arises from excitations very near or at the horizon, and this viewpoint has supported the “firewall” argument and arguments for a key role for the UV-dependent entanglement entropy in describing the quantum mechanics of black holes. However, closer investigation of both the total emission rate and the stress tensor of Hawking radiation supports the statement that its source is a near-horizon quantum region, or “atmosphere,” whose radial extent is set by the horizon radius scale. This is potentially important, since Hawking radiation needs to be modified to restore unitarity, and a natural assumption is that the scales relevant to such modifications are comparable to those governing the Hawking radiation. Moreover, related discussion suggests a resolution to questions regarding extra energy flux in “nonviolent” scenarios, that does not spoil black hole thermodynamics as governed by the Bekenstein–Hawking entropy.

Steven B. Giddings

Hawking radiation, the Stefan–Boltzmann law, and unitarization