Early universe models from noncommutative geometry

“If we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we must regard it rather as an accident that the Earth (and presumably whole solar system), contains a preponderance of negative electrons and positive protons. . ..” This is a sentence in the Nobel Lecture given by Paul A. M. Dirac in 1933. 1) This is the first proposal for baryon-anti-baryon symmetric universe. However, astrophysical observations have ruled out the presence of antimatter in the present universe up to the scale of clusters of galaxies. If our universe indeed began baryon symmetric, those imbalances in numbers of baryons and anti-baryons must be generated by some physical processes in the early universe. I show, in this talk, that decays of the heavy (right-handed) Majorana neutrinos in the early universe generate the imbalances between baryon and anti-baryon numbers. The presence of super heavy (right-handed) Majorana neutrinos is an important prediction of unified theories beyond the standard model. An integration of the heavy Majorana neutrinos induces very small masses for neutrinos via the seesaw mechanism. 2) Thus, small neutrino masses is a reflection of unification at very high energy scale. It is quite natural to consider that the heavy Majorana neutrinos are produced thermally in the early universe. When the temperature of the universe cools down to the masses of the heavy Majorana neutrinos, the heavy neutrinos begin to decay into Higgs boson and lepton or Higgs boson and anti-lepton. The decay may produce the lepton-number asymmetry if CP invariance is violated in the decay processes. The CP invariance can be easily violated by phases in new complex Yukawa coupling of Higgs boson to the right-handed neutrinos and left-handed leptons. The decay processes can easily be out of thermal equilibrium. Thus, the decay processes of heavy Majorana neutrinos can satisfy three Sakharov conditions 3) for baryogenesis. This produced lepton-number asymmetry is converted into the baryon-number asymmetry in the present universe through non-perturbation effects of the electroweak gauge theory. 5) This is called “leptogenesis”. 4) I show that the neutrino masses observed in various neutrino-oscillation experiments are just in the range predicted by the thermal leptogenesis. 6)

A partial unification model in non-commutative geometry

The standard model in noncommutative geometry and fermion doubling

Finding a plausible origin for right-handed neutrino Majorana masses in semirealistic compactifications of string theory remains one of the most difficult problems in string phenomenology. We argue that right-handed neutrino Majorana masses are induced by non-perturbative instanton effects in certain classes of string compactifications in which the $U(1)_{B-L}$ gauge boson has a St\"uckelberg mass. The induced operators are of the form $e^{-U}\nu_R\nu_R$ where $U$ is a closed string modulus whose imaginary part transforms appropriately under $B-L$. This mass term may be quite large since this is not a gauge instanton and $Re U$ is not directly related to SM gauge couplings. Thus the size of the induced right-handed neutrino masses could be a few orders of magnitude below the string scale, as phenomenologically required. It is also argued that this origin for neutrino masses would predict the existence of R-parity in SUSY versions of the SM. Finally we comment on other phenomenological applications of similar instanton effects, like the generation of a $\mu$-term, or of Yukawa couplings forbidden in perturbation theory.

Neutrino oscillation experiments point towards the existence of additional mostly sterile neutrino mass eigenstates in the eV mass range. At the same time, such sterile neutrinos are disfavoured by cosmology (Big Bang Nucleosynthesis, Cosmic Microwave Background and Large Scale Structure), unless they can be prevented from being thermalised in the early Universe. To this aim, we introduce a model of sterile neutrino secret interactions mediated by a new light pseudoscalar: The new interactions can accomodate sterile neutrinos in the early Universe, providing a good fit to all the up to date cosmological data.

Dwarf spheroidal galaxies (dSphs) are recognized as being highly dominated by Dark Matter (DM), making them excellent targets for testing DM models through astrophysical observations. One effective method involves estimating the coarse-grained phase-space density (PSD) of the galactic DM component. By comparing this PSD with that of DM particles produced in the early Universe, it is possible to establish lower bounds on the DM particle mass. These constraints are particularly relevant for models of warm DM, such as those involving sterile neutrinos. By utilizing the GravSphere code, we obtain a fit of the DM PSD based on the latest reliable stellar dynamics data for twenty of the darkest dSphs, refining earlier lower bounds on sterile neutrino masses in nonresonant production scenarios. Additionally, we introduce an alternative approach involving the Excess Mass Function (EMF), which yields even tighter constraints. Specifically, using the maximum PSD, we derive a lower bound of [Formula: see text] [Formula: see text]keV at 95% confidence level, while the EMF method provides a stronger limit of [Formula: see text] [Formula: see text]keV at 95% CL. For the general thermal relic fermion dark matter mass, the limits translate into [Formula: see text] [Formula: see text]keV and [Formula: see text] [Formula: see text]keV, respectively. Both methods are versatile and can be extended to more complex DM production mechanisms in the early Universe. For the first time, we also constrain parameters of models involving nonstandard cosmologies during the epoch of neutrino production. Our analysis yields [Formula: see text] [Formula: see text]keV for models with kination domination and [Formula: see text] [Formula: see text]keV for scenarios with extremely low reheating temperature.

These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces (branes) is formulated, and their effective Riemannian geometry is elaborated. This class of configurations is preserved under small deformations, and is therefore appropriate for matrix models. A realization of generic 4-dimensional geometries is sketched, and the relation with spectral geometry and with noncommutative gauge theory is explained. In a second part, dynamical aspects of these matrix geometries are considered. The one-loop effective action for the maximally supersymmetric IKKT or IIB matrix model is discussed, which is well-behaved on 4-dimensional branes.

The detection of a sterile neutrino could constitute the first observation of a particle that could have been produced before Big-Bang Nucleosynthesis (BBN), and could provide information about the yet untested pre-BBN era. The cosmological evolution in this era could be drastically different than typically assumed in what constitutes the standard cosmology, as happens in a variety of motivated particle models. In this work we assess the sensitivity to different pre-BBN cosmologies in which entropy is conserved of 0.01 eV to 1 MeV mass sterile neutrinos produced in the early Universe via resonant active-sterile oscillations, which requires a large lepton asymmetry. We identify mass ranges where it is possible to have two populations of the same sterile neutrino, one with a colder and one with a hotter momentum spectra, which is in principle an observable effect. Furthermore, we show the regions in mass and mixing where fully resonant production (i.e. simultaneously coherent and adiabatic) can occur. We find that in several of the cosmologies we consider, including the standard one, for a lepton asymmetry larger than ∼10−4 fully resonantly produced sterile neutrinos in the eV-mass range can evade all cosmological constraints.

It is generally expected that adding light sterile species would increase the effective number of neutrinos, Neff. In this paper we discuss a scenario that Neff can actually decrease due to the neutrino oscillation effect if sterile neutrinos have self-interactions. We specifically focus on the eV mass range, as suggested by the neutrino anomalies. With large self-interactions, sterile neutrinos are not fully thermalized in the early Universe because of the suppressed effective mixing angle or matter effect. As the Universe cools down, flavor equilibrium between active and sterile species can be reached after big bang nucleosynthesis (BBN) epoch, but leading to a decrease of Neff. In such a scenario, we also show that the conflict with cosmological mass bounds on the additional sterile neutrinos can be relaxed further when more light species are introduced. To be consistent with the latest Planck results, at least 3 sterile species are needed.

The possibility of light sterile neutrinos allows for the resonant production of leptonnumber in the early universe through matter-affected neutrino mixing. For a given mixingof the active and sterile neutrino states it has been found that the lepton numbergeneration process is chaotic and strongly oscillatory. We undertake a new studyof the sensitivity of this process to initial conditions through the quantum rateequations. We confirm the chaoticity of the process in this solution, and moreoverfind that the resultant lepton number and the sign of the asymmetry produce afractal in the parameter space of mass, mixing angle and initial baryon number.This has implications for future searches for sterile neutrinos, where arbitrarilyhigh sensitivity may not be determinate in forecasting the lepton number of theuniverse.

Assuming a Zee-like matrix for the right-handed neutrino Majorana masses in the see-saw mechanism, one gets maximal mixing for vacuum solar oscillations, a very small value for $U_{e3}$ and an approximate degeneracy for the two lower neutrino masses. The scale of right-handed neutrino Majorana masses is in good agreement with the value expected in a SO(10) model with Pati-Salam $SU(4)\ts SU(2)\ts SU(2)$ intermediate symmetry.

We study the imprints of high scale non-thermal leptogenesis on cosmic microwave background (CMB) from the measurements of inflationary spectral index (ns) and tensor-to-scalar ratio (r), which otherwise is inaccessible to the conventional laboratory experiments. We argue that non-thermal production of baryon (lepton) asymmetry from subsequent decays of inflaton to heavy right-handed neutrinos (RHN) and RHN to SM leptons is sensitive to the reheating dynamics in the early Universe after the end of inflation. Such dependence provides detectable imprints on the ns−r plane which is well constrained by the Planck experiment. We investigate two separate cases, (I) inflaton decays to radiation dominantly and (II) inflaton decays to RHN dominantly which further decays to the SM particles to reheat the Universe adequately. Considering a class of α− attractor inflation models, we obtain the allowed mass ranges for RHN for both cases and thereafter furnish the estimates for ns and r. The prescription proposed here is general and can be implemented in various kinds of single-field inflationary models given the conditions for non-thermal leptogenesis are satisfied.

The evolution of a flat, isotropic and homogeneous universe is studied. The background geometry in the early phases of the universe is conjectured to be filled with causal bulk viscous fluid and dark energy. The energy density relations obtained from the assumption of covariant conservation of energy‐momentum tensor of the background matter in the early universe are used to derive the basic equation for the Hubble parameter H. The viscous properties described by ultra‐relativistic equations of state and bulk viscosity taken from recent heavy‐ion collisions and lattice QCD calculations have been utilized to give an approximate solution of the field equations. The cosmological constant is conjectured to be related to the energy density of the vacuum. In this treatment, there is a clear evidence for singularity at vanishing cosmic time t indicating the dominant contribution from the dark energy. The time evolution of H seems to last for much longer time than the ideal case, where both cosmological constant and viscosity coefficient are entirely vanishing.

Primordial black holes (PBH), while still constituting a viable dark matter component, are expected to evaporate through Hawking radiation. Assuming the semi-classical approximation holds up to near the Planck scale, PBHs are expected to evaporate by the present time, emitting a significant flux of particles in their final moments, if produced in the early Universe with an initial mass of ∼ 1015 g. These “exploding” black holes will release a burst of Standard Model particles alongside any additional degrees of freedom, should they exist. We explore the possibility that heavy neutral leptons (HNL), mixing with active neutrinos, are emitted in the final evaporation stages. We perform a multimessenger analysis. We calculate the expected number of active neutrinos from such an event, including contributions due to the HNL decay for different assumptions on the mixings, that could be visible in IceCube. We also estimate the number of gamma-ray events expected at HAWC. By combining the two signals, we infer sensitivities on the active-sterile neutrino mixing and on the sterile neutrino mass. We find that, for instance, for the scenario where U τ 4 ≠ 0, IceCube and HAWC could improve current constraints by a few orders of magnitude, for HNLs masses between 0.1–1 GeV, and a PBH explosion occurring at a distance of ∼ 10-4 pc from Earth.

We present an alternative formulation of the left-right symmetric theory\nwhere the scalar sector consists of two Higgs doublets which differs from the\nstandard version of the left-right model that makes use of $L-$ and $R-$ Higgs\ntriplets and a Higgs bi-doublet. The basic idea is to consider few extra\ncharged iso-singlet fields and the fermion masses can be realized by\nintegrating out these heavy isosinglet fields. We also give a detailed\ndiscussion on neutrinoless double beta decay in this particular left-right\nsymmetric theory where the right-handed Majorana neutrino can be of MeV range.\nWith this right-handed Majorana mass around MeV scale, the contribution to\nneutrinoless double beta decay coming from the right-handed current can be\ncomparable with the contributions coming from the standard left-handed sector\nonly if the right-handed gauge boson mass is around 5 TeV, and with this\noperative scale of $W_R$ around few TeV, it is possible to probe at LHC. We\nhave briefly commented on cosmological constraints coming from the big-bang\nnucleosynthesis and Universe cosmology to the right-handed neutrinos involved\nin this discussion.\n