Geometrical origins of the universe dark sector: string-inspired torsion and anomalies as seeds for inflation and dark matter.

In a modest attempt to present potentially new paradigms in cosmology, including its inflationary epoch, and initiate discussions, I review in this article some novel, string-inspired cosmological models, which entail a purely geometrical origin of the dark sector of the Universe but also of its observed matter-antimatter asymmetry. The models contain gravitational (string-model independent, Kalb-Ramond (KR)) axion fields coupled to primordial gravitational anomalies via CP-violating interactions. The anomaly terms are four-space-time-dimensional remnants of the Green-Schwarz counterterms appearing in the definition of the field strength of the spin-one antisymmetric tensor field of the (bosonic) massless gravitational string multiplet, which also plays the role of a totally antisymmetric component of torsion. I show how in such cosmologies the presence of primordial gravitational waves can lead to anomaly condensates and dynamical inflation of a 'running-vacuum-model' type, without external inflatons, but also to leptogenesis in the radiation era due to anomaly induced Lorentz and CPT violating KR axion backgrounds. I also discuss how the torsion-related KR-axion could acquire a mass during the QCD epoch, thus playing the role of (a component of) dark matter. Phenomenological considerations of the inflationary and post-inflationary (in particular, modern) eras of the model are briefly discussed, including its potential for alleviating the observed tensions in the cosmological data of the current epoch. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

The role of temperature dependent string-inspired CPT violating backgrounds in leptogenesis and the chiral magnetic effect.

In a temperature dependent CPT-Violating (CPTV) axial time-like background (induced by the Kalb-Ramond tensor field of string theory) we discuss leptogenesis by solving the Boltzmann equation.The current work non-trivially modifies the framework of a previous phenomenological approach by the authors where the CPTV axial background was considered to be a constant (with no microscopic justification). The constant background approximation though is shown to capture the main phenomenological features of leptogenesis. On comparing our analysis to the related chiral magnetic effect for axial current condensates, we conclude that the Kalb-Ramond field does not play the role of the chiral chemical potential needed for that effect.

Singular lensing from the scattering on special space-time defects.

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent ("singular lensing"). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.

Leptogenesis from heavy right-handed neutrinos in CPT violating backgrounds.

We discuss leptogenesis in a model with heavy right-handed Majorana neutrinos propagating in a constant but otherwise generic CPT-violating axial time-like background (motivated by string theory). At temperatures much higher than the temperature of the electroweak phase transition, we solve approximately, but analytically (using Padé approximants), the corresponding Boltzmann equations, which describe the generation of lepton asymmetry from the tree-level decays of heavy neutrinos into Standard Model leptons. At such temperatures these leptons are effectively massless. The current work completes in a rigorous way a preliminary treatment of the same system, by some of the present authors. In this earlier work, lepton asymmetry was crudely estimated considering the decay of a right-handed neutrino at rest. Our present analysis includes thermal momentum modes for the heavy neutrino and this leads to a total lepton asymmetry which is bigger by a factor of two as compared to the previous estimate. Nevertheless, our current and preliminary results for the freezeout are found to be in agreement (within a ∼ 12.5 % uncertainty). Our analysis depends on a novel use of Padé approximants to solve the Boltzmann equations and may be more widely useful in cosmology.

Graviton propagation within the context of the D-material universe.

Motivated by the recent breakthrough of the detection of Gravitational Waves (GW) from coalescent black holes by the aLIGO interferometers, we study the propagation of GW in the D-material universe, which we have recently shown to be compatible with large-scale structure and inflationary phenomenology. The medium of D-particles induces an effective mass for the graviton, as a consequence of the formation of recoil-velocity field condensates due to the underlying Born-Infeld dynamics. There is a competing effect, due to a super-luminal refractive index, as a result of the gravitational energy of D-particles acting as a dark-matter component, with which propagating gravitons interact. We examine conditions for the condensate under which the latter effect is sub-leading. We argue that if quantum fluctuations of the recoil velocity are relatively strong, which can happen in the current era of the universe, then the condensate, and hence the induced mass of the graviton, can be several orders of magnitude larger than the magnitude of the cosmological constant today. Hence, we constrain the graviton mass using aLIGO and pulsar-timing observations (which give the most stringent bounds at present). In such a sub-luminal graviton case, there is also a gravitational Cherenkov effect for ordinary high-energy cosmic matter, which is further constrained by means of ultra-high-energy cosmic ray observations. Assuming cosmic rays of extragalactic origin, the bounds on the quantum condensate strength, based on the gravitational Cherenkov effect, are of the same order as those from aLIGO measurements, in contrast to the case where a galactic origin of the cosmic rays is assumed, in which case the corresponding bounds are much weaker.

Light-by-Light Scattering Constraint on Born-Infeld Theory.

The recent measurement by ATLAS of light-by-light scattering in LHC Pb-Pb collisions is the first direct evidence for this basic process. We find that it excludes a range of the mass scale of a nonlinear Born-Infeld extension of QED that is ≲100 GeV, a much stronger constraint than those derived previously. In the case of a Born-Infeld extension of the standard model in which the U(1)_{Y} hypercharge gauge symmetry is realized nonlinearly, the limit on the corresponding mass reach is ∼90 GeV, which, in turn, imposes a lower limit of ≳11 TeV on the magnetic monopole mass in such a U(1)_{Y} Born-Infeld theory.

The signal of ill-defined CPT weakening entanglement in the B d system.

In the presence of quantum-gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an entanglement-weakening term of the wrong exchange symmetry, the ω -effect. In the current paper we identify how to probe the complex ω in the entangled B d -system using the flavour (f)-CP(g) eigenstate decay channels: the connection between the intensities for the two time-ordered decays (f, g) and (g, f) is lost. Appropriate observables are constructed allowing independent experimental determinations of Re( ω ) and Im( ω ), disentangled from CPT violation in the evolution Hamiltonian Re( θ ) and Im( θ ). 2 σ tensions for both Re( θ ) and Im( ω ) are shown to be uncorrelated.

Nonlinear dynamics of dipoles in microtubules: Pseudospin model.

We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frame of the classical pseudospin model. We derive the system of nonlinear dynamical partial differential equations of motion for interacting dipoles and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to achieve a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.

On the possibility of tree-level leptogenesis from Kalb-Ramond torsion background.

In this work we consider a phenomenological model for leptogenesis in the context of a Standard Model Extension with an axial-like background coupling to fermions that violates both Lorentz and CPT symmetries. The latter is motivated by a background geometry of the early Universe involving a particular kind of torsion, arising from the Kalb-Ramond antisymmetric tensor field which appears in the gravitational multiplet of string theory, although we do not restrict ourselves to this framework. It is shown that leptogenesis can occur even at tree level and with only one generation of right-handed heavy Majorana neutrinos, due to [Formula: see text] and CPT violation introduced by the background geometry. Important issues for the model, including (a) its compatibility with a conventional-like cosmology and (b) current-era phenomenology (characterised by very stringent bounds on the allowed amount of torsion) are pointed out, and potential ways of resolving them, within the framework of string-theory models, are discussed.

Infinite class of PT-symmetric theories from one timelike Liouville Lagrangian.

Logarithmic timelike Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field ϕ. In Euclidean space, the Lagrangian of such a theory L=1/2(∇ϕ)^{2}-igϕexp(iaϕ) is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics), the energy spectrum is calculated in the semiclassical limit and the mth energy level in the nth sector is given by E_{m,n}∼(m+1/2)^{2}a^{2}/(16n^{2}).