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We search for regular tachyon kinks in an extended model, which includes the tachyon action recently proposed to describe the tachyon field. The extended model that we propose adds a new contribution to the tachyon action, which allows one to obtain stable tachyon kinks of regular profile, which may appropriately lead to the singular kink found by Sen sometime ago. Also, under specific conditions we may find periodic array of kink–antikink configurations.

Orbifolds in field theory are potentially singular objects for at their fixed points the curvature becomes infinite, therefore one may wonder whether field theory calculations near orbifold singularities can be trusted. String theory is perfectly well defined on orbifolds and can therefore be taken as a UV completion of field theory on orbifolds. We investigate the properties of field and string theory near orbifold singularities by reviewing the computation of a one-loop gauge field tadpole. We find that in string theory the twisted states give contributions that have a spread of a couple of string lengths around the singularity, but otherwise the field theory picture is confirmed. One additional surprise is that in some orbifold models one can identify local tachyons that give contributions near the orbifold fixed point.

We calculate the rate at which a free tachyon (faster than light particle) would emit gravitational radiation. It is very small.

We consider the sound radiation from an acoustic point-like source moving along a supersonic ("space-like") trajectory in a fluid at rest. We call it an acoustic "tachyonic" source. We describe the radiation emitted by this supersonic source. After quantizing the acoustic perturbations, we present the distribution of phonons generated by this classical tachyonic source and the classical wave interference pattern.

A model for the universe with tachyonic and fermionic fields interacting through a Yukawa-type potential is investigated. It is shown that the tachyonic field answers for the initial accelerated regime and for the subsequent decelerated regime so that it behaves as an inflaton at early times and as a matter field at intermediate times, while the fermionic field has the role of a dark energy constituent, since it leads to an accelerated regime at later times. The interaction between the fields via a Yukawa-type potential controls the duration of the decelerated era, since a stronger coupling makes a shorter decelerated period.

A minus sign is inserted, for good reason, into the formula for the energy–momentum tensor for tachyons. This leads to remarkable theoretical consequences and a plausible explanation for the phenomenon called dark energy in the cosmos.

We present several solutions for the five-dimensional gravity models in the presence of bulk ghosts and tachyons to argue that these "troublesome" fields can be a useful model-building tool. The ghost-like signature of the kinetic term for a bulk scalar creates a minimum in the scale factor, removing the necessity for a negative tension brane in models with the compactified fifth dimension. It is shown that the model with the positive tension branes and a ghost field in the bulk leads to the radion stabilization. The bulk scalar with the variable sign kinetic term can be used to model both positive and negative tension branes of a finite width in the compact dimension. Finally, we present several ghost and tachyon field configurations in the bulk that lead to the localization of gravity in four dimensions, including one solution with the Gaussian profile for the metric, g_μν(y) = η_μνexp{-αy²}, which leads to a stronger localization of gravity than the Randall–Sundrum model.

We construct momentum space expansions for the wave functions that solve the Klein–Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space–time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.

Following earlier studies that provided a consistent theory of kinematics for tachyons (faster-than-light particles), we here embark on a study of tachyon dynamics, both in classical physics and in the quantum theory. Examining a general scattering process, we come to recognize that the labels given to “in” and “out” states are not Lorentz invariant for tachyons; and this lets us find a sensible interpretation of negative energy states. For statistical mechanics, as well as for scattering problems, we study what should be the proper expression for density of states for tachyons. We review the previous work on quantization of a Dirac field for tachyons and go on to expand earlier considerations of neutrinos as tachyons in the context of cosmology. We stumble into the realization that tachyon neutrinos would contribute to gravitation with the opposite sign compared to tachyon antineutrinos. This leads to the gobsmacking prediction that the Cosmic Neutrino Background, if they are indeed tachyons, might explain both phenomena of Dark Matter and Dark Energy. This theoretical study also makes contact with the anticipated results from the experiments KATRIN and PTOLEMY, which focus on beta decay and neutrino absorption by Tritium.

This work expands previous efforts, within the classical theories of Special and General Relativity, to include tachyons (faster-than-light particles) along with ordinary (slower-than-light) particles at any energy. The objective here is to construct a Hamiltonian that includes both the particles and the gravitational field that they produce. We do this with a linear approximation for the Einstein field equations; and we also assume a time-independent gravitational metric implied by a static picture of the particles’ motion. The resulting formulas will allow serious modeling to test the idea that cosmic background neutrinos may be tachyons, which can produce the observed gravitational effects now ascribed to some mysterious Dark Matter.

In earlier work, we showed how to handle the Group Theoretical issue of the Little Group for spin 1/2 tachyons by introducing a special metric in the vector space of one-particle states. Here that technique is extended to tachyons of any spin. Examining the bi-linear algebra of the generating matrices for spin 5/2, we find a complete basis for the Gell-Mann matrices that form the Lie algebra for SU(3). A Dirac-like equation is developed for tachyons of any integer-plus-one-half spin; and it shows multiple distinct mass eigenvalues. The primary model shows a mass spectrum (in the case of $j=5/2$) that roughly mimics the known data on masses of the three neutrinos; the model can be tweaked to fit that experimental data precisely.

Usually considered highly speculative, tachyons can be treated via straightforward Einsteinian dynamics. Kinetic theory and thermodynamics for a gas of “dark” tachyons are readily constructed. Such a gas exhibits density and pressure which, for the dominant constituent of a suitable Friedmann–Robertson–Walker space–time, can drive cosmic evolution with features both similar to and distinct from those of a standard dark-energy/dark-matter model. Hence, tachyons might bear further consideration as a cosmic dark-matter candidate.

Recent theory of tachyon neutrinos, providing an explanation for Dark Matter, leads to two sets of experiments for testing that theory. One predicts an enhanced signal in detection of the Cosmic Neutrino Background. The other compares models of Dark Matter used to fit data on galaxy rotation curves and also gravitational lensing. This paper starts with a semi-review of the previous theoretical work. One sees new symmetries in comparing the theory of tachyons to that of ordinary particles. In addition, we present a debunking of the false claim that tachyons would produce a causal paradox; and an apparent contradiction within the new theory, related to Dark Energy, is identified and addressed.

Starting with geometrical premises, we infer the existence of fundamental cosmological scalar fields. We then consider physically relevant situations in which spacetime metric is induced by one or, in general, by two scalar fields, in accord with the Papapetrou algorithm. The first of these fields, identified with dark energy (DE), has exceedingly small but finite (subquantum) Hubble mass scale ($\approx 10^{-33}$ eV), and might be represented as a neutral superposition of quasi-static electric fields. The second field is identified with dark matter (DM) as an effectively scalar conglomerate composed of primordial neutrinos and antineutrinos in a special tachyonic state.

A Friedmann–Robertson–Walker cosmological model dominated by tachyonic — faster-than-light — dark matter can exhibit features similar to those of a standard dark energy/dark matter or $\mathrm{\Lambda }$CDM model. It can undergo expansion which decelerates to a minimum rate, passes through a “cosmic jerk,” then accelerates. But some features of a tachyon-dominated model are sufficiently distinct from those of the Standard Model that the two possibilities might be distinguished observationally. As a demonstration of concept, the distance-redshift relation of such a model is compared here with some observations of Type Ia supernovae. Other measures of the third time derivative of the cosmic scale factor — the true cosmic jerk — might be found to test a tachyonic-dark-matter hypothesis.

We revive the historically first neutrino dark matter model, but with an additional assumption that neutrinos might exist in tachyonic almost sterile states. To this end we propose a group-theoretical algorithm for the description of tachyons. The key point is that we employ a distinct tachyon Lorentz group with another (superluminal) parametrization which does not require traditional introduction of imaginary masses and negative energies, and therefore does not lead to violation of causality and unitarity. Our dark matter model represents effectively scalar tachyonic neutrino-antineutrino conglomerate. Distributed all over the universe, such fluid behaves as stable isothermal/stiff medium which produces somewhat denser regions (‘smoothed halos’) around galaxies and clusters. It is shown to be consistent with observational effects (galactic rotation curves).

We present a general, albeit brief review of the recent works on stability of tensor modes in the fourth and higher derivative models of quantum gravity. There are some indications that the presence of Planck-mass ghost does not imply an instability of the classical cosmological solutions with respect to metric perturbations if the initial frequency of such perturbation is far below the Planck scale. The situation is different for a tachyonic ghost, where there is no Planck-mass threshold.

We apply a new approach based on three relativistic groups (bradyon, tachyon and instanton) forming the ‘Lorentz groupoid’ which allows, in particular, to consider tachyons without introducing imaginary masses and negative energies (related, as known, to violation of causality and unitarity). This leads to effectively scalar conglomerate composed of tachyonic neutrino and antineutrino spinor wave functions as a viable model for stationary dark matter. We also briefly discuss a relevant early non-stationary high-energy stage of the universe evolution.

We consider some models of dark energy based on perfect fluids, tachyons and phantom scalar fields. It is shown that the cosmological perturbations in the generalized Chaplygin gas model, where the pressure is inversely proportional to the power of the energy density which is greater than 3 are compatible with observations. The tachyon model, implying as a possible outcome of the cosmological evolution en encounter with the big brake cosmological singularity is compared with supernovae data and some characteristics of such evolutions are numerically estimated. Finally we consider a cosmological model with two scalar fields (one of which is effectively phantom), based on PT symmetry.

The unique identification of dark energy (DE) and dark matter (DM) is performed on the base of a neutral composition of quasi-static electric fields generated by all fermions in the Universe (for DE) and the tachyon neutrino-antineutrino conglomerate (for DM).