Joao Magueijo

Lorentz invariance with an invariant energy scale.

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einsteins theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

Generalized Lorentz invariance with an invariant energy scale

The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the Lorentz transformations on momentum space. Several examples are discussed in which the speed of light varies with energy and elementary particles have a maximum momenta and/or energy. Energy and momentum conservation are suitably generalized and a proposal is made for how the new transformation laws apply to composite systems. We then use these results to explain the ultra high energy cosmic ray anomaly and we find a form of the theory that explains the anomaly, and leads also to a maximum momentum and a speed of light that diverges with energy. We finally propose that the spatial coordinates be identified as the generators of translation in Minkowski spacetime. In some examples this leads to a commutative geometry, but with an energy dependent Planck constant.

A Time varying speed of light as a solution to cosmological puzzles

We consider the cosmological implications of light travelling faster in the early Universe. We propose a prescription for deriving corrections to the cosmological evolution equations while the speed of light

String theories with deformed energy-momentum relations, and a possible nontachyonic bosonic string

c

Varying alpha theories and solutions to the cosmological problems

is changing. We then show how the horizon, flatness, and cosmological constant problems may be solved. We also study cosmological perturbations in this scenario and show how one may solve the homogeneity and isotropy problems. As it stands, our scenario appears to most easily produce extreme homogeneity, requiring structure to be produced in the standard big bang epoch. Producing significant perturbations during the earlier epoch would require a rather careful design of the function

Covariant and locally Lorentz invariant varying speed of light theories

c(t).

Nonlinear relativity in position space

The large entropy inside the horizon nowadays can also be accounted for in this scenario.

Solutions to the quasi-flatness and quasi-lambda problems

We consider a prescription for introducing deformed dispersion relations in the bosonic string action. We find that in a subset of such theories it remains true that the embedding coordinates propagate linearly on the worldsheet. While both the string modes and the center of mass propagate with deformed dispersion relations, the speed of light remains energy independent. We consider the canonical quantization of these strings, and find that it is possible to choose theories so that ghost modes still decouple, as usual. We also find that there are examples where the tachyon is eliminated from the spectrum of the free bosonic string.

Solving the flatness and quasi-flatness problems in Brans-Dicke cosmologies with a varying light speed

Abstract If the fine structure constant α = e 2 /(ℏ c ) were to change, then a number of interpretations would be possible, attributing this change either to variations in the electron charge, the dielectric constant of the vacuum, the speed of light, or Plancks constant. All these variations should be operationally equivalent and can be related by changes of standard units. We show how the varying speed of light cosmology recently proposed can be rephrased as a dielectric vacuum theory, similar to the one proposed by Bekenstein. The cosmological problems will therefore also be solved in such a theory.

Could supermassive black holes be quintessential primordial black holes

We propose definitions for covariance and local Lorentz invariance applicable when the speed of light