Valery A. Rubakov

Opening up extra dimensions at ultralarge scales.

The standard picture of viable higher-dimensional theories is that direct manifestations of extra dimensions occur at short distances only, whereas long-distance physics is effectively four-dimensional. We show that this is not necessarily true in models with infinite extra dimensions. As an example, we consider a five-dimensional scenario with three 3-branes in which gravity is five dimensional at both short- and very long-distance scales, with conventional four-dimensional gravity operating at intermediate length scales. A phenomenologically acceptable range of validity of four-dimensional gravity extending from microscopic to cosmological scales is obtained without strong fine-tuning of parameters.

Harrison-Zeldovich spectrum from conformal invariance

We show that flat spectrum of small perturbations of field(s) is generated in a simple way in a theory of multi-component scalar field provided this theory is conformally invariant, it has some global symmetry and the quartic potential is negative. We suggest a mechanism of converting these field perturbations into adiabatic scalar perturbations with flat spectrum.

Constraining sterile neutrino dark matter with phase space density observations

We apply phase space density considerations to obtain lower bounds on the mass of the sterile neutrino as a dark matter candidate. The bounds are different for non-resonant production, resonant production in the presence of lepton asymmetry and production in decays of heavier particles. In the former case our bound is comparable to but independent of the Lyman-α bound, and together with the x-ray upper limit it disfavors non-resonantly produced sterile neutrino dark matter. An interesting feature of the latter case is that warm dark matter may be composed of heavy particles.

Is the electric charge conserved in brane world

We discuss whether electric charge conservation may not hold in four-dimensional world in models with infinite extra dimensions, i.e., whether escape of charged particles from our brane is consistent with effectively four-dimensional electrodynamics on the brane. We introduce a setup with photon localized on the brane and show that charge leakage into extra dimension is allowed within this setup. The electric field induced on the brane by escaping charge does not obey four-dimensional Maxwells equations; this field gradually disappears in a causal way. We also speculate on the possibility of the escape of colored particles and formation of colorless free quark states on the brane.

Brane worlds: the gravity of escaping matter

Within the framework of a five-dimensional model with one 3-brane and an infinite extra dimension, we discuss a process in which matter escapes from the brane and propagates into the bulk to arbitrarily large distances. An example is a decay of a particle of mass 2m residing on the brane into two particles of mass m that leave the brane and accelerate away. We calculate, in the linearized theory, the metric induced by these particles on the brane. This metric does not obey the four-dimensional Einstein equations and corresponds to a spherical gravity wave propagating along the four-dimensional future lightcone. The four-dimensional spacetime left behind the spherical wave is flat, so the gravitational field induced in the brane world by matter escaping from the brane disappears in a causal way.

Gravity and antigravity in a brane world with metastable gravitons

Abstract In the framework of a five-dimensional three-brane model with quasi-localized gravitons we evaluate metric perturbations induced on the positive tension brane by matter residing thereon. We find that at intermediate distances, the effective four-dimensional theory coincides, up to small corrections, with General Relativity. This is in accord with Csaki, Erlich and Hollowood and in contrast to Dvali, Gabadadze and Porrati. We show, however, that at ultra-large distances this effective four-dimensional theory becomes dramatically different: conventional tensor gravity changes into scalar anti-gravity.

Cosmological density perturbations from conformal scalar field: infrared properties and statistical anisotropy

We consider a scenario in which primordial scalar perturbations are generated when complex conformal scalar field rolls down its negative quartic potential. Initially, these are the perturbations of the phase of this field; they are converted into the adiabatic perturbations at a later stage. A potentially dangerous feature of this scenario is the existence of perturbations in the radial field direction, which have red power spectrum. We show, however, that to the linear order in the small parameter — the quartic self-coupling — the infrared effects are completely harmless, as they can be absorbed into field redefinition. We then evaluate the statistical anisotropy inherent in the model due to the existence of the long-ranged radial perturbations. To the linear order in the quartic self-coupling the statistical anisotropy is free of the infrared effects. The latter show up at the quadratic order in the self-coupling and result in the mild (logarithmic) enhancement of the corresponding contribution to the statistical anisotropy. The resulting statistical anisotropy is a combination of a larger term which, however, decays as momentum increases, and a smaller term which is independent of momentum.

Is gravitino still a warm dark matter candidate

We make use of the phase space density approach to discuss gravitino as a warm dark matter candidate. Barring fine tuning between the reheat temperature in the Universe and superparticle masses, we find that warm gravitinos have both appropriate total mass density, Ω = ΩDM 0.2, and suitable primordial phase space density at low momenta provided that their mass is in the range 1 keV m 15 keV, the reheat temperature in the Universe is low, TR 10 TeV, and masses of some of the superparticles are sufficiently small, M 350 GeV. The latter property implies that the gravitino warm dark matter scenario will be either ruled out or supported by the LHC experiments.

Flowing to four dimensions

We analyze the properties of a model with four-dimensional brane-localized Higgs type potential of a six dimensional scalar field satisfying the Dirichlet boundary condition on the boundary of a transverse two-dimensional compact space. The regularization of the localized couplings generates classical renormalization group running. A tachyonic mass parameter grows in the infrared, in analogy with the QCD gauge coupling in four dimensions. We find a phase transition at a critical value of the bare mass parameter such that the running mass parameter becomes large in the infrared precisely at the compactification scale. Below the critical coupling, the theory is in symmetric phase, whereas above it spontaneous symmetry breaking occurs. Close to the phase transition point there is a very light mode in the spectrum. The massive Kaluza-Klein spectrum at the critical coupling becomes independent of the UV cutoff.

Superluminality in the Fierz–Pauli massive gravity

We study the propagation of helicity-1 gravitons in the Fierz–Pauli massive gravity in nearly Minkowski backgrounds. We show that, generically, there exist backgrounds consistent with field equations, in which the propagation is superluminal. The relevant distances are much longer than the ultraviolet cutoff length inherent in the Fierz–Pauli gravity, so superluminality occurs within the domain of validity of the effective low-energy theory. There remains a possibility that one may get rid of this property by imposing fine tuning relations between the coefficients in the nonlinear generalization of the Fierz–Pauli mass term, order by order in nonlinearity; however, these relations are not protected by any obvious symmetry. Thus, among others, superluminality is a problematic property to worry about when attempting to construct infrared modifications of general relativity.