Primordial supersymmetric inflation

We discuss the motivations for reconsidering cosmological inflation in supersymmetric theories as contrasted with conventional GUTs. Radiative corrections to the effective potential can be made arbitrarily small in supersymmetric GUTs, removing some of the obstacles to inflation. We analyze general renormalizable potentials at the tree level and show that the required fine-tuning of parameters becomes less acute if inflation takes place before the grand unified phase transition, a hypothesis we term primordial inflation. We show how the grand unified monopole problem can be solved in supersymmetric GUTs embodying primordial inflation.     

Primordial inflation with flat supergravity potentials

A new class of primordial inflation models (PRIMO) is presented, based upon the possibility of getting naturally flat potentials in N = 1 supergravity. These models may be considered as the natural cosmological extension of some recently proposed no-scale particle physics models, where all mass scales are derived from the Planck mass (M_p). PRIMO seem to satisfy all presently known cosmological constraints and they are guaranteed (a) to be void of SUSY minima with negative cosmological constant, (b) of a stable (around the origin) potential form against finite temperature effects.     

A maximally symmetric space with torsion

A maximally symmetric space, i.e., homogeneous and isotropic at every point, possessing totally antisymmetric torsion is dealt with. It is found that maximum symmetry restricts the dimension of the space to three. The three-curvature tensor for the space is obtained and from its form a three-metric is then constructed. The three-space is then allowed to evolve in time so that a four-metric of the formds ²= –dt ²+ (3)g _ij dx ⁱ dx ^j is possible. From this an equation of motion is obtained which predicts an initial- and final-state singularity.Part of this work was done as a doctoral thesis requirement at Queen Mary College, University of London.     

Primordial large-scale electromagnetic fields from gravitoelectromagnetic inflation

We investigate the origin and evolution of primordial electric and magnetic fields in the early universe, when the expansion is governed by a cosmological constant Λ₀${\Lambda }_0$. Using the gravitoelectromagnetic inflationary formalism with A₀=0$A_0=0$, we obtain the power of spectrums for large-scale magnetic fields and the inflaton field fluctuations during inflation. A very important fact is that our formalism is naturally non-conformally invariant.     

Primordial shear and the question of inflation

The role of primordial shear in two inflationary scenarios, Planck-time (Linde) inflation and the GUT inflation is discussed. In the Linde picture, including a simple “particle creation” term produces universes in which the temperature rapidly attains a stable asymptotic value just below the Planck temperature, whatever the Higgs field coupling constant. Such universes are truly isotropic by the time the GUT era is reached. (There is no supercooling because of particle creation.) In the GUT picture, inflation can occur notwithstanding the presence of anisotropy. However, in these models, initial anisotropy reduces the GUT era coherence length and it becomes more difficult to form the present universe from a single bubble.     

Spinor two-point functions in maximally symmetric spaces

The two-point function for spinors on maximally symmetric four-dimensional spaces is obtained in terms of intrinsic geometric objects. In the massless case, Weyl spinors in anti de Sitter space can not satisfy boundary conditions appropriate to the supersymmetric models. This is because these boundary conditions break chiral symmetry, which is proven by showing that the order parameter for a massless Dirac spinor is nonzero. We also give a coordinate-independent formula for the bispinor introduced by Breitenlohner and Freedman [1], and establish the precise connection between our results and those of Burges, Davis, Freedman and Gibbons [2].     

Vector two-point functions in maximally symmetric spaces

We obtain massive and massless vector two-point functions in maximally symmetric spaces (and vacua) of any number of dimensions. These include de Sitter space and anti-de Sitter space, and their Euclidean analogsS ⁿ andH ⁿ. Our method is based on a simple way of constructing every possible maximally symmetric bitensorT _a...bc...d(x, x) which carries tangent-space indicesa...b atx andc...d atx.     

Primordial fluctuations and non-Gaussianities in multifield Dirac-Born-Infeld inflation

We study Dirac-Born-Infeld inflation models with multiple scalar fields. We show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at the sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We show that this could strongly affect the observable curvature power spectrum as well as the amplitude of non-Gaussianities, although their shape remains as in the single-field Dirac-Born-Infeld case.     

The spinor heat kernel in maximally symmetric spaces

The heat kernelK(x, x, t) of the iterated Dirac operator on anN-dimensional simply connected maximally symmetric Riemannian manifold is calculated. On the odd-dimesional hyperbolic spacesK is a Minakshisundaram-DeWitt expansion which terminates to the coefficienta _N–1)/2 and is exact. On the odd spheres the heat kernel may be written as an image sum of WKB kernels, each term corresponding to a classical path (geodesic). In the even dimensional case the WKB approximation is not exact, but a closed form ofK is derived both in terms of (spherical) eigenfunctions and of a sum over classical paths. The spinor Plancherel measure () and function in the hyperbolic case are also calculated. A simple relation between the analytic structure of onH ^N and the degeneracies of the Dirac operator onS ^N is found.     

Generation of maximally entangled states in a two-component Bose-Einstein condensate

We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states （SSCS）, may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.     

Primordial fluctuations from inflation: a consistent histories approach

We show how the quantum-to-classical transition of the cosmological fluctuations produced during an inflationary stage can be described using the consistent histories approach. We identify the corresponding histories in the limit of infinite squeezing. To take the decaying mode into account, we propose an extension to coarse-grained histories.     

Primordial inflation and present-day cosmological constant from extra dimensions

A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as ρ _Λ ∼M ⁸/M _P ⁴, where M _P is the Planck scale and M is the weak interaction scale. The model is based on (4+D)-dimensional gravity, with D=2 extra dimensions with radius b(t) curled up at the ADD length scale b ₀=M _P /M ²∼0.1 mm. Vacuum fluctuations in the compactified space perturb b ₀ very slightly, generating a small present-day cosmological constant.The radius of the compactified dimensions is predicted to be b ₀≈k ^1/40.09 mm (or equivalently M≈2.4 TeV/k ^1/8), where the Casimir energy density is k/b ⁴.Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M∼10⁻¹⁷ cm, rolls down its potential to b ₀.     

Primordial gravity wave fossils and their use in testing inflation

A new effect is described by which primordial gravity waves leave a permanent signature in the large scale structure of the Universe. The effect occurs at second order in perturbation theory and is sensitive to the order in which perturbations on different scales are generated. We derive general forecasts for the detectability of the effect with future experiments and consider observations of the prereionization gas through the 21 cm line. It is found that the Square Kilometer Array will not be competitive with current cosmic microwave background constraints on primordial gravity waves from inflation. However, a more futuristic experiment could, through this effect, provide the highest ultimate sensitivity to tensor modes and possibly even measure the tensor spectral index. It is thus a potentially quantitative probe of the inflationary paradigm.     

Primordial curvature perturbation during and at the end of multi-field inflation

We study the generation of the primordial curvature perturbation in multi-field inflation. Considering both the evolution of the perturbation during inflation and the effects generated at the end of inflation, we present a general formula for the curvature perturbation. We provide the analytic expressions of the power spectrum, spectral tilt and non-Gaussianity for the separable potentials of two inflaton scalars, and apply them to some specific models.     

Primordial cosmological inflation versus local supersymmetry breaking in SUSY GUTs coupled toN=1 supergravity

We present a model for a SUSY GUT coupled toN=1 supergravity in which local supersymmetry breaks down in the gauge singlet sector. The constraints for the model to be physically acceptable are incompatible with inflation. The simultaneous breaking of local supersymmetry and gauge symmetry is proposed as a good prospect for inflation.     

Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model with second-order field equations

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.     

Principles of maximally classical and maximally realistic quantum mechanics

Recently Auberson, Mahoux, Roy and Singh have proved a long standing conjecture of Roy and Singh: In 2N-dimensional phase space, a maximally realistic quantum mechanics can have quantum probabilities of no more than N+1 complete commuting cets (CCS) of observables coexisting as marginals of one positive phase space density. Here I formulate a stationary principle which gives a nonperturbative definition of a maximally classical as well as maximally realistic phase space density. I show that the maximally classical trajectories are in fact exactly classical in the simple examples of coherent states and bound states of an oscillator and Gaussian free particle states. In contrast, it is known that the de Broglie-Bohm realistic theory gives highly nonclassical trajectories.     

Stability of proton and maximally symmetric minimal unification model for basic forces and building blocks of matter

With the hypothesis that all independent degrees of freedom of basic building blocks should be treated equally on the same footing and correlated by a possible maximal symmetry, we arrive at a 4-dimensional space-time unification model. In this model the basic building blocks are Majorana fermions in the spinor repre- sentation of 14-dimensional quantum space-time with a gauge symmetry GM4D = SO(1,3)×SU(32)×U(1)A×SU(3)F. The model leads to new physics including mirror particles of the standard model. It enables us to issue some fundamental questions that include: why our living space-time is 4-dimensional, why parity is not con- served in our world, how the stability of proton is, what the origin of CP violation is and what the dark matter can be.