International Journal of Modern Physics A

Inflation is today a part of the Standard Model of the Universe supported by the cosmic microwave background (CMB) and large scale structure (LSS) datasets. Inflation solves the horizon and flatness problems and naturally generates density fluctuations that seed LSS and CMB anisotropies, and tensor perturbations (primordial gravitational waves). Inflation theory is based on a scalar field φ (the inflaton) whose potential is fairly flat, leading to a slow-roll evolution. This review focuses on the following new aspects of inflation. We present the effective theory of inflation à la Ginsburg and Landau, in which the inflaton potential is a polynomial in the field φ and has the universal form , where , M ≪ M_Pl is the scale of inflation and N ~ 60 is the number of e-folds since the cosmologically relevant modes exit the horizon till inflation ends. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings become naturally small as powers of the ratio (M/M_Pl)². The spectral index and the ratio of tensor/scalar fluctuations are , , while the running index turns out to be and therefore can be neglected. The energy scale of inflation M ~ 0.7 × 10¹⁶GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov chain (MCMC) analysis of the available CMB+LSS data (including WMAP5) with fourth degree trinomial potentials showed: (a) the spontaneous breaking of the φ → - φ symmetry of the inflaton potential; (b) a lower bound for r in new inflation: r > 0.023 (95% CL) and r > 0.046 (68 CL); (c) the preferred inflation potential is a double-well, even function of the field with a moderate quartic coupling yielding as the most probable values n_s ≃ 0.964, r ≃ 0.051. This value for r is within reach of forthcoming CMB observations. The present data in the effective theory of inflation clearly prefer new inflation. Study of higher degree inflaton potentials shows that terms of degree higher than 4 do not affect the fit in a significant way. In addition, a horizon exit happens for , making higher order terms in the potential w negligible. We summarize the physical effects of generic initial conditions (different from Bunch–Davies) on the scalar and tensor perturbations during slow roll and introduce the transfer function D(k), which encodes the observable initial condition effects on the power spectra. These effects are more prominent in the low CMB multipoles: a change in the initial conditions during slow roll can account for the observed CMB quadrupole suppression. Slow-roll inflation is generically preceded by a short, fast-roll stage. Bunch–Davies initial conditions are the natural initial conditions for the fast-roll perturbations. During fast roll, the potential in the wave equations of curvature and tensor perturbations is purely attractive and leads to a suppression of the curvature and tensor CMB quadrupoles. An MCMC analysis of the WMAP+SDSS data including fast roll shows that the quadrupole mode exits the horizon about 0.2 e-fold before fast roll ends and its amplitude gets suppressed. In addition, fast roll fixes the initial inflation redshift to be z_init = 0.9 × 10⁵⁶ and the total number of e-folds of inflation to be N_tot ≃ 64. Fast roll fits the TT, the TE and the EE modes well, reproducing the quadrupole suppression. A thorough study of the quantum loop corrections reveals that they are very small and are controlled by powers of (H/M_Pl)² ~ 10^-9, a conclusion that validates the reliability of the effective theory of inflation. The present review shows how powerful the Ginsburg–Landau effective theory of inflation is in predicting observables that are being or will soon be contrasted with observations.

Quantum fluctuation of unstable modes about gravitational instantons causes the instability of flat space at finite temperature, leading to the spontaneous process of nucleating quantum black holes. The energy-density of quantum black holes, depending on the initial temperature, gives the cosmological term, which naturally accounts for the inflationary phase of the early universe. The reheating phase is attributed to the Hawking radiation and annihilation of these quantum black holes. Then, the radiation energy-density dominates over the energy-density of quantum black holes, the universe started the standard cosmology phase. In this phase the energy-density of quantum black holes depends on the reheating temperature. It asymptotically approaches to the cosmological constant in matter domination phase, consistently with current observations.

Following the formalism developed in Astrophys. J.375, 443 (1991), differential equations for the gauge invariant scalar part of the metric perturbation in the Friedmann–Robertson–Walker background with multiple inflatons with arbitrary field metric are obtained without any specific choice of gauge. Subsequently, an algorithm for the solution of these equations in the slow-roll approximation is given without any prior choice of the basis system in the field manifold. Vector and tensor perturbations are also briefly reviewed.

The ϕ⁴ real scalar field theory on a fuzzy sphere is studied numerically. We refine the phase diagram for this model where three distinct phases are known to exist: a uniformly ordered phase, a disordered phase, and a nonuniformly ordered phase where the spatial SO(3) symmetry of the round sphere is spontaneously broken and which has no classical equivalent. The three coexistence lines between these phases, which meet at a triple point, are carefully located, with particular attention paid to the one between the two ordered phases and the triple point itself. In the neighborhood of the triple point all phase boundaries are well approximated by straight lines which, surprisingly, have the same scaling. We argue that unless an extra term is added to enhance the effect of the kinetic term the infinite matrix limit of this model will not correspond to a real scalar field on the commutative sphere or plane.

We have previously proposed the idea of performing a card-drawing experiment of which the outcome potentially decides whether the Large Hadron Collider (LHC) should be closed or not. The purpose is to test theoretical models such as our own model that have an action with an imaginary part that has a similar form to the real part. The imaginary part affects the initial conditions not only in the past but even from the future. It was speculated that all the accelerators producing large amounts of Higgs particles such as the Superconducting Super Collider (SSC) would mean that the initial conditions must have been arranged so as not to allow these accelerators to work. If such effects existed, we could perhaps cause a very clear-cut "miracle" by having the effect of a drawn card to be the closure of the LHC. Here we shall, however, argue that the closure of an accelerator is hardly needed to demonstrate such an effect and seek to calculate how one could perform a verification experiment for the proposed type of effect from the future in the statistically least disturbing and least harmful way.

We shall also discuss how to extract the maximum amount of information about such as effect or model in the unlikely case that a card preventing the running of the LHC or the Tevatron is drawn, by estimating the relative importance of high beam energy or high luminosity for the purpose of our effect.

For the number of fermion flavors N = 2, we numerically solve the coupled Dyson–Schwinger equation for the fermion and gauge boson propagators of QED₃ using the fermion–gauge-boson vertex ansatz for a range of finite gauge boson mass ζ and chemical potential μ. For small chemical potential μ it is found that chiral symmetry gets restored when ζ is larger than a critical mass ζ_c and the value of ζ_c is not sensitive to the variation of chemical potential.

Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.

The radial part of the Klein–Gordon equation for the generalized Woods–Saxon potential is solved by using the Nikiforov–Uvarov method with spatially dependent mass within the new approximation scheme to the centrifugal potential term. The energy eigenvalues and corresponding normalized eigenfunctions are computed. The solutions in the case of constant mass are also obtained to check out the consistency of our new approximation scheme.

The process of Compton scattering γe^± → γe^± in strongly magnetized hot and cold electron–positron plasma is considered. The analytical expressions for the partial cross-sections in rarefied plasma and the simple expressions for the photon absorption rates in degenerate plasma are obtained. The numerical estimations of the absorption rates for various scattering channels are presented taking into account of the photon dispersion and wave function renormalization in strong magnetic field and plasma. The comparison of the scattering absorption rate with photon splitting probability shows the existence of plasma parameters range where these values are comparable with each other.

We investigate if theories yielding bouncing cosmological models also generate wormhole solutions. We show that two of them present sensible traversable static wormhole solutions, while for the third possibility such solutions are absent.

Quartic higher-derivative gravitational terms in the effective Lagrangian of the heterotic superstring theory renormalize the bare, four-dimensional gravitational coupling , due to the reduction process , according to the formula , where A_r and B_r are the moduli for the physical space g_ij(x^k) and internal space , respectively. The Euler characteristic is negative for a three-generation Calabi–Yau manifold, and therefore both the additional terms, of tree-level and one-loop origin, produce a decrease in κ^-2, which changes sign when κ^-2 = 0. The corresponding tree-level critical point is , if we set and λ = 15π², for compactification onto a torus. Values yield the anti-gravity region κ^-2 < 0, which is analytically accessible from the normal gravity region κ^-2 > 0. The only non-singular, vacuum minimum of the potential is located at the point , where , the quadratic trace anomaly dominates over , and a phase of de Sitter expansion may occur, as first envisaged by Starobinsky, in approximate agreement with the constraint due to the effect of gravitational waves upon the anisotropy of the cosmic microwave background radiation. There is no non-singular minimum of the potential .

(τ⁺τ^-) is an atom of simple hydrogenlike structure similar to positronium (e^-e⁺) and (μ⁺μ^-). In this paper energy levels and decay widths of different decay channels of (τ⁺τ^-) are given. Cross-section of production of this atomic system in e^-e⁺ annihilation taking into account radiative corrections is calculated. According to our estimates 31 (τ⁺τ^-) atoms are produced at VEPP-4M and 943 (τ⁺τ^-) atoms may be produced at BEPCII under the present experimental conditions.