A symmetric DBI action theory and its applications to inflationary cosmology

The Dirac-Born-Infeld (DBI) field theory in string theory is important and can provide the field of the universe’s inflation. At the same time, it provides a causal mechanism for generating the original density perturbation, thereby providing the necessary density perturbation for existing the dense and sparse matter distributions of the universe. We deduce a symmetric DBI action, introduce it into inflationary cosmology to calculate various inflation parameters, further calculate the scalar perturbation spectrum and the tensor-scalar ratio, which are compared with Planck + WMAP9 + BAO data, the power spectrum predicted by the new general DBI inflation theory satisfies the CMB Experiment constraints, i.e., is consistent with the current theories and experimental observations. Consequently, the theory of this paper conforms to current experiments and is supplying the current theories, and also a new way of explaining the inflation of the universe.

On Alfvén wave propagation along a circle on dipolar coordinates

The multipolar representation of the magnetic field has, for the lowest-order term, a magnetic dipole that dominates the far field. Thus the far-field representation of the magnetic field of the Earth, Sun and other celestial bodies is a dipole. Since these bodies consist of or are surrounded by plasma, which can support Alfvén waves, their propagation along dipole magnetic field lines is considered using a new coordinate system: dipolar coordinates. The present paper introduces multipolar coordinates, which are an example of conformal coordinates; conformal coordinates are orthogonal with equal scale factors, and can be extended from the plane to space, for instance as cylindrical or spherical dipolar coordinates. The application considered is to Alfvén waves propagating along a circle, that is a magnetic field line of a dipole, with transverse velocity and magnetic field perturbations; the various forms of the wave equation are linear second-order differential equations, with variable coefficients, specified by a background magnetic field, which is force free. The absence of a background magnetic force leads to a mean state of hydrostatic equilibrium, specified by the balance of gravity against the pressure gradient, for a perfect gas or incompressible liquid. The wave equation is simplified to a Gaussian hypergeometric type in the case of zero frequency, otherwise, for non-zero frequency, an extended Gaussian hypergeometric equation is obtained. The solution of the latter specifies the magnetic field perturbation spectrum, and also, via a polarisation relation, the velocity perturbation spectrum; both are plotted, over half a circle, for three values of the dimensionless frequency.

On braneworld monomial inflation

We investigate a monomial inflationary scalar model in the braneworld Randall–Sundrum type II model. In the high-energy regime, we determine the slow-roll parameters as well as the perturbation spectrum of the model. According to the known observational data, the corresponding results and the solutions of the equation of motion on the brane are discussed.

Brian Greene: The Speculative Sublime

Charles Dodgson warned a child correspondent of the dangers of living in the looking-glass world of mathematicians like himself, the high price of consistently believing “six impossible things before breakfast”: . . . Don’t be in such a hurry to believe next time—I’ll tell you why—If you set to work to believe everything you will tire out the muscles of the mind, and then you’ll be so weak you won’t be able to believe the simplest true things. Only last week a friend of mine set to work to believe Jack-the-giant-killer. He managed to do it, but he was so exhausted by it that when I told him it was raining (which was true) he couldn’t believe it, but rushed out into the street without his umbrella, the consequence of which was his hair got seriously damp, and one curl didn’t recover its right shape for nearly two days. . . . In all his books, Brian Greene is our tour guide on a journey into his particular looking-glass world—string theory, an exercise in the speculative sublime, a sublime only for aficionados, certainly not for you and me. Here is the abstract of an article cited a respectable 201 times: . . . We show that a string-inspired Planck scale modification of general relativity can have observable cosmological effects. Specifically, we present a complete analysis of the inflationary perturbation spectrum produced by a phenomenological Lagrangian that has a standard form on large scales but incorporates a string-inspired short distance cutoff, and find a deviation from the standard result. We use the de Sitter calculation as the basis of a qualitative analysis of other inflationary backgrounds, arguing that in these cases the cutoff could have a more pronounced effect, changing the shape of the spectrum. Moreover, the computational approach developed here can be used to provide unambiguous calculations of the perturbation spectrum in other heuristic models that modify trans-Planckian physics and thereby determine their impact on the inflationary perturbation spectrum. Finally, we argue that this model may provide an exception to constraints, recently proposed by Tanaka and Starobinsky, on the ability of Planck-scale physics to modify the cosmological spectrum. . . .

On braneworld inverse power-law inflation

In the framework of the braneworld Randall–Sundrum type II model, we investigate an inflationary scalar model in the high-energy regime. In this regime, the slow-roll parameters and the perturbation spectrum of the model are derived. The corresponding results are dealt with according to the known observational data. Then the solutions to the equations of motion on the brane are given.

Quantum gravity at Hubble scales determines the cosmological constant and the amplitude of primordial perturbations

Gravity controls the amount of information that is accessible to any specific observer. We quantify the notion of cosmic information (‘CosmIn’) for the case of an eternal observer in the universe. Demanding the finiteness of CosmIn requires the universe to have a late-time accelerated expansion phase. Combined with some generic features of the quantum structure of spacetime, this leads to the determination of (i) the numerical value of the cosmological constant, as well as (ii) the amplitude of the primordial, scale invariant perturbation spectrum in terms of a single free parameter, which specifies the energy scale at which the universe makes a transition from a pre-geometric phase to the classical phase. This formalism also shows that the quantum gravitational information content of spacetime can be tested by using precision cosmology.