A physical model for dimensional reduction and its effects on the observable parameters of the universe

We construct a physical model to study the effects of dimensional reduction that might have taken place during the inflationary phase of the universe. The model we propose is a (1 + D)-dimensional (D > 3), nonsingular, spatially homogeneous and isotropic Friedmann model. We consider dimensional reduction to take place in a stepwise manner and interpret each step as a phase transition. Independent of the details of the process of dimensional reduction, we impose suitable boundary conditions across the transitions and trace the effects of dimensional reduction to the currently observable parameters of the universe. In order to exhibit the cosmological features of the proposed model, we construct a (1 + 4)-dimensional toy model for both closed and open cases of Friedmann geometries. It is shown that in these models the universe makes transition into the lower dimension when the critical length parameter l _4,3, which signals dimensional reduction, reaches the Planck length in D = 3. The numerical models we present in this paper have the capability of making definite predictions about the cosmological parameters of the universe such as the Hubble parameter, age and density.     

Mimicking trans-Planckian effects in the CMB with conventional physics

We investigate the possibility that fields coupled to the inflaton can influence the primordial spectrum of density perturbations through their coherent motion. For example, the second field in hybrid inflation might be oscillating at the beginning of inflation rather than at the minimum of its potential. Although this effect is washed out if inflation lasts long enough, we note that there can be up to 30e-foldings of inflation prior to horizon crossing of COBE fluctuations while still giving a potentially visible distortion. Such pumping of the inflaton fluctuations by purely conventional physics can resemble trans-Planckian effects which have been widely discussed. The distortions which they make to the CMB could leave a distinctive signature which differs from generic effects like tilting of the spectrum.     

Choosability conjectures and multicircuits

This paper starts with a discussion of several old and new conjectures about choosability in graphs. In particular, the list-colouring conjecture, that ch′=χ′ for every multigraph, is shown to imply that if a line graph is (a : b)-choosable, then it is (ta : tb)-choosable for every positive integer t. It is proved that ch(H²)=χ(H²) for many “small” graphs H, including inflations of all circuits (connected 2-regular graphs) with length at most 11 except possibly length 9; and that ch″(C)=χ″(C) (the total chromatic number) for various multicircuits C, mainly of even order, where a multicircuit is a multigraph whose underlying simple graph is a circuit. In consequence, it is shown that if any of the corresponding graphs H² or T(C) is (a : b)-choosable, then it is (ta : tb)-choosable for every positive integer t.     

Non-gravitating scalar field in the FRW background

We study interacting scalar field theory non-minimally coupled to gravity in the FRW background. We show that for a specific choice of interaction terms, the energy–momentum tensor of the scalar field ϕ vanishes, and as a result the scalar field does not gravitate. The naive space dependent solution to equations of motion gives rise to singular field profile. We carefully analyze the energy–momentum tensor for such a solution and show that the singularity of the solution gives a subtle contribution to the energy–momentum tensor. The space dependent solution therefore is not non-gravitating. Our conclusion is applicable to other space–time dependent non-gravitating solutions as well. We study hybrid inflation scenario in this model when purely time dependent non-gravitating field is coupled to another scalar field χ.     

Effects of the modified uncertainty principle on the inflation parameters

In this Letter we study the effects of the Modified Uncertainty Principle as proposed in Ali et al. (2009) [7] on the inflationary dynamics of the early universe in both standard and Randall–Sundrum type II scenarios. We find that the quantum gravitational effect increase the amplitude of density fluctuation, which is oscillatory in nature, with an increase in the tensor-to-scalar ratio.     

Breaks or long memory behavior: An empirical investigation

Are structural break models true switching models or long memory processes? The answer to this question remains ambiguous. In recent years, many papers have dealt with this problem. Some studies have shown that, under specific conditions, switching models and long memory processes can easily be confused. In this paper, using several generating models (the mean-plus-noise model, the stochastic permanent break model, the Markov switching model, the threshold autoregressive (TAR) model, the sign model, and the structural change model) and several estimation techniques (the Geweke–Porter–Hudak (GPH) technique, detrended fluctuation analysis (DFA), the exact local Whittle (ELW) method, and wavelet methods) we show that, even if the answer is quite simple in some cases, it can be mitigated in other cases. Using French and American inflation rates, we found that the most appropriate process that takes into account the important features of these series is a model that simultaneously combines changes in regimes and long memory behavior. The main result of this study indicates that estimating a long memory parameter without taking into account the presence of breaks in the data sets may lead to misspecification and hence to overestimating the true parameter.     

Controlling Inflation: The Infinite Horizon Case

This paper studies the two-dimensional singular stochastic control problem over an infinite time-interval arising when the Central Bank tries to contain the inflation by acting on the nominal interest rate. It is shown that this problem admits a variational formulation which can be differentiated (in some sense) to lead to a stochastic differential game with stopping times between the conservative and the expansionist tendencies of the Bank. Substantial regularity of the free boundary associated to the differential game is obtained. Existence of an optimal policy is established when the regularity of the free boundary is strengthened slightly, and it is shown that the optimal process is a diffusion reflected at the boundary. Accepted 22 May 1998     

Galileons and naked singularities

A simple trace-coupled Galileon model is shown to admit spherically symmetric static solutions with naked spacetime curvature singularities.