Yuuiti Sendouda

Measuring the primordial power spectrum on small scales is a powerful tool in inflation model building, yet constraints from Cosmic Microwave Background measurements alone are insufficient to place bounds stringent enough to be appreciably effective. For the very small scale spectrum, those which subtend angles of less than 0.3 degrees on the sky, an upper bound can be extracted from the astrophysical constraints on the possible production of primordial black holes in the early universe. A recently discovered observational by-product of an enhanced power spectrum on small scales, induced gravitational waves, have been shown to be within the range of proposed space based gravitational wave detectors; such as NASA's LISA and BBO detectors, and the Japanese DECIGO detector. In this paper we explore the impact such a detection would have on models of inflation known to lead to an enhanced power spectrum on small scales, namely the Hilltop-type and running mass models. We find that the Hilltop-type model can produce observable induced gravitational waves within the range of BBO and DECIGO for integral and fractional powers of the potential within a reasonable number of e-folds. We also find that the running mass model can produce a spectrum within the range of these detectors, but require that inflation terminates after an unreasonably small number of e-folds. Finally, we argue that if the thermal history of the Universe were to accomodate such a small number of e-folds the Running Mass Model can produce Primordial Black Holes within a mass range compatible with Dark Matter, i.e. within a mass range 10^{20}g< M_{BH}<10^{27}g.

We show that the ghost degrees of freedom of Einstein gravity with a Weyl term can be tamed by a simple mechanism that invokes local Lorentz symmetry breaking. We demonstrate how the mechanism works in a cosmological setting. The presence of the Weyl term forces a redefinition of the quantum vacuum state of the tensor perturbations. As a consequence the amplitude of their spectrum blows up when the Lorentz-violating scale becomes comparable to the Hubble radius. Such a behaviour is in sharp contrast to what happens in standard Weyl gravity where the gravitational ghosts smoothly damp out the spectrum of primordial gravitational waves.

In order to assess the role of ghosts in cosmology, we study the evolution of linear cosmological perturbations during inflation when a Weyl term is added to the action. Our main results are that vector perturbations can no longer be ignored and that scalar modes diverge in the newtonian gauge but remain bounded in the comoving slicing.

We present an analytical method to calculate the small angle CMB temperature angular power spectrum due to cosmic (super-)string segments, following our previous paper [Phys. Rev. D 82 (2010), 063518, arXiv:1006.0687]. In particular, using our method, we clarify the dependence on the intercommuting probability P. The power spectrum is dominated by Poisson-distributed string segments. The power spectrum for a general value of P has a plateau on large angular scales and shows a power-law decrease on small angular scales. The resulting spectrum in the case of conventional cosmic strings is in very good agreement with the numerical result obtained by Fraisse et al. Then we estimate the upper bound on the dimensionless tension of the string for various values of P by assuming that the fraction of the CMB power spectrum due to cosmic (super-)strings is less than ten percents at various angular scales up to ℓ= 2000. The amplitude of the spectrum increases as the intercommuting probability. As a consequence, strings with smaller intercommuting probabilities are found to be more tightly constrained.