Yuuiti Sendouda

Hamiltonian Formulation of f(Riemann) Theories of Gravity

We present a canonical formulation of gravity theories whose Lagrangian is an arbitrary function of the Riemann tensor, which, for example, arises in the low-energy limit of superstring theories. Our approach allows a unified treatment of various subcases and an easy identification of the degrees of freedom of the theory.

Junction Conditions in f(R) Theories of Gravity

Taking advantage of the conformal equivalence of f(R) theories of gravity with General Relativity coupled to a scalar field we generalize the Israel junction conditions for this class of theories by direct integration of the field equations. We suggest a specific non-minimal coupling of matter to gravity which opens the possibility of a new class of braneworld scenarios.

Non-Gaussianity in the Cosmic Microwave Background temperature fluctuations from cosmic (super-)strings

We compute analytically the small-scale temperature fluctuations of the cosmic microwave background from cosmic (super-)strings and study the dependence on the string intercommuting probability P. We develop an analytical model which describes the evolution of a string network and calculate the numbers of string segments and kinks in a horizon volume. Then we derive the probability distribution function (pdf) which takes account of finite angular resolution of observation. The resultant pdf consists of a Gaussian part due to frequent scatterings by long string segments and a non-Gaussian tail due to close encounters with kinks. The dispersion of the Gaussian part is reasonably consistent with that obtained by numerical simulations by Fraisse et al.. On the other hand, the non-Gaussian tail contains two phenomenological parameters which are determined by comparison with the numerical results for P = 1. Extrapolating the pdf to the cases with P < 1, we predict that the non-Gaussian feature is suppressed for small P.

Observable spectra of induced gravitational waves from inflation

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 NASAs 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 1020gMBH1027g.

Constraints on primordial black holes from the Galactic gamma-ray background

The fraction of the Universe going into primordial black holes (PBHs) with initial mass M_* \approx 5 \times 10^{14} g, such that they are evaporating at the present epoch, is strongly constrained by observations of both the extragalactic and Galactic gamma-ray backgrounds. However, while the dominant contribution to the extragalactic background comes from the time-integrated emission of PBHs with initial mass M_*, the Galactic background is dominated by the instantaneous emission of those with initial mass slightly larger than M_* and current mass below M_*. Also, the instantaneous emission of PBHs smaller than 0.4 M_* mostly comprises secondary particles produced by the decay of directly emitted quark and gluon jets. These points were missed in the earlier analysis by Lehoucq et al. using EGRET data. For a monochromatic PBH mass function, with initial mass (1+\mu) M_* and \mu << 1, the current mass is (3\mu)^{1/3} M_* and the Galactic background constrains the fraction of the Universe going into PBHs as a function of \mu. However, the initial mass function cannot be precisely monochromatic and even a tiny spread of mass around M_* would generate a current low-mass tail of PBHs below M_*. This tail would be the main contributor to the Galactic background, so we consider its form and the associated constraints for a variety of scenarios with both extended and nearly-monochromatic initial mass functions. In particular, we consider a scenario in which the PBHs form from critical collapse and have a mass function which peaks well above M_*. In this case, the largest PBHs could provide the dark matter without the M_* ones exceeding the gamma-ray background limits.

Observable induced gravitational waves from an early matter phase

Assuming that inflation is succeeded by a phase of matter domination, which corresponds to a low temperature of reheating Tr < 109GeV, we evaluate the spectra of gravitational waves induced in the post-inflationary universe. We work with models of hilltop-inflation with an enhanced primordial scalar spectrum on small scales, which can potentially lead to the formation of primordial black holes. We find that a lower reheat temperature leads to the production of gravitational waves with energy densities within the ranges of both space and earth based gravitational wave detectors.

Skewness in CMB temperature fluctuations from curved cosmic (super-)strings

We compute the one-point probability distribution function of small-angle cosmic microwave background temperature fluctuations due to curved cosmic (super-)strings with a simple model of string network by performing Monte Carlo simulations. Taking into account of the correlation between the curvature and the velocity of string segments, there appear non-Gaussian features, specifically non-Gaussian tails and a skewness, in the one-point pdf. The obtained sample skewness for the conventional field-theoretic cosmic strings is g1 ≈ −0.14, which is consistent with the result reported by Fraisse et al. We also discuss the dependence of the pdf on the intercommuting probability. We find that the standard deviation of the Gaussian part increases and non-Gaussian features are suppressed as the intercommuting probability decreases. For sufficiently small intercommuting probability, the skewness is given by (a few) × 10−2.

Rapid merger of binary primordial black holes: An implication for GW150914

We propose a new scenario for the evolution of a binary of primordial black holes (PBHs). We consider a dynamical friction by ambient dark matter, scattering of dark matter particles with a highly eccentric orbit besides the standard two-body relaxation process to refill the loss cone, and interaction between the binary and a circumbinary disk, assuming that PBHs do not constitute the bulk of dark matter. Binary PBHs lose the energy and angular momentum by these processes, which could be sufficiently efficient for a typical configuration. Such a binary coalesces due to the gravitational wave emission in a time scale much shorter than the age of the universe. We estimate the density parameter of the resultant gravitational wave background. Astrophysical implication concerning the formation of intermediate-mass to supermassive black holes is also discussed.

Type-I cosmic-string network

We study the network of Type-I cosmic strings using the field-theoretic numerical simulations in the Abelian-Higgs model. For Type-I strings, the gauge field plays an important role, and thus we find that the correlation length of the strings is strongly dependent upon the parameter \beta, the ratio between the self-coupling constant of the scalar field and the gauge coupling constant, namely, \beta=\lambda/2e^2. In particular, if we take the cosmic expansion into account, the network becomes densest in the comoving box for a specific value of \beta for \beta<1.

Probing pre-inflationary anisotropy with directional variations in the gravitational wave background

We perform a detailed analysis on a primordial gravitational-wave background amplified during a Kasner-like pre-inflationary phase allowing for general triaxial anisotropies. It is found that the predicted angular distribution map of gravitational-wave intensity on large scales exhibits topologically distinctive patterns according to the degree of the pre-inflationary anisotropy, thereby serving as a potential probe for the pre-inflationary early universe with future all-sky observations of gravitational waves. We also derive an observational limit on the amplitude of such anisotropic gravitational waves from the B -mode polarisation of the cosmic microwave background.