Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations

We derive the complete spectrum of gravitational waves induced by primordial scalar perturbations ranging over all observable wavelengths. This scalar-induced contribution can be computed directly from the observed scalar perturbations and general relativity and is, in this sense, independent of the cosmological model for generating the perturbations. The spectrum is scale-invariant on small scales, but has an interesting scale-dependence on large and intermediate scales, where scalar-induced gravitational waves do not redshift and are hence enhanced relative to the background density of the Universe. This contribution to the tensor spectrum is significantly different in form from the direct model-dependent primordial tensor spectrum and, although small in magnitude, it dominates the primordial signal for some cosmological models. We confirm our analytical results by direct numerical integration of the equations of motion.Comment: 19 pages, 5 figure

Cosmic microwave background bispectrum of tensor passive modes induced from primordial magnetic fields

If the seed magnetic fields exist in the early Universe, tensor components of their anisotropic stresses are not compensated prior to neutrino decoupling and the tensor metric perturbations generated from them survive passively. Consequently, due to the decay of these metric perturbations after recombination, the so-called integrated Sachs-Wolfe effect, the large-scale fluctuations of CMB radiation are significantly boosted. This kind of CMB anisotropy is called the "tensor passive mode." Because these fluctuations deviate largely from the Gaussian statistics due to the quadratic dependence on the strength of the Gaussian magnetic field, not only the power spectrum but also the higher-order correlations have reasonable signals. With these motives, we compute the CMB bispectrum induced by this mode. When the magnetic spectrum obeys a nearly scale-invariant shape, we obtain an estimation of a typical value of the normalized reduced bispectrum as $\ell_1(\ell_1 + 1)\ell_3(\ell_3+1)|b_{\ell_1\ell_2\ell_3}| \sim (130-6) \times 10^{-16} (B_{1 \rm Mpc} / 4.7 {\rm nG})^6$ depending on the energy scale of the magnetic field production from $10^{14}$GeV to $10^3$GeV. Here, $B_{1 {\rm Mpc}}$ is the strength of the primordial magnetic field smoothed on $1 {\rm Mpc}$. From the above estimation and the current observational constraint on the primordial non-Gaussianity, we get a rough constraint on the magnetic field strength as $B_{1 {\rm Mpc}} < 2.6 - 4.4 {\rm nG}$.Comment: 5 pages, 2 figures. Accepted for publication in PR

Probing the Nature of the Weakest Intergalactic Magnetic Fields with the High Energy Emission of Gamma-Ray Bursts

We investigate the delayed, secondary GeV-TeV emission of gamma-ray bursts and its potential to probe the nature of intergalactic magnetic fields. Geometrical effects are properly taken into account for the time delay between primary high energy photons and secondary inverse Compton photons from electron-positron pairs, which are produced in $\gamma$-$\gamma$ interactions with background radiation fields and deflected by intervening magnetic fields. The time-dependent spectra of the delayed emission are evaluated for a wide range of magnetic field strengths and redshifts. The typical flux and delay time of secondary photons from bursts at $z \sim 1$ are respectively $\sim 10^{-8}$ GeV cm$^{-2}$ s$^{-1}$ and $\sim 10^4$ s if the field strengths are $\sim 10^{-18}$ G, as might be the case in intergalactic void regions. We find crucial differences between the cases of coherent and tangled magnetic fields, as well as dependences on the field coherence length.Comment: 19 pages, 9 figures, formulation revised, accepted for publication in Ap

Effects of a primordial magnetic field with log-normal distribution on the cosmic microwave background

We study the effect of primordial magnetic fields (PMFs) on the anisotropies of the cosmic microwave background (CMB). We assume the spectrum of PMFs is described by log-normal distribution which has a characteristic scale, rather than power-law spectrum. This scale is expected to reflect the generation mechanisms and our analysis is complementary to previous studies with power-law spectrum. We calculate power spectra of energy density and Lorentz force of the log-normal PMFs, and then calculate CMB temperature and polarization angular power spectra from scalar, vector, and tensor modes of perturbations generated from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang, and ACBAR data sets, we find that the current CMB data set places the strongest constraint at $k\simeq 10^{-2.5}$ Mpc$^{-1}$ with the upper limit $B\lesssim 3$ nG.Comment: 14 pages, 6 figure

EoS of finite density QCD with Wilson fermions by Multi-Parameter Reweighting and Taylor expansion

The equation of state (EoS), quark number density and susceptibility at nonzero quark chemical potential $\mu$ are studied in lattice QCD simulations with a clover-improved Wilson fermion of 2-flavors and RG-improved gauge action. To access nonzero $\mu$, we employ two methods : a multi-parameter reweighting (MPR) in $\mu$ and $\beta$ and Taylor expansion in $\mu/T$. The use of a reduction formula for the Wilson fermion determinant enables to study the reweighting factor in MPR explicitly and heigher-order coefficients in Taylor expansion free from errors of noise method, although calculations are limited to small lattice size. As a consequence, we can study the reliability of the thermodynamical quantities through the consistency of the two methods, each of which has different origin of the application limit. The thermodynamical quantities are obtained from simulations on a $8^3\times 4$ lattice with an intermediate quark mass($m_{\rm PS}/m_{\rm V}=0.8)$. The MPR and Taylor expansion are consistent for the EoS and number density up to $\mu/T\sim 0.8$ and for the number susceptibility up to $\mu/T \sim 0.6$. This implies within a given statistics that the overlap problem for the MPR and truncation error for the Taylor expansion method are negligible in these regions. In order to make MPR methods work, the fluctuation of the reweighting factor should be small. We derive the equation of the reweighting line where the fluctuation is small, and show that the equation of the reweighting line is consistent with the fluctuation minimum condition.Comment: 20 pages, 11 figures. Accepted to JHEP. Discussions are added. Figures for Taylor coefficients (Fig. 7) are modifie

Exactly solvable model for cosmological perturbations in dilatonic brane worlds

We construct a model where cosmological perturbations are analytically solved based on dilatonic brane worlds. A bulk scalar field has an exponential potential in the bulk and an exponential coupling to the brane tension. The bulk scalar field yields a power-law inflation on the brane. The exact background metric can be found including the back-reaction of the scalar field. Then exact solutions for cosmological perturbations which properly satisfy the junction conditions on the brane are derived. These solutions provide us an interesting model to understand the connection between the behavior of cosmological perturbations on the brane and the geometry of the bulk. Using these solutions, the behavior of an anisotropic stress induced on the inflationary brane by bulk gravitational fields is investigated.Comment: 30 pages, typos corrected, reference adde

Effects of Neutrino Oscillation on the Supernova Neutrino Spectrum

The effects of three-flavor neutrino oscillation on the supernova neutrino spectrum are studied. We calculate the expected event rate and energy spectra, and their time evolution at the Superkamiokande (SK) and the Sudbury Neutrino Observatory (SNO), by using a realistic neutrino burst model based on numerical simulations of supernova explosions. We also employ a realistic density profile based on a presupernova model for the calculation of neutrino conversion probability in supernova envelopes. These realistic models and numerical calculations allow us to quantitatively estimate the effects of neutrino oscillation in a more realistic way than previous studies. We then found that the degeneracy of the solutions of the solar neutrino problem can be broken by the combination of the SK and SNO detections of a future Galactic supernova.Comment: 10 pages, 14 figures, corrected versio

Primordial magnetic fields generated by the non-adiabatic fluctuations at pre-recombination era

In the pre-recombination era, cosmological density fluctuations can naturally generate magnetic fields through Thomson scatterings. In previous studies, only the magnetic field generation from the initially-adiabatic fluctuations has been considered. Here we investigate the generation of cosmological magnetic fields sourced by the primordial non-adiabatic fluctuations based on the cosmological perturbation theory, using the tight-coupling approximations between photon and baryon fluids. It is found that the magnetic fields from the non-adiabatic fluctuations can arise at the first-order expansion of the tight coupling approximation. This result is in contrast to the case of adiabatic initial fluctuations, where the magnetic fields can be generated only at the second-order. In a general case where the primordial density perturbations contain small non-adiabatic fluctuations on the top of the dominant adiabatic ones, we show that the leading source of magnetic fields is given by the second-order coupling of the adiabatic and non-adiabatic fluctuations. We calculate the power spectrum of the generated magnetic fields when the non-adiabatic fluctuations have a blue power spectrum, which has been suggested by recent cosmological observations.Comment: 16 pages, 2 figures, minor corrections, references added, to be published in JCA

Primordial fluctuations in bulk inflaton model

An inflationary brane model driven by a bulk inflaton with exponential potential is proposed. We find a family of exact solutions that describe power-law inflation on the brane. These solutions enable us to derive exact solutions for metric perturbations analytically. By calculating scalar and tensor perturbations, we obtain a spectrum of primordial fluctuations at the end of the inflation. The amplitudes of scalar and tensor perturbations are enhanced in the same way if the energy scale of the inflation is sufficiently higher than the tension of the brane. Then the relative amplitude of scalar and tensor perturbations is not suppressed even for high-energy inflation. This is a distinguishable feature from the inflation model driven by inflaton on the brane where tensor perturbations are suppressed for high-energy inflation. We also point out that massive Kaluza-Klein modes are not negligible at high-frequencies on 3-space of our brane.Comment: 16 pages, 3 figures, reference adde

Cosmology and two-body problem of D-branes

In this paper, we investigate the dynamics and the evolution of the scale factor of a probe Dp-brane which move in the background of source Dp-branes. Action of the probe brane is described by the Born-Infeld action and the interaction with the background R-R field. When the probe brane moves away from the source branes, it expands by power law, whose index depends on the dimension of the brane. If the energy density of the gauge field on the brane is subdominant, the expansion is decelerating irrespective of the dimension of the brane. On the other hand, when the probe brane is a Nambu-Goto brane, the energy density of the gauge field can be dominant, in which case accelerating expansion occurs for $p \leq 4$. The accelerating expansion stops when the brane has expanded sufficiently so that the energy density of the gauge field become subdominant.Comment: 6 pages, 7 figures, reference added, accepted for publication in PR