We analytically calculate to second order the correction to the asymptotic form of quasinormal frequencies of four dimensional Schwarzschild black holes based on the monodromy analysis proposed by Motl and Neitzke. According to our calculation, all the second order corrections are purely imaginary. For gravitational axial perturbation, the numerical values of the imaginary part of the correction are in good agreement with the available numerical results. However, our result for the real part shows sizeable discrepancy with the numerical one for large angular momentum ($l=6$). This might indicate certain limitations in the numerical methods used in the literature and more study is needed to settle this issue.

We analyze the effect of gravitational radiation reaction on generic orbits around a body with an axisymmetric mass quadrupole moment $Q$ to linear order in $Q$, to the leading post-Newtonian order, and to linear order in the mass ratio. This system admits three constants of the motion in absence of radiation reaction: energy, angular momentum along the symmetry axis, and a third constant analogous to the Carter constant. We compute instantaneous and time-averaged rates of change of these three constants. For a point particle orbiting a black hole, Ryan has computed the leading order evolution of the orbit’s Carter constant, which is linear in the spin. Our result, when combined with an interaction quadratic in the spin (the coupling of the black hole’s spin to its own radiation reaction field), gives the next to leading order evolution. The effect of the quadrupole, like that of the linear spin term, is to circularize eccentric orbits and to drive the orbital plane towards antialignment with the symmetry axis. In addition we consider a system of two point masses where one body has a single mass multipole or current multipole of order $l$. To linear order in the mass ratio, to linear order in the multipole, and to the leading post-Newtonian order, we show that there does not exist an analog of the Carter constant for such a system (except for the cases of an $l=1$ current moment and an $l=2$ mass moment). Thus, the existence of the Carter constant in Kerr depends on interaction effects between the different multipoles. With mild additional assumptions, this result falsifies the conjecture that all vacuum, axisymmetric spacetimes possess a third constant of the motion for geodesic motion.

In their original study of conformal gravity, a candidate alternate gravitational theory, Mannheim and Kazanas showed that in any empty vacuum region exterior to a localized static spherically symmetric gravitational source, the geometry would reduce to the standard attractive gravity Schwarzschild geometry on solar system distance scales. In a recent paper Flanagan has argued that this would not be the case if the source has associated with it a macroscopic scalar field which makes a nonzero contribution to the energy-momentum tensor in the otherwise empty exterior region. In this paper we examine Flanagan’s analysis and show that even with such long range scalar fields, the standard Schwarzschild phenomenology is still recovered.

We derive a microscopic bound on the maximal field variation of the inflaton during warped D-brane inflation. By a result of Lyth, this implies an upper limit on the amount of gravitational waves produced during inflation. We show that a detection at the level $r>0.01$ would falsify slow roll D-brane inflation. In DBI (Dirac-Born-Infeld) inflation, detectable tensors may be possible in special compactifications, provided that $r$ decreases rapidly during inflation. We also show that for the special case of DBI inflation with a quadratic potential, current observational constraints imply strong upper bounds on the five-form flux.

We analyze the evolution of cosmological perturbations in the cyclic model, paying particular attention to their behavior and interplay over multiple cycles. Our key results are: (1) galaxies and large scale structure present in one cycle are generated by the quantum fluctuations in the preceding cycle without interference from perturbations or structure generated in earlier cycles and without interfering with structure generated in later cycles; (2) the ekpyrotic phase, an epoch of gentle contraction with equation of state $w\gg 1$ preceding the hot big bang, makes the universe homogeneous, isotropic and flat within any given observer’s horizon; and (3) although the universe is uniform within each observer’s horizon, the structure of the cyclic universe on very large scales is more complex, owing to the effects of superhorizon length perturbations, and cannot be described globally as a Friedmann-Robertson-Walker cosmology. In particular, we show that the ekpyrotic contraction phase is so effective in smoothing, flattening and isotropizing the universe within the horizon that this phase alone suffices to solve the horizon and flatness problems even without an extended period of dark energy domination (a kind of low energy inflation). Instead, the cyclic model rests on a genuinely novel, noninflationary mechanism (ekpyrotic contraction) for resolving the classic cosmological conundrums.

We show that axinos, which are dominantly generated by the decay of the next-to-lightest supersymmetric particles produced from the leptonic $Q$-ball ($L$-ball), become warm dark matter suitable for the solution of the missing satellite problem and the cusp problem. In addition, ${\Omega }_b-{\Omega }_{\mathrm{DM}}$ coincidence is naturally explained in this scenario.

The propagation of a linearly polarized laser beam in the external transverse magnetic field is studied. We explore the effective Lagrangian of the electromagnetic field. With the help of the effective Lagrangian, Stokes parameters, induced ellipticity, and the angular rotation of the polarization plane of the beam are evaluated. Ellipticity measured in the PVLAS experiment allows us to obtain the relation between two parameters in the effective Lagrangian.

The parameters of the minimal supersymmetric standard model appear to require uncomfortably precise adjustment in order to reconcile the electroweak symmetry breaking scale with the lower mass limits on a neutral Higgs scalar boson. This problem can be significantly ameliorated in models with a running gluino mass parameter that is smaller than the wino mass near the scale of unification of gauge couplings. A compressed superpartner mass spectrum results; compared to models with unified gaugino masses, the ratios of the squark and gluino masses to the lightest superpartner mass are reduced. I argue that in this scenario the annihilation of binolike neutralino pairs to top-antitop quark pairs through top-squark exchange can most naturally play the crucial role in ensuring that the thermal relic dark matter density is not too large, with only a small role played by coannihilations. The lightest superpartner mass must then exceed the top-quark mass, and the lighter top squark cannot decay to a top quark. These conditions have important implications for collider searches.

We investigate the predictions for fermion masses in the minimal realistic nonsupersymmetric $SU(5)$ model with the standard model matter content. The possibility to achieve $b-\tau$ unification is studied taking into account all relevant effects. In addition, we show how to establish an upper bound on the ultraviolet cutoff $\Lambda$ of the theory which is compatible with the Yukawa couplings at the grand unified scale and proton decay. We find $\Lambda \simeq {10}^{17}\mathrm{GeV}$, to be considered a conservative upper bound on the cutoff. We also provide up-to-date values of all the fermions masses at the electroweak scale.

We present approximate formulas for the tensor BB, EE, TT, and TE multipole coefficients for large multipole order $\ell$. The error in using the approximate formula for the BB multipole coefficients is less than cosmic variance for $\ell >10$. These approximate formulas make various qualitative properties of the calculated multipole coefficients transparent: specifically, they show that, whatever values are chosen for cosmological parameters, the tensor EE multipole coefficients will always be larger than the BB coefficients for all $\ell >15$, and that these coefficients will approach each other for $\ell \ll 100$. These approximations also make clear how these multipole coefficients depend on cosmological parameters.

The cosmic microwave background power spectra are studied for different families of single field new and chaotic inflation models in the effective field theory approach to inflation. We implement a systematic expansion in $1/N_e$, where $N_e\sim 50$ is the number of e-folds before the end of inflation. We study the dependence of the observables ($n_s$, $r$ and $d{n}_s/d\ln k$) on the degree of the potential ($2n$) and confront them to the WMAP3 and large scale structure data: This shows in general that fourth degree potentials ($n=2$) provide the best fit to the data; the window of consistency with the WMAP3 and LSS data narrows for growing $n$. New inflation yields a good fit to the $r$ and $n_s$ data in a wide range of field and parameter space. Small field inflation yields $r<0.16$ while large field inflation yields $r>0.16$ (for $N_e=50$). All members of the new inflation family predict a small but negative running $-4(n+1)\times {10}^{-4}\le d{n}_s/d\ln k\le -2\times {10}^{-4}$. (The values of $r$, $n_s$, $d{n}_s/d\ln k$ for arbitrary $N_e$ follow by a simple rescaling from the $N_e=50$ values.) A reconstruction program is carried out suggesting quite generally that for $n_s$ consistent with the WMAP3 and LSS data and $r<0.1$ the symmetry breaking scale for new inflation is $|{\varphi }_0|\sim 10M_{\mathrm{Pl}}$ while the field scale at Hubble crossing is $|{\varphi }_c|\sim M_{\mathrm{Pl}}$. The family of chaotic models features $r\ge 0.16$ (for $N_e=50$) and only a restricted subset of chaotic models are consistent with the combined WMAP3 bounds on $r$, $n_s$, $d{n}_s/d\ln k$ with a narrow window in field amplitude around $|{\varphi }_c|\sim 15M_{\mathrm{Pl}}$. We conclude that a measurement of $r<0.16$ (for $N_e=50$) distinctly rules out a large class of chaotic scenarios and favors small field new inflationary models. As a general consequence, new inflation emerges more favored than chaotic inflation.

We use our model of the small scale structure on cosmic strings to develop further the result of Siemens, Olum, and Vilenkin that the gravitational radiation length scale on cosmic strings is smaller than the previously assumed $\Gamma G\mu t$. We discuss some of the properties of cosmic string loops at this cutoff scale, and we argue that recent network simulations point to two populations of cosmic string loops, one near the horizon scale and one near the gravitational radiation cutoff.

Effects of a generalized dark energy fluid are investigated on cosmic density fluctuations such as a cosmic microwave background. As a general dark energy fluid, we take into consideration the possibility of the anisotropic stress for dark energy, which has not been discussed much in the literature. We comprehensively study its effects on the evolution of density fluctuations along with that of the nonadiabatic pressure fluctuation of dark energy, then give constraints on such a generalized dark energy from current observations. We show that, though we cannot find any stringent limits on the anisotropic stress or the nonadiabatic pressure fluctuation themselves, the constraints on the equation of state of dark energy can be affected in some cases by the nature of dark energy fluctuation characterized by these properties. This may have important implications in the strategy to study the nature of dark energy.

For a standard model Higgs boson with mass between 115 GeV and 150 GeV, the two-photon decay mode is important for discovery at the Large Hadron Collider (LHC). We describe the interactions of a light Higgs boson in a more model-independent fashion and consider the parameter space where there is no two-photon decay mode. We argue from generalities that analysis of the $t\overline{t}h$ discovery mode outside its normal thought of range of applicability is especially needed under these circumstances. We demonstrate the general conclusion with a specific example of parameters of a type I two-Higgs doublet theory, motivated by ideas in strongly coupled model building. We then specify a complete set of branching fractions and discuss the implications for the LHC.

Meson Green’s functions and decay constants $f_{\Gamma }$ in different channels $\Gamma$ are calculated using the field correlator method. Both, spectrum and $f_{\Gamma }$, appear to be expressed only through universal constants: the string tension $\sigma$, ${\alpha }_s$, and the pole quark masses. For the $S$-wave states the calculated masses agree with the experimental numbers within $\pm 5\mathrm{MeV}$. For the $D$ and $D_s$ mesons the values of $f_{\mathrm{P}}(1S)$ are equal to 210(10) and $260(10)\mathrm{MeV}$, respectively, and their ratio $f_{D_s}/f_D=1.24(3)$, agrees with a recent CLEO experiment. The values $f_{\mathrm{P}}(1S)=182$, 216, 438 MeV are obtained for the $B$, $B_s$, and $B_c$ mesons with the ratio $f_{B_s}/f_B=1.19(2)$ and $f_D/f_B=1.14(2)$. The decay constants $f_{\mathrm{P}}(2S)$ for the first radial excitations as well as the decay constants $f_{\mathrm{V}}(1S)$ in the vector channel are also calculated. The difference of about 20% between $f_{D_s}$ and $f_D$, $f_{B_s}$ and $f_B$ directly follows from our analytical formulas.

The expectation value of the complex phase factor of the fermion determinant is computed in the microscopic domain of QCD at nonzero chemical potential. We find that the average phase factor is nonvanishing below a critical value of the chemical potential equal to half the pion mass and vanishes exponentially in the volume for larger values of the chemical potential. This holds for QCD with dynamical quarks as well as for quenched and phase quenched QCD. The average phase factor has an essential singularity for zero chemical potential and cannot be obtained by analytic continuation from imaginary chemical potential or by means of a Taylor expansion. The leading order correction in the $p$-expansion of the chiral Lagrangian is calculated as well.

Spectra of the stochastic gravitational wave backgrounds from cosmic strings are calculated and compared with present and future experimental limits. Motivated by theoretical expectations of light cosmic strings in superstring cosmology, improvements in experimental sensitivity, and recent demonstrations of large, stable loop formation from a primordial network, this study explores a new range of string parameters with masses lighter than previously investigated. A standard “one-scale” model for string loop formation is assumed. Background spectra are calculated numerically for dimensionless string tensions $G\mu /c^2$ between ${10}^{-7}$ and ${10}^{-18}$, and initial loop sizes as a fraction of the Hubble radius $\alpha$ from 0.1 to ${10}^{-6}$. The spectra show a low frequency power-law tail, a broad spectral peak due to loops decaying at the present epoch (including frequencies higher than their fundamental mode, and radiation associated with cusps), and a flat (constant energy density) spectrum at high frequencies due to radiation from loops that decayed during the radiation-dominated era. The string spectrum is distinctive and unlike any other known source. The peak of the spectrum for light strings appears at high frequencies, significantly affecting predicted signals. The spectra of the cosmic string backgrounds are compared with current millisecond pulsar limits and Laser Interferometer Space Antenna (LISA) sensitivity curves. For models with large stable loops ($\alpha =0.1$), current pulsar-timing limits exclude $G\mu /c^2>{10}^{-9}$, a much tighter limit on string tension than achievable with other techniques, and within the range of current models based on brane inflation. LISA may detect a background from strings as light as $G\mu /c^2\approx {10}^{-16}$, corresponding to field theory strings formed at roughly ${10}^{11}\mathrm{GeV}$.

We study the flavor evolution of a dense gas initially consisting of pure monoenergetic ${\nu }_e$ and ${\overline{\nu }}_e$. Using adiabatic invariants and the special symmetry in such a system we are able to calculate the flavor evolution of the neutrino gas for the cases with slowly decreasing neutrino number densities. These calculations give new insights into the results of recent large-scale numerical simulations of neutrino flavor transformation in supernovae. For example, our calculations reveal the existence of what we term the “collective precession mode.” Our analyses suggest that neutrinos which travel on intersecting trajectories subject to destructive quantum interference nevertheless can be in this mode. This mode can result in sharp transitions in the final energy-dependent neutrino survival probabilities across all trajectories, a feature seen in the numerical simulations. Moreover, this transition is qualitatively different for the normal and inverted neutrino mass hierarchies. Exploiting this difference, the neutrino signals from a future galactic supernova can potentially be used to determine the actual neutrino mass hierarchy.