While the topology of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a nontrivial topology will generate pairs of matching circles of temperature fluctuations in maps of the cosmic microwave background, the so-called circles-in-the-sky. A general search for such pairs of circles would be extremely costly and would therefore need to be confined to restricted parameter ranges. To draw quantitative conclusions from the negative results of such partial searches for the existence of circles we need a concrete theoretical framework. Here we provide such a framework by obtaining constraints on the angular parameters of these circles as a function of cosmological density parameters and the observer’s position. As an example of the application of our results, we consider the recent search restricted to pairs of nearly back-to-back circles with negative results. We show that assuming the Universe to be very nearly flat, with its total matter-energy density satisfying the bounds $0<|{\Omega }_0-1|\lesssim {10}^{-5}$, compatible with the predictions of typical inflationary models, this search, if confirmed, could in principle be sufficient to exclude a detectable nontrivial cosmic topology for most observers. We further relate explicitly the fraction of observers for which this result holds to the cosmological density parameters.

The most recent results from direct searches for dark matter particles in the Galactic halo are examined in terms of an effective minimal supersymmetric extension of the standard model at the electroweak scale without unification of gaugino masses. We show that the annual-modulation effect at $8.2\sigma$ C.L. recently presented by the DAMA Collaboration, as the result of a combined analysis of the DAMA/NaI and the DAMA/LIBRA experiments for a total exposure of 0.82 ton yr, fits remarkably well with what is expected for relic neutralinos for a wide variety of weakly interacting massive particle distribution functions. Bounds derivable from other measurements of direct searches for dark matter particles are analyzed. We stress the role played by the uncertainties affecting the neutralino-quark couplings arising from the involved hadronic quantities. We also examine how present data on cosmic antiprotons can help in constraining the neutralino configurations selected by the DAMA effect, in connection with the values of the astrophysical parameters. Perspectives for measurements of antideuterons, possibly produced in the Galactic halo by self-annihilation of neutralinos belonging to the DAMA configurations, are examined. Finally, we discuss how findings at the LHC would impact on these issues.

We calculate the reionization history for different models of the stellar population and explore the effects of primordial magnetic fields, dark matter decay and dark matter annihilation on reionization. We find that stellar populations based on a Scalo-type initial mass function for Population II stars can be ruled out as sole sources for reionization, unless star formation efficiencies of more than 10% or very high photon escape fractions from the parental halo are adopted. When considering primordial magnetic fields, we find that the additional heat injection from ambipolar diffusion and decaying MHD turbulence has a significant impact on the thermal evolution and the ionization history of the post-recombination universe and on structure formation. The magnetic Jeans mass changes the typical mass scale of the star-forming halos, and depending on the adopted stellar model we derive upper limits to the magnetic field strength between 0.7 and 5 nG (comoving). For dark matter annihilation, we find an upper limit to the thermally averaged mass-weighted cross section of $⟨\sigma v⟩/m_{\mathrm{DM}}\le {10}^{-33}{\mathrm{cm}}^3/\mathrm{s}/\mathrm{eV}$. For dark matter decay, our calculations yield a lower limit to the lifetime of dark matter particles of $\tau \ge 3\times {10}^{23}\mathrm{s}$. These limits are in agreement with constraints from recombination and provide an independent confirmation at a much later epoch.

Recently $B$ factories have published new results on the $B\to K\eta \gamma$ decays being inspired by the theoretical suggestion to search for new physics in $B\to P_1{P}_2\gamma$ decays. Using heavy-meson chiral perturbation theory, we find a mechanism which governs the amplitude in parts of the Dalitz plot where either $K$ or $\eta$ mesons are soft. The dominant contributions in these cases are coming from the nonresonant decay modes. We discuss also the $B\to K{\eta }^{\prime }\gamma$ Dalitz plot. Our partially integrated rates are in agreement with the experimental findings.

In the covariant light-front quark model, we study $J/\psi \to D_{(s)}$ transition form factors and utilize them to evaluate the branching fractions of various $J/\psi$ weak decay channels. For the Cabbibo allowed semileptonic decay modes $J/\psi \to D_{s}l\nu$, the predicted branching ratios are at the order of ${10}^{-10}$, which may be marginally measured at BESIII. The results for the semileptonic decay modes presented here are about 2–8 times larger than those calculated in the QCD sum rules approach, which is mainly due to the different treatment of nonperturbative QCD dynamics between these two approaches. Furthermore, we also give a rough estimation of the nonleptonic modes within the framework of the factorization approach, whose branching fraction numbers can be as large as ${10}^{-9}$ and are consistent with that obtained in the QCD sum rules within the theoretical uncertainties.

We have shown that nonzero $U_{e3}$ is generated in a seesaw type softly broken $A_4$ symmetric model through a single parameter perturbation in $m_D$ in a single element. We have explored all possible 9 cases to study the neutrino mixing angles considering the best fitted values of $\Delta m_{\odot }^2$ and $\Delta m_{\mathrm{atm}}^2$ with all parameters real. We have extended our analysis for the complex case and demonstrated large low energy $CP$ violation ($J_{CP}\simeq {10}^{-2}$) and $m_{ee}$ in addition to mixing and mass pattern. We have also investigated leptogenesis and for a reasonable choice of model parameters compatible with low energy data, the Wilkinson Microwave Anisotropy Probe (WMAP) value of baryon asymmetry $6\times {10}^{-10}$ is obtained for right-handed neutrino mass scale $M_0\simeq {10}^{13}\mathrm{GeV}$. We have obtained a relation among the phases responsible for leptogenesis and have shown that those phases also have correlations with low energy $CP$ violating phases.

We measure the time-dependent $CP$ asymmetry in $B^0\to K_S^0{\pi }^0\gamma$ decays for two regions of $K_S^0\mathrm{\text{−}}{\pi }^0$ invariant mass, $m(K_S^0{\pi }^0)$, using the final BABAR data set of $467\times {10}^6$ $B\overline{B}$ pairs collected at the PEP-II $e^{+}{e}^{-}$ collider at SLAC. We find $339\pm 24$ $B^0\to K^{*0}\gamma$ candidates and measure $S_{K^{*}\gamma }=-0.03\pm 0.29\pm 0.03$ and $C_{K^{*}\gamma }=-0.14\pm 0.16\pm 0.03$. In the range $1.1<m(K_S^0{\pi }^0)<1.8\mathrm{GeV}/c^2$ we find $133\pm 20$ $B^0\to K_S^0{\pi }^0\gamma$ candidates and measure $S_{K_S^0{\pi }^0\gamma }=-0.78\pm 0.59\pm 0.09$ and $C_{K_S^0{\pi }^0\gamma }=-0.36\pm 0.33\pm 0.04$. The uncertainties are statistical and systematic, respectively.

We present an alternative technique for evaluating multiloop Feynman diagrams, using the integration by fractional expansion method. Here we consider generic diagrams that contain propagators with radiative corrections which topologically correspond to recursive constructions of bubble type diagrams. The main idea is to reduce these subgraphs, replacing them by their equivalent multiregion expansion. One of the main advantages of this integration technique is that it allows one to reduce massive cases with the same degree of difficulty as in the massless case.

The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free $\omega$ parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ($\omega \to \pm \infty$), a dimensionally reduced cylindrical four-dimensional general relativity theory ($\omega =0$), and a theory representing a class of theories ($\omega =-3$), all with a Maxwell term. The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates $\{M,P_M;Q,P_Q\}$, where $M$ is the mass parameter, which for $\omega <-\frac{3}{2}$ and for $\omega =\pm \infty$ needs a careful renormalization, $P_M$ is the conjugate momenta of $M$, $Q$ is the charge parameter, and $P_Q$ is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schrödinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field $\overline{\varphi }$. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.

Recent observational evidence seems to allow the possibility that our Universe may currently be under a dark energy effect of a phantom nature. A suitable effective phantom fluid behavior can emerge in brane cosmology; in particular, within the normal non-self-accelerating Dvali-Gabadadze-Porrati branch, without any exotic matter and due to curvature effects from induced gravity. The phantomlike behavior is based in defining an effective energy density that grows as the brane expands. This effective description breaks down at some point in the past when the effective energy density becomes negative and the effective equation of state parameter blows up. In this paper we investigate if the phantomlike regime can be enlarged by the inclusion of a Gauss-Bonnet (GB) term into the bulk. The motivation is that such a GB component would model additional curvature effects on the brane setting. More precisely, our aim is to determine if the GB term, dominating and modifying the early behavior of the brane universe, may eventually extend the regime of validity of the phantom mimicry on the brane. However, we show that the opposite occurs: the GB effect seems instead to induce a breakdown of the phantomlike behavior at an even smaller redshift.

In the context of six-dimensional conical braneworlds we consider a simple and explicit model that incorporates long-distance modification of gravity and regularization of codimension-2 singularities. To resolve the conical singularities we replace the codimension-2 branes with ringlike codimension-1 branes, filling in the interiors with regular caps. The six-dimensional Planck scale in the cap is assumed to be much greater than the bulk Planck scale, which gives rise to the effect analogous to brane-induced gravity. Weak gravity on the regularized brane is studied in the case of a sharp conical bulk. We show by a linear analysis that gravity at short distances is effectively described by the four-dimensional Brans-Dicke theory, while the higher dimensional nature of gravity emerges at long distances. The linear analysis breaks down at some intermediate scale, below which four-dimensional Einstein gravity is shown to be recovered thanks to the second-order effects of the brane bending.

There is a significant possibility that astrophysical black holes with nearly extremal spins exist. Numerical simulations of such systems require suitable initial data. In this paper, we examine three methods of constructing binary-black-hole initial data, focusing on their ability to generate black holes with nearly extremal spins: (i) Bowen-York initial data, including standard puncture data (based on conformal flatness and Bowen-York extrinsic curvature), (ii) standard quasiequilibrium initial data (based on the extended-conformal-thin-sandwich equations, conformal flatness, and maximal slicing), and (iii) quasiequilibrium data based on the superposition of Kerr-Schild metrics. We find that the two conformally flat methods (i) and (ii) perform similarly, with spins up to about 0.99 obtainable at the initial time. However, in an evolution, we expect the spin to quickly relax to a significantly smaller value around 0.93 as the initial geometry relaxes. For quasiequilibrium superposed Kerr-Schild data [method (iii)], we construct initial data with initial spins as large as 0.9997. We evolve superposed Kerr-Schild data sets with spins of 0.93 and 0.97 and find that the spin drops by only a few parts in ${10}^4$ during the initial relaxation; therefore, we expect that superposed Kerr-Schild initial data will allow evolutions of binary black holes with relaxed spins above 0.99. Along the way to these conclusions, we also present several secondary results: the power-law coefficients with which the spin of puncture initial data approaches its maximal possible value; approximate analytic solutions for large spin puncture data; embedding diagrams for single spinning black holes in methods (i) and (ii); nonunique solutions for method (ii). All of the initial-data sets that we construct contain subextremal black holes, and when we are able to push the spin of the excision boundary surface into the superextremal regime, the excision surface is always enclosed by a second, subextremal apparent horizon. The quasilocal spin is measured by using approximate rotational Killing vectors, and the spin is also inferred from the extrema of the intrinsic scalar curvature of the apparent horizon. Both approaches are found to give consistent results, with the approximate-Killing-vector spin showing the least variation during the initial relaxation.

The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. Weakly nonlinear effects in galaxy clustering on large scales recently attracted great interest, since the precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given. We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.

We revisit arguments that simple models of inflation with a small red tilt in the scalar power spectrum generically yield an observable tensor spectrum. We show that criteria for fine-tuning based upon the algebraic simplicity of the potential depend strongly upon the explicit assumptions they incorporate, particularly regarding the end of inflation. In addition, some models with algebraically simple potentials require carefully tuned initial field configurations, and not all types of fine-tuning are identifiable via the algebraic simplicity of the potential. Conversely, in the absence of a strong prior on the mechanism that ends inflation, we demonstrate the existence of potentials with vanishingly small tensor amplitudes which are natural in terms of both their algebraic form and initial conditions. We thus argue that proposed experiments (CMBPol or BBO) which make highly sensitive measurements of the tensor amplitude cannot definitively rule out the inflationary paradigm.

We obtain the equation governing the evolution of the cosmological gravitational-wave background, accounting for the presence of cosmic neutrinos, up to second order in perturbation theory. In particular, we focus on the epoch during radiation dominance, after neutrino decoupling, when neutrinos yield a relevant contribution to the total energy density and behave as collisionless ultrarelativistic particles. Besides recovering the standard damping effect due to neutrinos, a new source term for gravitational waves is shown to arise from the neutrino anisotropic stress tensor. The importance of such a source term, so far completely disregarded in the literature, is related to the high velocity dispersion of neutrinos in the considered epoch; its computation requires solving the full second-order Boltzmann equation for collisionless neutrinos.

We quantize an inhomogeneous cosmological model using techniques that include polymeric quantization. More explicitly, we construct well-defined operators to represent the constraints and find the physical Hilbert space formed by their solutions, which reproduces the conventional Fock quantization for the inhomogeneities. The initial singularity is resolved in this inhomogeneous model in an extremely simple way and without imposing special boundary conditions, thus ensuring the robustness and generality of this resolution. Furthermore, this quantization constitutes a well-founded step towards the extraction of physical results and consequences from loop quantum cosmology, given the central role of the inhomogeneities in modern cosmology.

We study the $f(R)$ theory of gravity using the metric approach. In particular we investigate the recently proposed model by Hu and Sawicki; Appleby and Battye; and Starobinsky. In this model, the cosmological constant is zero in flat space time. The model passes both the solar system and the laboratory tests. But the model parameters need to be fine-tuned to avoid the finite time singularity recently pointed to in the literature. We check the concordance of this model with the $H(z)$ and baryon acoustic oscillation data. We find that the model resembles the $\Lambda \mathrm{CDM}$ at high redshift. However, for some parameter values there are variations in the expansion history of the universe at low redshift.

Particle production and its effects on the inflaton field are investigated during the preheating phase of chaotic inflation using a model consisting of a massive scalar inflaton field coupled to $N$ massless quantum scalar fields. The effects of spacetime curvature and interactions between the quantum fields are ignored. A large $N$ expansion is used to obtain a coupled set of equations including a backreaction equation for the classical inflaton field. Previous studies of preheating using these equations have been done. Here the first numerical solutions to the full set of equations are obtained for various values of the coupling constant and the initial amplitude of the inflaton field. States are chosen so that initially the backreaction effects on the inflaton field are small and the mode equations for the quantum fields take the form of Mathieu equations. Potential problems relating to the parametric amplification of certain modes of the quantum fields are identified and resolved. A detailed study of the damping of the inflaton field is undertaken. Some predictions of previous studies are verified and some new results are obtained.

We model massive compact objects in galactic nuclei as stationary, axially symmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are functions of the scalar charge. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightly for the weakly naked and vastly for the strongly naked singularities with the increase of the scalar charge. The pointlike caustics drift away from the optical axis and do not depend on the scalar charge. In the strong deflection limit approximation, we compute numerically the position of the relativistic images and their separability for weakly naked singularities. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as Janis-Newman-Winicour naked singularities.

We study the effect of anomalous $Wtb$ couplings on the $\overline{B}\to X_s\gamma$ branching ratio. The considered couplings are introduced as parts of gauge-invariant dimension-six operators that are built out of the standard model fields only. One-loop contributions from the charged-current vertices are assumed to be of the same order as the tree-level flavor-changing neutral current ones. Bounds on the corresponding Wilson coefficients are derived.