Using the Newman and Penrose [E. T. Newman and R. Penrose, J. Math. Phys. (N.Y.) 3, 566 (1962).] spin-coefficient formalism, we examine the full Bianchi identities of general relativity in the context of gravitational lensing, where the matter and space-time curvature are projected into a lens plane perpendicular to the line of sight. From one component of the Bianchi identity, we provide a rigorous, new derivation of a Poisson equation for the projected matter density where the source term involves second derivatives of the observed weak gravitational lensing shear. We also show that the other components of the Bianchi identity reveal no new results. Numerical integration of the Poisson equation in test cases shows an accurate mass map can be constructed from the combination of a ground-based, wide-field image and a Hubble Space Telescope image of the same system.

We study the feasibility of observing an invisibly decaying $Z^{\prime }$ at the LHC through the process $pp\to Z{Z}^{\prime }\to {\ell }^{+}{\ell }^{-}X{X}^{†}$, where $X$ is any neutral, (quasi-) stable particle, whether a standard model neutrino or a new state. The measurement of the invisible width through this process facilitates both a model-independent measurement of ${\Gamma }_{Z^{\prime }\to \overline{\nu }\nu }$ and potentially detection of light neutral hidden states. Such particles appear in many models, where the $Z^{\prime }$ is a messenger to a hidden sector, and also if dark matter is charged under the $U(1{)}^{\prime }$ of the $Z^{\prime }$. We find that with as few as $30{\mathrm{fb}}^{-1}$ of data the invisibly decaying $Z^{\prime }$ can be observed at $5\sigma$ over standard model background for a 1 TeV $Z^{\prime }$ with reasonable couplings. If the $Z^{\prime }$ does not couple to leptons and therefore cannot be observed in the Drell-Yan channel, this process becomes a discovery mode. For reasonable hidden sector couplings, masses up to 2 TeV can be probed at the LHC. If the $Z^{\prime }$ does couple to leptons, then the rate for this invisible decay is predicted by on-peak data and the presence of additional hidden states can be searched for. With $100{\mathrm{fb}}^{-1}$ of data, the presence of excess decays to hidden states can be excluded at 95% C.L., if they comprise 20–30% of the total invisible cross section.

We consider a new interaction between a heavy Majorana neutrino ($N$) and a charged Higgs boson ($H^{\pm }$), and show that it can have drastic implications on lepton-number-violating (LNV) signal of same-sign dileptons at the CERN LHC. The LNV signal of heavy Majorana neutrinos previously considered at the LHC, $pp\to {\ell }^{+}N\to {\ell }^{+}{\ell }^{+}{W}^{-}$, may be overwhelmed by $pp\to {\ell }^{+}N\to {\ell }^{+}{\ell }^{+}{H}^{-}$. With the subsequent decays $H^{-}\to \overline{t}b$ or $H^{-}\to W^{-}{H}^0$, the heavy Majorana neutrino production leads to the spectacular events of ${\ell }^{+}{\ell }^{+}b\overline{b}+2$ jets. We also explore the case $m_N<m_{H^{+}}$, where the decay $H^{+}\to {\ell }^{+}N$ can become the dominant $N$-production mechanism at the LHC. In particular, we show that the process $gb\to t{H}^{-}$ followed by $t\to b{W}^{+}$ and $H^{-}\to {\ell }^{-}N\to {\ell }^{-}{\ell }^{-}{W}^{+}$ could lead to another type of spectacular events of ${\ell }^{-}{\ell }^{-}b+4$ jets.

The two-body open charm decays $Z^{+}(4430)\to D^{+}{\overline{D}}^{*0}$, $D^{*+}{\overline{D}}^0$, $D^{*+}{\overline{D}}^{*0}$ occur through the rescattering mechanism and their branching ratios are strongly suppressed if $Z^{+}(4430)$ is a $D_1{\overline{D}}^{*}$ molecular state. In contrast, $Z^{+}(4430)$ falls apart into these modes easily with large phase space and they become the main decay modes if $Z^{+}(4430)$ is a tetraquark state. Experimental search of these two-body open charm modes and the hidden charm mode ${\chi }_{cJ}\rho$ will help distinguish different theoretical schemes.

We discuss the effects of neutrino mixing and the neutrino mass hierarchy when considering the capture of the cosmic neutrino background (CNB) on radioactive nuclei. The implications of mixing and hierarchy at future generations of tritium decay experiments are considered. We find that the CNB should be detectable at these experiments provided that the resolution for the kinetic energy of the outgoing electron can be pushed to a few 0.01 eV for the scenario with inverted neutrino mass hierarchy, about an order of magnitude better than that of the upcoming KATRIN experiment. Another order of magnitude improvement is needed in the case of normal neutrino mass hierarchy. We also note that mixing effects generally make the prospects for CNB detection worse due to an increased maximum energy of the normal beta decay background.

We describe new solutions for open string moving in ${\mathrm{AdS}}_5$ and ending in the boundary, namely, dual to Wilson loops in $\mathcal{N}=4$ SYM theory. First we introduce an ansatz for Euclidean curves whose shape contains an arbitrary function. They are Bogomol’nyi-Prasad-Sommerfield monopoles (BPS) and the dual surfaces can be found exactly. After an inversion they become closed Wilson loops whose expectation value is $W=\exp (-\sqrt{\lambda })$. After that we consider several Wilson loops for $\mathcal{N}=4$ SYM in a $pp$-wave metric and find the dual surfaces in an ${\mathrm{AdS}}_5$ $pp$-wave background. Using the fact that the $pp$-wave is conformally flat, we apply a conformal transformation to obtain novel surfaces describing strings moving in AdS space in Poincare coordinates and dual to Wilson loops for $\mathcal{N}=4$ SYM in flat space.

We discuss the $(g_0{\phi }^p{)}_d$ self-interacting scalar field theory, in the strong-coupling regime. We assume the presence of macroscopic boundaries confining the field in a hypercube of side $L$. We also consider that the system is in thermal equilibrium at temperature ${\beta }^{-1}$. For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality $\frac{S}{E}<2\pi R$, where $R$ stands for the radius of the smallest sphere that circumscribes the system. Employing the strong-coupling perturbative expansion, we obtain the renormalized mean energy $E$ and entropy $S$ for the system up to the order $(g_0{)}^{-(2/p)}$, presenting an analytical proof that the specific entropy also satisfies in some situations a quantum bound. Defining ${\epsilon }_d^{(r)}$ as the renormalized zero-point energy for the free theory per unit length, the dimensionless quantity $\xi =\frac{\beta }{L}$ and $h_1(d)$ and $h_2(d)$ as positive analytic functions of $d$, for the case of high temperature, we get that the specific entropy satisfies $\frac{S}{E}<2\pi R\frac{h_1(d)}{h_2(d)}\xi$. When considering the low-temperature behavior of the specific entropy, we have $\frac{S}{E}<2\pi R\frac{h_1(d)}{{\epsilon }_d^{(r)}}{\xi }^{1-d}$. Therefore the sign of the renormalized zero-point energy can invalidate this quantum bound. If the renormalized zero-point energy is a positive quantity, at intermediate temperatures and in the low-temperature limit, there is a quantum bound.

We study the stationary axisymmetric self-gravitating nonlinear $\sigma$ model in five-dimensional spacetime admitting three commutating Killing vector fields. We show that the only asymptotically flat black ring solution with a regular rotating event horizon is the black ring characterized by mass and two angular momenta with constant mapping.

We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are two distinct one-parameter families of asymptotic solutions, one is asymptotic to the proper Friedmann universe, while the other is asymptotic to the quasi-Friedmann universe, i.e., the Friedmann universe with anomalous solid angle. The asymptotically proper Friedmann solution is possible only if the universe is accelerated or the potential is negative. If the potential is positive, the density perturbation in the asymptotically proper Friedmann solution rapidly falls off at spatial infinity, while the mass perturbation is compensated. In the asymptotically quasi-Friedmann solution, the density perturbation falls off only in proportion to the inverse square of the areal radius and the relative mass perturbation approaches a nonzero constant at spatial infinity. The present result shows that a necessary condition holds in order that a self-gravitating body grows self-similarly due to the constant accretion of quintessence in an accelerating universe.

We give a general derivation, for any static spherically symmetric metric, of the relation $T_h=\frac{\mathcal{K}}{2\pi }$ connecting the black hole temperature ($T_h$) with the surface gravity ($\mathcal{K}$), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi-classical regime, i.e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space-time. The effects of backreaction are also included. For such a black hole the Hawking temperature is computed in a closed form. A graphical analysis reveals interesting features regarding the variation of the Hawking temperature (including corrections due to noncommutativity and backreaction) with the small radius of the black hole. The entropy and tunneling rate valid for the leading order in the noncommutative parameter are calculated. We also show that the noncommutative Bekenstein-Hawking area law has the same functional form as the usual one.

The recently suggested interpretation P. Castorina, D. Kharzeev, and H. Satz, [Eur. Phys. J. C 52, 187 (2007).] of the universal hadronic freeze-out temperature $T_f$ ($\simeq 170\mathrm{MeV}$)—found for all high-energy scattering processes that produce hadrons $e^{+}{e}^{-}$, $pp$, $p\overline{p}$, $\pi p$, etc., and $N{N}^{\prime }$ (heavy-ion collisions)—as an Unruh temperature triggers here the search for the gravitational black hole (BH) that in its near-horizon approximation better simulates this hadronic phenomenon. To identify such a BH we begin our gravity-gauge theory phenomenologies matching by asking the question: which BH behind that Rindler horizon could reproduce the experimental behavior of $T_f(\sqrt{s})$ in $N{N}^{\prime }$, where $\sqrt{s}$ is the collision energy? Provided certain natural assumptions hold, we show that the exact string BH turns out to be the best candidate (as it fits the available data on $T_f(\sqrt{s})$) and that its limiting case, the Witten BH, is the unique candidate to explain the constant $T_f$ for all elementary scattering processes at large energy. We also are able to propose an effective description of the screening of the hadronic string tension $\sigma ({\mu }_b)$ due to the baryon density effects on $T_f$.

A spatially flat Robertson-Walker spacetime driven by a cosmological constant is nonconformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially isotropic perturbations of the metric and the quantum state. These results are independent of the free renormalization parameters.

Nonlinear deformations of relativistic symmetries at the Planck scale are usually addressed in terms of modified dispersion relations. We explore here an alternative route by directly deforming the two-point functions of an underlying field theory. The proposed deformations depend on a length parameter (Planck length) and preserve the basic symmetries of the corresponding theory. We also study the physical consequences implied by these modifications at the Planck scale by analyzing the response function of an accelerated detector in Minkowski space, an inertial one in de Sitter space, and also in a black hole spacetime.

In this paper, we study the large scale structure formation of the normal branch in the DGP model (Dvail, Gabadadze, and Porrati brane world model) by applying the scaling method developed by Sawicki, Song, and Hu for solving the coupled perturbed equations of motion of on-brane and off-brane. There is a detectable departure of perturbed gravitational potential from the cold dark matter model with vacuum energy even at the minimal deviation of the effective equation of state $w_{\mathrm{eff}}$ below $-1$. The modified perturbed gravitational potential weakens the integrated Sachs-Wolfe effect which is strengthened in the self-accelerating branch DGP model. Additionally, we discuss the validity of the scaling solution in the de Sitter limit at late times.

We study inflationary cosmology and the late-time accelerated expansion of the universe in nonminimal Yang-Mills (YM) theory, in which the YM field couples to a function of the scalar curvature. It is shown that power-law inflation can be realized due to the nonminimal YM field-gravitational coupling which may be caused by quantum corrections. Moreover, it is demonstrated that both inflation and the late-time accelerated expansion of the universe can be realized in a modified YM-$F(R)$ gravity which is consistent with solar-system tests. Furthermore, it is shown that this result can be realized also in a nonminimal vector-$F(R)$ gravity. In addition, we consider the duality of the nonminimal electromagnetic theory and that of the nonminimal YM theory, and also discuss the cosmological reconstruction of the YM theory.

Combined analyses of WMAP 3-year and ACBAR cosmic microwave anisotropies angular power spectra have presented evidence for gravitational lensing at $>3\sigma$ level. This signal could provide a relevant test for cosmology. After evaluating and confirming the statistical significance of the detection in light of the new WMAP 5-year data, we constrain a new parameter $A_L$ that scales the lensing potential such that $A_L=0$ corresponds to unlensed while $A_L=1$ is the expected lensed result in the standard $\Lambda \mathrm{\text{−}}\mathrm{CDM}$ model. We find from $\mathrm{WMAP}5+\mathrm{ACBAR}$ a $2.5\sigma$ indication for a lensing contribution larger than expected, with $A_L={3.1}_{-1.5}^{+1.8}$ at 95% C.L. The result is stable under the assumption of different templates for an additional Sunyaev-Zel’dovich foreground component or the inclusion of an extra background of cosmic strings. We find negligible correlation with other cosmological parameters as, for example, the energy density in massive neutrinos. While unknown systematics may be present, dark energy or modified gravity models could be responsible for the over-smoothness of the power spectrum. Near-future data, most notably from the Planck satellite mission, will scrutinize this interesting possibility.

The “bubble universes” of Coleman and De Luccia play a crucial role in string cosmology. Since our own Universe is supposed to be of this kind, bubble cosmology should supply definite answers to the long-standing questions regarding cosmological initial conditions. In particular, it must explain how an initial singularity is avoided, and also how the initial conditions for inflation were established. I argue that the simplest nonanthropic approach to these problems involves a requirement that the spatial sections defined by distinguished bubble observers should not be allowed to have arbitrarily small volumes. Casimir energy is a popular candidate for a quantum effect which can ensure this, but (because it violates energy conditions) there is a danger that it could lead to nonperturbative instabilities in string theory. I make a simple proposal for the initial conditions of a bubble universe, and show that my proposal ensures that the system is nonperturbatively stable. Thus, low-entropy conditions can be established at the beginning of a bubble universe without violating the second law of thermodynamics and without leading to instability in string theory. These conditions are inherited from the ambient spacetime.

We study the signature change in a perfect fluid Friedmann-Robertson-Walker quantum cosmological model. In this work the Schutz’s variational formalism is applied to recover the notion of time. This gives rise to a Schrödinger-Wheeler-DeWitt equation with arbitrary ordering for the scale factor. We use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor which coincides with the ontological interpretation. We show that these solutions exhibit signature transitions from a finite Euclidean to a Lorentzian domain. Moreover, such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid is present.

We extend our earlier model of the small-scale structure of cosmic string networks through an improved treatment of the separation of long and short scales. We find that the production of small loops (at the gravitational radiation scale) is a robust feature of string networks, in addition to a population of loops near the horizon scale. We obtain quantitative agreement with the scaling of loop production functions as found in simulations by two groups.