It has been suggested that space-time might undergo fluctuations because of its intrinsic quantum nature. These fluctuations would pose a fundamental limit to the ability of measuring distances with arbitrary precision, beyond any limitations due to standard quantum mechanics. Laser interferometers have recently been proposed as being suited for a search for the existence of space-time fluctuations. Here we present results of a search for space-time fluctuations of very low fluctuation frequencies, in the range from 1 μHz to 0.5 Hz. Rigid optical interferometers made out of sapphire and operated at cryogenic temperature were used. We find an upper limit of $1\times {10}^{-24}{\mathrm{Hz}}^{-1}$ for the normalized distance noise spectral density at 6 μHz, and of $1\times {10}^{-28}{\mathrm{Hz}}^{-1}$ above 5 mHz, and establish an experimental limit for the parameter of a recently proposed random-walk hypothesis.

We present positive energy theorems in asymptotically translationally invariant space-times which can be applicable to black strings and charged branes. We also address the bound property of the tension and charge of branes.

We construct here a special class of perfect fluid collapse models which generalizes the homogeneous dust collapse solution in order to include nonzero pressures and inhomogeneities into evolution. It is shown that a black hole is necessarily generated as the end product of continued gravitational collapse, rather than a naked singularity. We examine the nature of the central singularity forming as a result of endless collapse and it is shown that no nonspacelike trajectories can escape from the central singularity. Our results provide some insights into how the dynamical collapse works and into the possible formulations of the cosmic censorship hypothesis, which is as yet a major unsolved problem in black hole physics.

The redshift evolution of the growth rate of the gravitational potential, $d(D/a)/dz,$ is an excellent discriminator of dark energy parameters and, in principle, more powerful than standard classical tests of cosmology. This evolution is directly observable through the integrated Sachs-Wolfe effect in cosmic microwave background (CMB) anisotropies. We consider the prospects of measuring the growth rate via a novel method employed through measurements of CMB polarization towards galaxy clusters. The potentially achievable errors on dark energy parameters are comparable and fully complementary to those expected from other upcoming tests of dark energy, making this test a highly promising tool of precision cosmology.

We have found the following general relativity (GR) result: when a light ray is emitted and travels in a (nearly) uniform gravitational field g, its parabolic trajectory is that of one that would be traced by a massive Newtonian particle in a field three times greater, $3g.$ So, if a photon departs from a point on the Earth’s surface, with an initial horizontal direction, and goes over a distance $\Delta L\left[\right(\Delta L/R)\ll 1],$ its linear vertical deflection is $\Delta H_{\mathrm{GR}}=\frac{3}{2}\left[g\right(\Delta {L)}^2{/c}^2].$ The Newtonian result would be three times smaller. That is to say, the principle of equivalence is responsible for one-third of the vertical deflection. We think that this remarkable difference deserves research into the possibility of a GR test based on the vertical fall of terrestrial light.

We consider how the time-dependent decay process of an unstable D-brane should be described in the full (quantum) open-closed string theory. It is argued that the system, starting from the unstable D-brane configuration, will evolve in time into the time-independent open string tachyon vacuum configuration which we assume to be finite, with the total energy conserved. As a concrete realization of this idea, we construct a toy model describing the open and closed string tachyons which admits such a time-dependent solution. The structure of our model has some resemblance to that of open-closed string field theory.

We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self-interacting scalar field in $3+1$ dimensions. We use a numerical method, established some time ago, which is based on a well-known theorem on functional determinants. The proper handling of zero modes and of renormalization is discussed. The numerical results show in particular that the quantum corrections strongly increase when one approaches the thin-wall case. In the thin-wall limit the numerical results are found to join into those obtained by a gradient expansion.

Commutative supersymmetric Yang-Mills is known to be renormalizable for $\mathcal{N}=1,2,$ while finite for $\mathcal{N}=4.\mathrm{}$ However, in the noncommutative version of the model $\left({\mathrm{NCSQED}}_4\right)$ the UV-IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of ${\mathrm{NCSQED}}_4$ by working systematically within the covariant superfield formulation. In the Landau gauge, it has already been shown for $\mathcal{N}=1\mathrm{}$ that the gauge field two-point function is free of harmful UV-IR infrared singularities, in the one-loop approximation. Here we show that this result holds without restrictions on the number of allowed supersymmetries and for any arbitrary covariant gauge. We also investigate the divergence structure of the gauge field three-point function in the one-loop approximation. It is first proved that the cancellation of the leading UV-IR infrared divergences is a gauge invariant statement. Surprisingly, we have also found that there exist subleading harmful UV-IR infrared singularities whose cancellation only takes place in a particular covariant gauge. Thus we conclude that these last mentioned singularities are in the gauge sector and, therefore, do not jeopardize the perturbative expansion and/or the renormalization of the theory.

Exact Bogomol’nyi-Prasad-Sommerfield (BPS) solutions of multiwalls are obtained in five-dimensional supergravity. The solutions contain $2n$ parameters similarly to the moduli space of the corresponding global SUSY models and have a smooth limit of vanishing gravitational coupling. The models are constructed as gravitational deformations of massive $T^{*}\mathbf{C}{P}^n$ nonlinear sigma models by using the off-shell formulation of supergravity and massive quaternionic quotient method with $\mathrm{U}\mathrm{}\left(1\right)\mathrm{}\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ gauging. We show that the warp factor can have at most a single stationary point in this case. We also obtain BPS multiwall solutions even for models which reduce to generalizations of massive $T^{*}\mathbf{C}{P}^n$ models with only $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}^n$ isometry in the limit of vanishing gravitational coupling. At particular values of the parameters, the isometry of the quaternionic manifolds is enhanced.

The quantum time evolution of ${\phi }^4$-field theory for a spatially homogeneous system in 2+1 space-time dimensions is investigated numerically for out-of-equilibrium initial conditions on the basis of the Kadanoff-Baym equations including the tadpole and sunset self-energies. Whereas the tadpole self-energy yields a dynamical mass, the sunset self-energy is responsible for dissipation and an equilibration of the system. In particular we address the dynamics of the spectral (“off-shell”) distributions of the excited quantum modes and the different phases in the approach to equilibrium described by Kubo-Martin-Schwinger relations for thermal equilibrium states. The investigation explicitly demonstrates that the only translation invariant solutions representing the stationary fixed points of the coupled equation of motions are those of full thermal equilibrium. They agree with those extracted from the time integration of the Kadanoff-Baym equations for $\overrightarrow{t}\infty .$ Furthermore, a detailed comparison of the full quantum dynamics to more approximate and simple schemes such as that of a standard kinetic (on-shell) Boltzmann equation is performed. Our analysis shows that the consistent inclusion of the dynamical spectral function has a significant impact on relaxation phenomena. The different time scales that are involved in the dynamical quantum evolution towards a complete thermalized state are discussed in detail. We find that far off-shell $1\leftrightarrow 3$ processes are responsible for chemical equilibration, which is missed in the Boltzmann limit. Finally, we briefly address the case of (bare) massless fields. For sufficiently large couplings $\lambda$ we observe the onset of Bose condensation, where our scheme within symmetric ${\phi }^4$ theory breaks down.

We extend the treatment of the problem of the gravitational waves produced by a particle of negligible mass orbiting a Kerr black hole using black hole perturbation theory in the time domain to elliptic and inclined orbits. We model the particle by smearing the singularities in the source term using narrow Gaussian distributions. We compare results (energy and angular momentum fluxes) for such orbits with those computed using the frequency domain formalism.

We show that it is possible to formulate gravity with a complex vierbein based on $SL(2,C)$ gauge invariance. The proposed action is a four-form where the metric is not introduced but results as a function of the complex vierbein. This formulation is based on the first order formalism. The novel feature here is that integration of the spin-connection gauge field gives rise to kinetic terms for a massless graviton, a massive graviton with the Fierz-Pauli mass term, and a scalar field. The resulting theory is equivalent to bigravity. We then show that by extending the gauge group to $GL(2,C)$ the formalism can be easily generalized to apply to a noncommutative space with the star product. We give the deformed action and derive the Seiberg-Witten map for the complex vierbein and gauge fields.

It has been proposed that the entropy of any object must satisfy fundamental (holographic or Bekenstein) bounds set by the object’s size and perhaps its energy. However, most discussions of these bounds have ignored the possibility that objects violating the putative bounds could themselves become important components of Hawking radiation. We show that this possibility cannot a priori be neglected in existing derivations of the bounds. Thus this effect could potentially invalidate these derivations; but it might also lead to observational evidence for the bounds themselves.

We study the gravitational waves in spacetimes of arbitrary dimension. They generalize the pp waves and the Kundt waves, obtained earlier in four dimensions. Explicit solutions of the Einstein and Einstein-Maxwell equations are derived for an arbitrary cosmological constant.

We present long-term stable and convergent evolutions of an excised wobbling black hole. Our results clearly demonstrate that the use of a densitized lapse function extends the lifetime of simulations dramatically. We also show the improvement in the stability of single static black holes when an algebraic densitized lapse condition is applied. In addition, we introduce a computationally inexpensive approach for tracking the location of the singularity suitable for mildly distorted black holes. The method is based on investigating the fall-off behavior and asymmetry of appropriate grid variables. This simple tracking method allows one to adjust the location of the excision region to follow the coordinate motion of the singularity.

By using the ’t Hooft’s “brick wall” model and the Pauli-Villars regularization scheme we calculate the statistical-mechanical entropies arising from the quantum scalar field in different coordinate settings, such as the Painlevé and Lemaitre coordinates. At first glance, it seems that the entropies would be different from that in the standard Schwarzschild coordinate since the metrics in both the Painlevé and Lemaitre coordinates do not possess the singularity at the event horizon as that in the Schwarzschild-like coordinate. However, after an exact calculation we find that, up to the subleading correction, the statistical-mechanical entropies in these coordinates are equivalent to that in the Schwarzschild-like coordinate. The result is not only valid for black holes and de Sitter spaces, but also for the case that the quantum field exerts back reaction on the gravitational field provided that the back reaction does not alter the symmetry of the spacetime.

We investigate the primordial scalar perturbations in thermal dissipative inflation where the radiation component (thermal bath) persists and the density fluctuations are thermally originated. The perturbation generated in this model is hybrid; i.e., it consists of both adiabatic and isocurvature components. We calculate the fractional power ratio (S) and the correlation coefficient $\left(\cos \Delta \right)$ between the adiabatic and the isocurvature perturbations at the commencing of the radiation regime. Since the adiabatic or isocurvature decomposition of hybrid perturbations generally is gauge dependent at superhorizon scales, when there is substantial energy exchange between the inflaton and the thermal bath, we carefully perform a proper decomposition of the perturbations. We find that the adiabatic and the isocurvature perturbations are correlated, even though the fluctuations of the radiation component are considered uncorrelated with that of the inflaton. We also show that both S and $\cos \Delta$ depend mainly on the ratio between the dissipation coefficient $\Gamma$ and the Hubble parameter H during inflation. The correlation is positive $(\cos \Delta >0)$ for strong dissipation cases where $\Gamma /H>\mathrm{}0.2,$ and is negative for weak dissipation instances where $\Gamma /H<\mathrm{}\mathrm{0.2.}\mathrm{}$ Moreover, S and $\cos \Delta$ in this model are not independent of each other. The predicted relation between S and $\cos \Delta$ is consistent with the Wilkinson Microwave Anisotropy Probe observation. Other testable predictions are also discussed.

We study classes of five-dimensional cosmological solutions with negative curvature, which are obtained from static solutions by an exchange of a spatial and temporal coordinate and, in some cases, by an analytic continuation. Such solutions provide a suitable laboratory to address the time-dependent AdS/CFT correspondence. For a specific example we address in detail the calculation of the boundary stress energy and the Wilson line and find disagreement with the standard AdS/CFT correspondence. We trace these discrepancies to time-dependent effects, such as particle creation, which we further study for specific backgrounds. We also identify specific time-dependent backgrounds that reproduce the correct conformal anomaly. For such backgrounds the calculation of the Wilson line in the adiabatic approximation indicates only a Coulomb repulsion.

We show that UV photons produced by decaying particles can partially reionize the Universe and explain the large optical depth observed by the Wilkinson Microwave Anisotropy Probe. Together with UV fluxes from early formed stars and quasars, it is possible that the Universe is fully ionized at $z\lesssim 6$ and partially ionized at $z\gtrsim 6$ as observed by the Sloan Digital Sky Survey for a large parameter space of the decaying particle. This scenario will be discriminated by future observations, especially by the EE polarization power spectrum of cosmic microwave background radiation.

It has been shown that the renormalization group (RG) flow connecting different vacua may occur due to the multitrace operators in four-dimensional conformal field theory (CFT). In the AdS/CFT set-up, the double-trace operators correspond to the tachyonic scalar field living in the bulk five-dimensional AdS. In this paper, we consider a five-dimensional black hole as a bulk spacetime instead of pure AdS. In the framework of the AdS/CFT correspondence, the AdS black hole is believed to describe dual CFT at finite temperature. From the AdS side, we consider the difference in energy between the two vacua by a one-loop calculation for the scalar field with a tachyonic mass in a five-dimensional AdS black hole. In order to check the dS/CFT correspondence, the corresponding calculations are done in five-dimensional de Sitter space. The difference between the two vacua is specified by the difference in the boundary conditions of the scalar field. We show that, for an AdS black hole, an instability might occur which could be the manifestation of the Hawking-Page phase transition. For a stable phase of an AdS black hole as well as for a de Sitter bulk, the proposed c function found beyond the leading order approximation shows a monotonic behavior consistent with the c theorem.