The Newton equation describing particle motion in a constant external field force on canonical, Lie-algebraic, and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of the particle is generated. We also indicate that in the case of spatial coordinates commuting in a Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces.

We discuss whether some perturbed Friedmann-Robertson-Walker (FRW) universes could be creatable, i.e., could have vanishing energy, linear momentum, and angular momentum, as it could be expectable if the Universe arose as a quantum fluctuation. On account of previous results, the background is assumed to be either closed (with very small curvature) or flat. In the first case, fully arbitrary linear perturbations are considered, whereas in the flat case, we assume the existence of the following: (i) inflationary scalar perturbations, that is to say, Gaussian adiabatic scalar perturbations having an spectrum close to the Harrison-Zel’dovich one, and (ii) arbitrary tensor perturbations. We conclude that any closed perturbed universe is creatable, and also that, irrespective of the spectrum and properties of the inflationary gravitational waves, perturbed flat FRW universes with standard inflation are not creatable. Some considerations on preinflationary scalar perturbations are also presented. The creatable character of perturbed FRW universes is studied, for the first time, in this paper.

Two first order strongly hyperbolic formulations of scalar-tensor theories of gravity allowing nonminimal couplings (Jordan frame) are presented along the lines of the $3+1$ decomposition of spacetime. One is based on the Bona-Massó formulation, while the other one employs a conformal decomposition similar to that of Baumgarte-Shapiro-Shibata-Nakamura. A modified Bona-Massó slicing condition adapted to the scalar-tensor theory is proposed for the analysis. This study confirms that the scalar-tensor theory has a well-posed Cauchy problem even when formulated in the Jordan frame.

Wilkinson Microwave Anisotropy Probe (WMAP) observations have accurately determined the position of the first two peaks and dips in the cosmic microwave background (CMB) temperature power spectrum. These encode information on the ratio of the distance to the last scattering surface to the sound horizon at decoupling. However prerecombination processes can contaminate this distance information. In order to assess the amplitude of these effects, we use the WMAP data and evaluate the relative differences of the CMB peak and dip multipoles. We find that the position of the first peak is largely displaced with respect to the expected position of the sound horizon scale at decoupling. In contrast, the relative spacings of the higher extrema are statistically consistent with those expected from perfect harmonic oscillations. This provides evidence for a scale dependent phase shift of the CMB oscillations which is caused by gravitational driving forces affecting the propagation of sound waves before recombination. By accounting for these effects we have performed a Markov Chain Monte Carlo likelihood analysis of the location of WMAP extrema to constrain, in combination with recent BAO data, a constant dark energy equation of state parameter $w$. For a flat universe we find a strong $2\sigma$ upper limit $w<-1.10$, and including the Hubble Space Telescope prior, we obtain $w<-1.14$, which is only marginally consistent with limits derived from the Supernova Legacy Survey sample. On the other hand, we infer larger limits for nonflat cosmologies. From the full CMB likelihood analysis, we also estimate the values of the shift parameter $R$ and the multipole $l_a$ of the acoustic horizon at decoupling for several cosmologies, to test their dependence on model assumptions. Although the analysis of the full CMB spectra should always be preferred, using the position of the CMB peaks and dips provides a simple and consistent method for combining CMB constraints with other data sets.

We examine the unparticle $CP$-conserving phase effects on the direct $CP$ asymmetry for both polarized and unpolarized leptons in the inclusive $b\to d{\ell }^{+}{\ell }^{-}$ transition, where the flavor-changing neutral currents are forbidden at tree level but are induced by one-loop penguin diagrams. The averaged polarized and unpolarized $CP$ asymmetries depict strong dependency on the unparticle parameters. In particular, a sizable discrepancy corresponding to the standard model is achieved when the scale dimension value is $1<d_{\mathcal{U}}<2$. We see that the unparticle stuff significantly enhances, suppresses, or changes the sign of the $CP$ asymmetry depending on the definite value of the scaling dimension $d_{\mathcal{U}}$. Especially, when $d_{\mathcal{U}}\sim 1.1$ the $CP$ asymmetries vanish.

We calculate gravitational form factors of vector mesons using a holographic model of QCD. These provide restrictions on the generalized parton distributions of vector mesons, via the sum rules connecting stress tensor form factors to generalized parton distributions. We concentrate on the traceless part of the stress tensor, which suffices to fix the momentum and angular momentum sum rules. The vector mesons appear noticeably more compact measured by the gravitational form factors than by the charge form factor.

We show that for a force mediated by a vector particle coupled to a conserved $U(1)$ charge, the apparent range and strength can depend on the size and density of the source, and the proximity to other sources. This chameleon effect is due to screening from a light charged scalar. Such screening can weaken astrophysical constraints on new gauge bosons. As an example we consider the constraints on chameleonic gauged $B-L$. We show that although Casimir measurements greatly constrain any $B-L$ force much stronger than gravity with range longer than $0.1\mu \mathrm{m}$, there remains an experimental window for a long-range chameleonic $B-L$ force. Such a force could be much stronger than gravity, and long or infinite range in vacuum, but have an effective range near the surface of the earth which is less than a micron.

We study the exclusive $b\to u{\ell }^{-}{\overline{\nu }}_{\ell }(\ell =\tau ,\mu ,e)$ decays in the minimal supersymmetric standard model with and without $R$-parity violation. From the experimental measurements of branching ratios $\mathcal{B}(B_u^{-}\to {\tau }^{-}{\overline{\nu }}_{\tau })$, $\mathcal{B}(B_u^{-}\to M^{\prime 0}{\ell }^{\prime -}{\overline{\nu }}_{{\ell }^{\prime }})$ and $\mathcal{B}({\overline{B}}_d^0\to M^{\prime +}{\ell }^{\prime -}{\overline{\nu }}_{{\ell }^{\prime }})$ $({\ell }^{\prime }=\mu ,e,M^{\prime }=\pi ,\rho )$, we derive new upper bounds on the relevant new physics parameters within the decays. Using the constrained new physics parameter spaces, we predict the charged Higgs effects and the $R$-parity violating effects on the branching ratios, the normalized forward-backward asymmetries of charged leptons, and the ratios of longitudinal to transverse polarization of the vector mesons, which have not been measured or have not been well measured yet. We find that the charged Higgs effects and the $R$-parity violating effects could be large and measurable in some cases. Our results could be used to probe new physics effects in the leptonic decays as well as the semileptonic decays, and will correlate with searches for direct supersymmetric signals in future experiments.

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics, in the presence of magnetics fields of arbitrary strength, by solving the Schwinger-Dyson equation for the fermion self-energy in the rainbow approximation. We employ the Ritus eigenfunction formalism which provides a neat solution to the technical problem of summing over all Landau levels. It is well known that magnetic fields catalyze the generation of fermion mass $m$ for arbitrarily small values of electromagnetic coupling $\alpha$. For intense fields it is also well known that $m\propto \sqrt{eB}$. Our approach allows us to span all regimes of parameters $\alpha$ and $eB$. We find that $m\propto \sqrt{eB}$ provided $\alpha$ is small. However, when $\alpha$ increases beyond the critical value ${\alpha }_c$ which marks the onslaught of dynamical fermion masses in vacuum, we find $m\propto \Lambda$, the cutoff required to regularize the ultraviolet divergences. Our method permits us to verify the results available in literature for the limiting cases of $eB$ and $\alpha$. We also point out the relevance of our work for possible physical applications.

The photon polarization in radiative decays $B\to Y\gamma$ is known to be a subtle probe of the effective Lagrangian structure and possible New Physics effects. We discuss exclusive decay mode $B^{-}\to \phi K^{-}\gamma$ where the experimentally distinct final state makes analysis especially promising. The possibility to extract information on the photon polarization out of the data entirely depends on the partial waves’ interference pattern in the $\phi K^{-}$ system.

We argue that in the paper we comment on the authors failed to prove that all known solutions of the Bogomol’nyi-Prasad-Sommerfield sector of duality-based Calogero model are indeed all solutions.

We study constraints on $f(R)$ dark energy models from solar system experiments combined with experiments on the violation of the equivalence principle. When the mass of an equivalent scalar field degree of freedom is heavy in a region with high density, a spherically symmetric body has a thin shell so that an effective coupling of the fifth force is suppressed through a chameleon mechanism. We place experimental bounds on the cosmologically viable models recently proposed in the literature that have an asymptotic form $f(R)=R-\lambda R_c[1-(R_c/R{)}^{2n}]$ in the regime $R\gg R_c$. From the solar system constraints on the post-Newtonian parameter $\gamma$, we derive the bound $n>0.5$, whereas the constraints from the violations of the weak and strong equivalence principles give the bound $n>0.9$. This allows a possibility to find the deviation from the $\Lambda$-cold dark matter ($\Lambda \mathrm{CDM}$) cosmological model. For the model $f(R)=R-\lambda R_c(R/R_c{)}^p$ with $0<p<1$ the severest constraint is found to be $p<{10}^{-10}$, which shows that this model is hardly distinguishable from the $\Lambda \mathrm{CDM}$ cosmology.

We consider a universe with a compact extra dimension and a cosmological constant emerging from a suitable ultraviolet cutoff on the zero-point energy of the vacuum. We derive the Casimir force between parallel conducting plates as a function of the following scales: plate separation, radius of the extra dimension and cutoff energy scale. We find that there are critical values of these scales where the Casimir force between the plates changes sign. For the cutoff energy scale required to reproduce the observed value of the cosmological constant, we find that the Casimir force changes sign and becomes repulsive for plate separations less than a critical separation $d_0=0.6\mathrm{mm}$, assuming a zero radius of the extra dimension (no extra dimension). This prediction contradicts Casimir experiments which indicate an attractive force down to plate separations of 100 nm. For a nonzero extra dimension radius, the critical separation $d_0$ gets even larger than 0.6 mm and remains inconsistent with Casimir force experiments. We conclude that with or without the presence of a compact extra dimension, vacuum energy with any suitable cutoff cannot play the role of the cosmological constant.

We introduce a new $\kappa$-star product describing the multiplication of quantized $\kappa$-deformed free fields. The $\kappa$ deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the $\kappa$ deformation of field oscillators algebra; we relate these two deformations. We demonstrate that for a suitable choice of $\kappa$-deformed field oscillators algebra, the $\kappa$-deformed version of the microcausality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the $\kappa$-deformed mass shell. We show by constructing the $\kappa$-deformed Fock space that the use of the $\kappa$-deformed oscillator algebra permits one to preserve the bosonic statistics of $n$-particle states. The proposed star product is extended to the product of $n$ fields, which for $n=4$ defines the interaction vertex in perturbative description of the noncommutative quantum $\lambda {\phi }^4$ field theory. It appears that the classical four-momentum conservation law is satisfied at the interaction vertices.

In this article we address the problem of getting the temperature dependence of the $\pi \mathrm{\text{−}}\pi$ scattering lengths in the frame of the linear sigma model. Using the real time formalism, we calculate all the relevant one loop diagrams. The temperature corrections are only considered in the pion sector, due to the Boltzmann suppression for heavier fields like the sigma meson. From this analysis we obtain the thermal behavior of the s waves scattering lengths $a_0^0$ and $a_0^2$ associated to isospin $I=0$ and $I=2$, respectively. If we normalize with the zero temperature value it turns out that $\frac{a_0^0(T)}{a_0^0}$ grows with temperature, whereas the opposite occurs with $\frac{a_0^2(T)}{a_0^2}$. Finally we compare our results with other determinations of the scattering lengths based on the Nambu-Jona-Lasinio model and chiral perturbation theory.

We analyze the stability of the structure equations of the vacuum in the brane world models, by using both the linear (Lyapunov) stability analysis, and the Jacobi stability analysis, the Kosambi-Cartan-Chern theory. In the brane world models the four-dimensional effective Einstein equations acquire extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the three-brane in the bulk. Generally, the spherically symmetric vacuum solutions of the brane gravitational field equations have properties quite distinct as compared to the standard black hole solutions of general relativity. We close the structure equations by assuming a simple linear equation of state for the dark pressure. In this case the vacuum is Jacobi stable only for a small range of values of the proportionality constant relating the dark pressure and the dark radiation. The unstable trajectories on the brane behave chaotically, in the sense that after a finite radial distance it would be impossible to distinguish the trajectories that were very near each other at an initial point. Hence the Jacobi stability analysis offers a powerful method for constraining the physical properties of the vacuum on the brane.

Modifying the Kerr-Schild transformation used to generate black and white hole spacetimes, new dynamic black and white holes are obtained using a time-dependent Kerr-Schild scalar field. Physical solutions are found for black holes that shrink with time and for white holes that expand with time. The black hole spacetimes are physical only in the vicinity of the black hole, with the physical region increasing in radius with time. The white hole spacetimes are physical throughout. Unlike the standard Schwarzschild solution the singularities are nonisolated, since the time dependence introduces a mass-energy distribution. The surfaces in the metrics where $g_{tt}=g^{rr}=0$ are dynamic, moving inward with time for the black holes and outward for the white holes, which leads to a question of whether these spacetimes truly have event horizons—a problem shared with Vaidya’s cosmological black hole spacetimes. By finding a surface that shrinks or expands at the same rate as the null geodesics move, and within which null geodesics move inward or outward faster than the surfaces shrink or expand, respectively, it is verified that these do in fact behave like black and white holes.

We study the thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization and does not favor the Bousso-Hawking normalization.

The 21-cm anisotropies from the neutral hydrogen distribution prior to the era of reionization are a sensitive probe of primordial non-Gaussianity. Unlike the case with cosmic microwave background, 21-cm anisotropies provide multi-redshift information with frequency selection and are not damped at arcminute angular scales. We discuss the angular trispectrum of the 21-cm background anisotropies and discuss how the trispectrum signal generated by the primordial non-Gaussianity can be measured with the three-to-one correlator and the corresponding angular power spectrum. We also discuss the separation of primordial non-Gaussian information in the trispectrum with that generated by the subsequent nonlinear gravitational evolution of the density field. While with the angular bispectrum of 21-cm anisotropies one can limit the second-order corrections to the primordial fluctuations below $f_{\mathrm{NL}}\sim 1$, using the trispectrum information we suggest that the third-order coupling term, $f_2$ or $g_{\mathrm{NL}}$, can be constrained to be around 10 with future 21-cm observations over the redshift interval of 50 to 100.

The Stokes $V$ parameter characterizes asymmetry of amplitudes between right- and left-handed waves, and the nonvanishing value of the $V$ parameter yields a circularly polarized signal. Cosmologically, the $V$ parameter may be a direct probe for parity violation in the Universe. In this paper, we theoretically investigate a measurement of this parameter, particularly focusing on the gravitational-wave backgrounds observed via ground-based interferometers. In contrast to the traditional analysis that only considers the total amplitude (or equivalently ${\Omega }_{\mathrm{GW}}$), the signal analysis including a circular-polarized mode has a rich structure due to the multidimensionality of target parameters. We show that, by using the network of next-generation detectors, separation between polarized and unpolarized modes can be performed with small statistical loss induced by their correlation.