We present the graviton propagator for an infinite derivative, $D$-dimensional, nonlocal action, up to quadratic order in curvature around a Minkowski background, and discuss the conditions required for this class of gravity theory to be ghost-free. We then study the gravitational entropy for de-Sitter and anti-de Sitter backgrounds, before comparing with a recently derived result for a Schwarzschild black hole, generalized to arbitrary $D$ dimensions, whereby the entropy is given simply by the area law. A novel approach of decomposing the entropy into its $(r,t)$ and spherical components is adopted in order to illustrate the differences more clearly. We conclude with a discussion of de-Sitter entropy in the framework of a nonsingular bouncing cosmology.

A recent debate has ensued over the claim by Pikovski et al. [Nat. Phys. 11, 668 (2015)] that systems with internal degrees of freedom undergo a universal, gravity-induced, type of decoherence that explains their quantum-to-classical transition. This decoherence is supposed to arise from the different gravitational redshifts experienced by such systems when placed in a superposition of two wave packets at different heights in a gravitational field. Here we investigate some aspects of the discussion with the aid of simple examples. In particular, we first resolve an apparent conflict between the reported results and the equivalence principle by noting that the static and free-fall descriptions focus on states associated with different hypersurfaces. Next, we emphasize that predictions regarding the observability of interference become relevant only in the context of concrete experimental settings. As a result, we caution against hasty claims of universal validity. Finally, we dispute the claim that, at least in the scenarios discussed by Pikovski et al., gravitation is responsible for the reported results, and we question the alleged ability of decoherence to explain the quantum-to-classical transition. In consequence, we argue against the extraordinary assertion by Pikovski et al. that gravity can account for the emergence of classicality.

In this paper, we consider third-order Lovelock gravity with a cosmological constant term in an $n$-dimensional spacetime ${\mathcal{M}}^4\times {\mathcal{K}}^{n-4}$, where ${\mathcal{K}}^{n-4}$ is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum ${\mathcal{K}}^{n-4}$ space. Applying the latter constraint, we determine the second- and third-order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and $\mathrm{\Lambda }$, we obtain the four-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by $\rho =(\gamma p-\tau )/[\omega (1+\gamma )]$, we find the exact solution for the shape function which represents both asymptotically flat and nonflat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a four-dimensional spacetime implies a negative effective cosmological constant.

We study the secular dynamics of compact binaries (consisting of white dwarfs, neutron stars or black holes) with tertiary companions in hierarchical triple systems. As the inner binary (with initially negligible eccentricity) undergoes orbital decay due to gravitational radiation, its eccentricity can be excited by gravitational forcing from the tertiary. This excitation occurs when the triple system passes through an “apsidal precession resonance,” when the precession rate of the inner binary, driven by the gravitational perturbation of the external companion and general relativity, matches the precession rate of the outer binary. The eccentricity excitation requires the outer companion to be on an eccentric orbit, with the mutual inclination between the inner and outer orbits less than $\sim 40°$. Gravitational wave (GW) signals from the inner binary can be significantly modified as the system evolves through the apsidal precession resonance. For some system parameters (e.g., a white dwarf binary with a brown dwarf tertiary), the resonance can happen when the binary emits GWs in the ${10}^{-4}-{10}^{-1}\mathrm{Hz}$ range (the sensitivity band of LISA).

The paper gives full details of the computation within the canonical formalism of Arnowitt, Deser, and Misner of the local-in-time part of the fourth post-Newtonian, i.e. of power eight in one over speed of light, conservative Hamiltonian of spinless compact binary systems. The Hamiltonian depends only on the bodies’ positions and momenta. Dirac delta distributions are taken as source functions. Their full control is furnished by dimensional continuation, by means of which the occurring ultraviolet (UV) divergences are uniquely regularized. The applied near-zone expansion of the time-symmetric Green function leads to infrared (IR) divergences. Their analytic regularization results in one single ambiguity parameter. Unique fixation of it was successfully performed in T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 89, 064058 (2014) through far-zone matching. Technically as well as conceptually (backscatter binding energy), the level of the Lamb shift in quantum electrodynamics is reached. In a first run a computation of all terms is performed in three-dimensional space using analytic Riesz-Hadamard regularization techniques. Then divergences are treated locally (i.e., around particles’ positions for UV and in the vicinity of spatial infinity for IR divergences) by means of combined dimensional and analytic regularization. Various evolved analytic expressions are presented for the first time. The breakdown of the Leibniz rule for distributional derivatives is addressed as well as the in general nondistributive law when regularizing value of products of functions evaluated at their singular point.

In recent years, Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless, the interplay between Planck-scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challenges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We propose here a general strategy of analysis of the effects of modifications of the dispersion relation in Friedmann-Robertson-Walker spacetimes, applicable both to cases where the relativistic equivalence of frames is spoiled (“preferred-frame scenarios”) and to the alternative possibility of “DSR-relativistic theories,” theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent. We show that the Jacob-Piran ansatz implicitly assumes that spacetime translations are not affected by the Planck scale, while under rather general conditions, the same Planck-scale quantum-spacetime structures producing modifications of the dispersion relation also affect translations. Through the explicit analysis of one of the effects produced by modifications of the dispersion relation, an effect amounting to Planck-scale corrections to travel times, we show that our concerns are not merely conceptual but rather can have significant quantitative implications.

We demonstrate that a slowly rotating compact body subjected to a stationary tidal field undergoes a dynamical response, in which the fluid variables and the interior metric vary on the time scale of the rotation period. This dynamical response requires the tidal field to have a gravitomagnetic component generated by external mass currents; the response to a gravitoelectric tidal field is stationary. We confirm that in a calculation carried out to first order in the body’s rotation, the exterior geometry bears no trace of this internal dynamics; it remains stationary in spite of the time-dependent interior.

We provide an exhaustive numerical exploration of the predictions of loop quantum cosmology with a postbounce phase of inflation for the primordial power spectrum of scalar and tensor perturbations. We extend previous analysis by characterizing the phenomenologically relevant parameter space and by constraining it using observations. Furthermore, we characterize the shape of loop quantum cosmology corrections to observable quantities across this parameter space. Our analysis provides a framework to contrast more accurately the theory with forthcoming polarization data, and it also paves the road for the computation of other observables beyond the power spectra, such as non-Gaussianity.

We discuss the nature of phase transitions in the fermionic King model which describes tidally truncated quantum self-gravitating systems. This distribution function takes into account the escape of high-energy particles and has a finite mass. On the other hand, the Pauli exclusion principle puts an upper bound on the phase-space density of the system and stabilizes it against gravitational collapse. As a result, there exists a statistical equilibrium state for all accessible values of energy and temperature. We plot the caloric curves and investigate the nature of phase transitions as a function of the degeneracy parameter in both microcanonical and canonical ensembles, extending the work of Chavanis [Int. J. Mod. Phys. B 20, 3113 (2006)] for box-confined configurations. We consider stable and metastable states and emphasize the importance of the latter for systems with long-range interactions. Phase transitions can take place between a “gaseous” phase unaffected by quantum mechanics and a “condensed” phase dominated by quantum mechanics. The phase diagram exhibits two critical points, one in each ensemble, beyond which the phase transitions disappear. There also exists a region of negative specific heats and a situation of ensemble inequivalence for sufficiently large systems. In the microcanonical ensemble, gravitational collapse (gravothermal catastrophe) results in the formation of a small degenerate object containing a small mass. This is accompanied by the expulsion of a hot envelope containing a large mass. In the canonical ensemble, gravitational collapse (isothermal collapse) leads to a small degenerate object containing almost all the mass. It is surrounded by a tenuous envelope. We apply the fermionic King model to the case of dark matter halos made of massive neutrinos following the work of de Vega, Salucci, and Sanchez [Mon. Not. R. Astron. Soc. 442, 2717 (2014)]. The gaseous phase describes large halos and the condensed phase describes dwarf halos. Partially degenerate configurations describe intermediate-size halos. We argue that large dark matter halos cannot harbor a fermion ball because these nucleus-halo configurations are thermodynamically unstable (saddle points of entropy). Large dark matter halos may rather contain a central black hole resulting from a dynamical instability of relativistic origin occurring during the gravothermal catastrophe. We relate the existence of black holes to the microcanonical critical point and determine the minimum halo mass above which black holes can form. We also compare fermionic and bosonic models of dark matter and discuss the value of the mass of the dark matter particle in each case.

Primordial or big bang nucleosynthesis (BBN) is one of the three historically strong evidences for the big bang model. Standard BBN is now a parameter-free theory, since the baryonic density of the Universe has been deduced with an unprecedented precision from observations of the anisotropies of the cosmic microwave background radiation. There is a good agreement between the primordial abundances of ${}^4\mathrm{He}$, D, ${}^3\mathrm{He}$, and ${}^7\mathrm{Li}$ deduced from observations and from primordial nucleosynthesis calculations. However, the ${}^7\mathrm{Li}$ calculated abundance is significantly higher than the one deduced from spectroscopic observations and remains an open problem. In addition, recent deuterium observations have drastically reduced the uncertainty on $\mathrm{D}/\mathrm{H}$, to reach a value of 1.6%. It needs to be matched by BBN predictions whose precision is now limited by thermonuclear reaction rate uncertainties. This is especially important as many attempts to reconcile Li observations with models lead to an increased D prediction. Here, we reevaluate the $d(p,\gamma ){}^3\mathrm{He}$, $d(d,n){}^3\mathrm{He}$, and $d(d,p){}^3\mathrm{H}$ reaction rates that govern deuterium destruction, incorporating new experimental data and carefully accounting for systematic uncertainties. Contrary to previous evaluations, we use theoretical ab initio models for the energy dependence of the $S$ factors. As a result, these rates increase at BBN temperatures, leading to a reduced value of $\mathrm{D}/\mathrm{H}=(2.45\pm 0.10)\times {10}^{-5}$ ($2\sigma$), in agreement with observations.

We propose a simple model that elucidates the generation of halo velocity bias. The fluid equation approximation is often adopted in modeling the evolution of the halo density field. In this approach, halos are often taken to be point particles even though in reality they are finite-sized objects. In this paper, we generalize the fluid equation approximation to halos to include the finite extent of halos by taking into account the halo profile. We compute the perturbation of the halo density and velocity field to second order and find that the profile correction gives rise to $k^2$ correction terms in Fourier space. These corrections are more important for velocity than for density. In particular, the profile correction generates $k^2$ correction term in the velocity bias; this correction term does not decay away in the long term limit, but it is not constant. We model the halo profile evolution using the spherical collapse model. We also measure the evolution of protohalo profile at various redshifts numerically. We find that the spherical collapse model gives a reasonable description of the numerical profile evolution. Static halo profile is often adopted in modeling halos in theories such as the excursion set theory. Our work highlights the importance of including the profile evolution in the calculations.

Assuming a double-well bare potential for a self-interacting scalar field, with the Higgs vacuum expectation value, it is shown that nonperturbative quantum corrections naturally lead to ultralight particles of $\text{mass}\simeq {10}^{-23}\mathrm{eV}$, if these nonperturbative effects occur at a time consistent with the electroweak phase transition. This mechanism could be relevant in the context of Bose-Einstein condensate studies for the description of cold dark matter. Given the numerical consistency with the electroweak transition, an interaction potential for Higgs and dark matter fields is proposed, where spontaneous symmetry breaking for the Higgs field leads to the generation of ultralight particles, in addition to the usual Higgs mechanism. This model also naturally leads to extremely weak interactions between the Higgs and dark matter particles.

We present details of numerical simulations of the gravitational radiation produced by a first order thermal phase transition in the early Universe. We confirm that the dominant source of gravitational waves is sound waves generated by the expanding bubbles of the low-temperature phase. We demonstrate that the sound waves have a power spectrum with a power-law form between the scales set by the average bubble separation (which sets the length scale of the fluid flow $L_{\mathrm{f}}$) and the bubble wall width. The sound waves generate gravitational waves whose power spectrum also has a power-law form, at a rate proportional to $L_{\mathrm{f}}$ and the square of the fluid kinetic energy density. We identify a dimensionless parameter ${\tilde{\mathrm{\Omega }}}_{\mathrm{GW}}$ characterizing the efficiency of this “acoustic” gravitational wave production whose value is $8\pi {\tilde{\mathrm{\Omega }}}_{\mathrm{GW}}\simeq 0.8\pm 0.1$ across all our simulations. We compare the acoustic gravitational waves with the standard prediction from the envelope approximation. Not only is the power spectrum steeper (apart from an initial transient) but the gravitational wave energy density is generically larger by the ratio of the Hubble time to the phase transition duration, which can be 2 orders of magnitude or more in a typical first order electroweak phase transition.

We point out that, for Dirac neutrinos, in addition to the standard thermal cosmic neutrino background ($\mathrm{C}\nu \mathrm{B}$), there could also exist a nonthermal neutrino background with comparable number density. As the right-handed components are essentially decoupled from the thermal bath of standard model particles, relic neutrinos with a nonthermal distribution may exist until today. The relic density of the nonthermal (nt) background can be constrained by the usual observational bounds on the effective number of massless degrees of freedom $N_{\mathrm{eff}}$ and can be as large as $n_{{\nu }_{\mathrm{nt}}}\lesssim 0.5n_{\gamma }$. In particular, $N_{\mathrm{eff}}$ can be larger than 3.046 in the absence of any exotic states. Nonthermal relic neutrinos constitute an irreducible contribution to the detection of the $\mathrm{C}\nu \mathrm{B}$ and, hence, may be discovered by future experiments such as PTOLEMY. We also present a scenario of chaotic inflation in which a nonthermal background can naturally be generated by inflationary preheating. The nonthermal relic neutrinos, thus, may constitute a novel window into the very early Universe.

Cosmological constraints are usually derived under the assumption of a six-parameter $\mathrm{\Lambda }\mathrm{CDM}$ theoretical framework or simple one-parameter extensions. In this paper we present, for the first time, cosmological constraints in a significantly extended scenario, varying up to 12 cosmological parameters simultaneously, including the sum of neutrino masses, the neutrino effective number, the dark energy equation of state, the gravitational wave background and the running of the spectral index of primordial perturbations. Using the latest Planck 2015 data release (with polarization), we found no significant indication for extensions to the standard $\mathrm{\Lambda }\mathrm{CDM}$ scenario, with the notable exception of the angular power spectrum lensing amplitude, $A_{\text{lens}}$, which is larger than the expected value at more than 2 standard deviations, even when combining the Planck data with BAO and supernovae type Ia external data sets. In our extended cosmological framework, we find that a combined $\text{Planck}+\mathrm{BAO}$ analysis constrains the value of the rms density fluctuation parameter to ${\sigma }_8={0.781}_{-0.063}^{+0.065}$ at 95 % C.L., helping to relieve the possible tensions with the CFHTlenS cosmic shear survey. We also find a lower value for the reionization optical depth $\tau ={0.058}_{-0.043}^{+0.040}$ at 95 % C.L. with respect to the one derived under the assumption of $\mathrm{\Lambda }\mathrm{CDM}$. The scalar spectral index $n_S$ is now compatible with a Harrison-Zeldovich spectrum to within 2.5 standard deviations. Combining the Planck data set with the Hubble Space Telescope prior on the Hubble constant provides a value for the equation of state $w<-1$ at more than 2 standard deviations, while the neutrino effective number is fully compatible with the expectations of the standard three neutrino framework.

In this manuscript the $B\to \pi \tau {\overline{\nu }}_{\tau }$ decay is investigated in the context of the type II 2HDM extension of the Standard Model. In particular, a prediction for the ratio of semileptonic branching fractions from $\ell =\tau$ and $\ell =e,\mu$ is produced, and an exclusion based on the MSSM parameters $\tan \beta$ and $m_H^{+}$ from a recent Belle measurement is reported. An alternative variable to the ratio of branching fractions is discussed that could result in increased sensitivity to rule out contributions from additional scalar mediators.

We study the prospects for excluding or discovering vectorlike leptons using multilepton events at the LHC. We consider models in which the vectorlike leptons decay to tau leptons. If the vectorlike leptons are weak isosinglets, then discovery in multilepton states is found to be extremely challenging. For the case that the vectorlike leptons are weak isodoublet, we argue that there may be an opportunity for exclusion for masses up to about 275 GeV by direct searches with existing LHC data at $\sqrt{s}=8\mathrm{TeV}$. We also discuss prospects for exclusion or discovery at the LHC with future $\sqrt{s}=13\mathrm{TeV}$ data.

We investigate the phase structure of three-flavor QCD in the presence of finite quark chemical potential $\mu /T\lesssim 1.2$ by using the nonperturbatively $O(a)$ improved Wilson fermion action on lattices with a fixed temporal extent $N_{\mathrm{t}}=6$ and varied spatial linear extents $N_{\mathrm{s}}=8$, 10, 12. Especially, we focus on locating the critical end point that characterizes the phase structure, and extracting the curvature of the critical line on the $\mu \text{−}{m}_{\pi }$ plane. For Wilson-type fermions, the correspondence between bare parameters and physical parameters is indirect. Hence we present a strategy to transfer the bare parameter phase structure to the physical one, in order to obtain the curvature. Our conclusion is that the curvature is positive. This implies that, if one starts from a quark mass in the region of crossover at zero chemical potential, one would encounter a first-order phase transition when one raises the chemical potential.

For field theories with a topological charge $Q$, it is often of interest to measure the topological susceptibility ${\chi }_{\mathrm{t}}=(⟨Q^2⟩-⟨Q{⟩}^2)/V$. If we manage to perform a Monte Carlo simulation where $Q$ changes frequently, ${\chi }_{\mathrm{t}}$ can be evaluated directly. However, for local update algorithms and fine lattices, the autocorrelation time with respect to $Q$ tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of ${\chi }_{\mathrm{t}}$ is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in nonlinear $\sigma$-models and in two-dimensional Abelian gauge theory yield accurate results for ${\chi }_{\mathrm{t}}$, which confirm that the method is applicable. We also obtain promising results in four-dimensional SU(2) Yang-Mills theory, which suggest the applicability of this method in QCD.