We present an erratum with respect to the paper. The results presented are based on an incorrect expression for the standard detection statistic, which does not include the correction to the cross-correlation term that is required when the detector sensitivities are assumed to be known. We are grateful to Joe Romano for pointing out the problem and providing helpful feedback in the revision efforts.

To model a realistic situation for the beginning we consider massive real scalar ${\varphi }^4$ theory in a ($1+1$)-dimensional asymptotically static Minkowski spacetime with an intermediate stage of expansion. To have an analytic headway we assume that scalars have a big mass. At past and future infinities of the background we have flat Minkowski regions which are joint by the inflationary expansion region. We use the tree-level Keldysh propagator in the theory in question to calculate the expectation value of the stress-energy tensor which is, thus, due to the excitations of the zero-point fluctuations. Then we show that even for large mass, if the de Sitter expansion stage is long enough, the quantum loop corrections to the expectation value of the stress-energy tensor are not negligible in comparison with the tree-level contribution. That is revealed itself via the excitation of the higher-point fluctuations of the exact modes: during the expansion stage a nonzero particle number density for the exact modes is generated. This density is not Planckian and serves as a quench which leads to a thermalization in the out Minkowski stage.

The potential conflict between torsion and gauge symmetry in the Riemann-Cartan curved spacetime was noted by Kibble in his 1961 pioneering paper and has since been discussed by many authors. Kibble suggested that, to preserve gauge symmetry, one should forgo the covariant derivative in favor of the ordinary derivative in the definition of the field strength $F_{\mu \nu }$ for massless gauge theories, while for massive vector fields, covariant derivatives should be adopted. This view was further emphasized by Hehl et al. in their influential 1976 review paper. We address the question of whether this deviation from normal procedure by forgoing covariant derivatives in curved spacetime with torsion could give rise to inconsistencies in the theory, such as the quantum renormalizability of a realistic interacting theory. We demonstrate in this paper the one-loop renormalizability of a realistic gauge theory of gauge bosons interacting with Dirac spinors, such as the SU(3) chromodynamics, for the case of a curved Riemann-Cartan spacetime with totally antisymmetric torsion. This affirmative confirmation is one step toward providing justification for the assertion that the flat-space definition of the gauge-field strength should be adopted as the proper definition.

We consider 5D brane world models with broken global 4D Poincaré invariance (4D part of the spacetime metric is not conformal to the Minkowski spacetime). The bulk is filled with the negative cosmological constant and may contain a perfect fluid. In the case of empty bulk (the perfect fluid is absent), it is shown that one brane solution always has either a physical or a coordinate singularity in the bulk. We cut off these singularities in the case of compact two brane model and obtain regular exact solutions for both 4D Poincaré broken and restored invariance. When the perfect fluid is present in the bulk, we get the master equation for the metric coefficients in the case of arbitrary bulk perfect fluid equation of state (EoS) parameters. In two particular cases of EoS, we obtain the analytic solutions for thin and thick branes. First one generalizes the well known Randall-Sundrum model with one brane to the case of the bulk anisotropic perfect fluid. In the second solution, the 4D Poincaré invariance is restored. Here, the spacetime goes asymptotically to the anti-de Sitter one far from the thick brane.

We present the first complete (i.e., ambiguity-free) derivation of the equations of motion of two nonspinning compact objects up to the 4PN (post-Newtonian) order, based on the Fokker action of point particles in harmonic coordinates. The last ambiguity parameter is determined from first principle, by resorting to a matching between the near-zone and far-zone fields, and a consistent computation of the 4PN tail effect in $d$ dimensions. Dimensional regularization is used throughout for treating IR divergences appearing at 4PN order, as well as UV divergences due to the modeling of the compact objects as point particles.

Loop quantum cosmology has recently been applied in order to extend the analysis of primordial perturbations to the Planck era and discuss the possible effects of quantum geometry on the cosmic microwave background. Two approaches to loop quantum cosmology with admissible ultraviolet behavior leading to predictions that are compatible with observations are the so-called hybrid and dressed metric approaches. In spite of their similarities and relations, we show in this work that the effective equations that they provide for the evolution of the tensor and scalar perturbations are somewhat different. When backreaction is neglected, the discrepancy appears only in the time-dependent mass term of the corresponding field equations. We explain the origin of this difference, arising from the distinct quantization procedures. Besides, given the privileged role that the big bounce plays in loop quantum cosmology, e.g. as a natural instant of time to set initial conditions for the perturbations, we also analyze the positivity of the time-dependent mass when this bounce occurs. We prove that the mass of the tensor perturbations is positive in the hybrid approach when the kinetic contribution to the energy density of the inflaton dominates over its potential, as well as for a considerably large sector of backgrounds around that situation, while this mass is always nonpositive in the dressed metric approach. Similar results are demonstrated for the scalar perturbations in a sector of background solutions that includes the kinetically dominated ones; namely, the mass then is positive for the hybrid approach, whereas it typically becomes negative in the dressed metric case. More precisely, this last statement is strictly valid when the potential is quadratic for values of the inflaton mass that are phenomenologically favored.

Constraints on inflationary $B$ modes using cosmic microwave background polarization data commonly rely on either template cleaning or cross-spectra between maps at different frequencies to disentangle Galactic foregrounds from the cosmological signal. Assumptions about how the foregrounds scale with frequency are therefore crucial to interpreting the data. Recent results from the Planck satellite collaboration claim significant evidence for a decorrelation in the polarization signal of the spatial pattern of Galactic dust between 217 and 353 GHz. Such a decorrelation would suppress power in the cross-spectrum between high-frequency maps, where the dust is strong, and lower-frequency maps, where the sensitivity to cosmological $B$ modes is strongest. Alternatively, it would leave residuals in lower-frequency maps cleaned with a template derived from the higher-frequency maps. If not accounted for, both situations would result in an underestimate of the dust contribution and thus an upward bias on measurements of the tensor-to-scalar ratio, $r$. In this paper, we revisit this measurement and find that the no-decorrelation hypothesis cannot be excluded with the Planck data. There are three main reasons for this: (i) There is significant noise bias in cross-spectra between Planck data splits that needs to be accounted for. (ii) There is strong evidence for unknown instrumental systematics, the amplitude of which we estimate using alternative Planck data splits. (iii) There are significant correlations between measurements in different sky patches that need to be taken into account when assessing the statistical significance. Between $\ell =55–90$ and over 72% of the sky, the dust $BB$ correlation between 217 and 353 GHz is ${1.001}_{-.004/.000}^{+.004/.021}$ ($68\%\mathrm{stat}/\mathrm{syst}$.) and shows no significant trend with the sky fraction.

Calculations of the cosmic microwave background (CMB) lensing power implemented into the standard cosmological codes such as camb and class usually treat the surface of last scatter as an infinitely thin screen. However, since the CMB anisotropies are smoothed out on scales smaller than the diffusion length due to the effect of Silk damping, the photons which carry information about the small-scale density distribution come from slightly earlier times than the standard recombination time. The dominant effect is the scale dependence of the mean redshift associated with the fluctuations during recombination. We find that fluctuations at $k=0.01{\mathrm{Mpc}}^{-1}$ come from a characteristic redshift of $z\approx 1090$, while fluctuations at $k=0.3{\mathrm{Mpc}}^{-1}$ come from a characteristic redshift of $z\approx 1130$. We then estimate the corrections to the lensing kernel and the related power spectra due to this effect. We conclude that neglecting it would result in a deviation from the true value of the lensing kernel at the half percent level at small CMB scales. For an all-sky, noise-free experiment, this corresponds to a $\sim 0.1\sigma$ shift in the observed temperature power spectrum on small scales ($2500\lesssim l\lesssim 4000$).

The Higgs-dilaton model is a scale-invariant extension of the Standard Model nonminimally coupled to gravity and containing just one additional degree of freedom on top of the Standard Model particle content. This minimalistic scenario predicts a set of measurable consistency relations between the inflationary observables and the dark-energy equation-of-state parameter. We present an alternative derivation of these consistency relations that highlights the connections and differences with the $\alpha$-attractor scenario. We study how far these constraints allow one to distinguish the Higgs-dilaton model from $\mathrm{\Lambda }\mathrm{CDM}$ and $w\mathrm{CDM}$ cosmologies. To this end we first analyze existing data sets using a Markov chain Monte Carlo approach. Second, we perform forecasts for future galaxy surveys using a Fisher matrix approach, both for galaxy clustering and weak lensing probes. Assuming that the best fit values in the different models remain comparable to the present ones, we show that both Euclid- and SKA2-like missions will be able to discriminate a Higgs-dilaton cosmology from $\mathrm{\Lambda }\mathrm{CDM}$ and $w\mathrm{CDM}$.

Interacting fixed points in four-dimensional gauge theories coupled to matter are investigated using perturbation theory up to three loop order. It is shown how fixed points, scaling exponents, and anomalous dimensions are obtained as a systematic power series in a small parameter. The underlying ordering principle is explained and contrasted with conventional perturbation theory and Weyl consistency conditions. We then determine the conformal window with asymptotic safety from the complete next-to-next-to-leading order in perturbation theory. Limits for the conformal window arise due to fixed point mergers, the onset of strong coupling, or vacuum instability. A consistent picture is uncovered by comparing various levels of approximation. The theory remains perturbative in the entire conformal window, with vacuum stability dictating the tightest constraints. We also speculate about a secondary conformal window at strong coupling and estimate its lower limit. Implications for model building and cosmology are indicated.

In this article we present the next-to-leading order QCD predictions for $Wb\overline{b}+n\text{−}\mathrm{jet}$ ($n=0$, 1, 2, 3) production at the Large Hadron Collider with $\sqrt{s}=13\mathrm{TeV}$. We work in the four-flavor number scheme with a nonvanishing bottom-quark mass and include all subprocesses at leading electroweak order as well as all heavy-fermion-loop effects. We show the impact of QCD corrections for total as well as differential cross sections and make an assessment of theoretical uncertainties of $Wb\overline{b}$ production viewed as an irreducible background to $H(\to b\overline{b})W$ studies. For the calculations we have employed an upgraded version of the BlackHat library which can handle massive fermions in combination with SHERPA. Our results can be explored through publicly available $n$-tuple sets.

We consider Yang-Mills theories quantized in the Landau gauge in the presence of the Gribov horizon via the refined Gribov-Zwanziger (RGZ) framework. As the restriction of the gauge path integral to the Gribov region is taken into account, the resulting gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory simulations. In this work, we explore a higher correlation function in the refined Gribov-Zwanziger theory: the ghost-gluon interaction vertex, at one-loop level. We show explicit compatibility with kinematical constraints, as required by the Ward identities of the theory, and obtain analytical expressions in the limit of vanishing gluon momentum. We find that the RGZ results are nontrivial in the infrared regime, being compatible with lattice Yang-Mills simulations in both SU(2) and SU(3), as well as with solutions from Schwinger-Dyson equations in different truncation schemes, Functional Renormalization Group analysis, and the renormalization group-improved Curci-Ferrari model.

We study single-top production at linear lepton colliders with $\sqrt{s}=0.5$, 1, and 3 TeV. A preliminary analysis shows that despite the large $t\overline{t}$ background at $\sqrt{s}=0.5$ and 1 TeV it is possible to obtain a good sensitivity to the $tbW$ vertex, even more so at 3 TeV when single top becomes the dominant mode of production. Concerning the four-dimension six operators involved, two of them simultaneously generate $ttZ$ couplings and their sensitivity decreases with energy. The opposite is true for the other two operators. Single-top production at these machines is also useful to probe charged-current four-fermion operators $e\nu bt$, some of which are related to $tbW$ operators through the equations of motion.

The $e^{+}{e}^{-}\to K_S{K}_L{\pi }^0$ cross section is measured in the center-of-mass energy range $\sqrt{s}=1.3–2.0\mathrm{GeV}$. The analysis is based on the data sample with an integrated luminosity of $33.5{\mathrm{pb}}^{-1}$ collected with the SND detector at the VEPP-2000 $e^{+}{e}^{-}$ collider.

We use the covariant formulation proposed by Tattersall, Lagos, and Ferreira [Phys. Rev. D 96, 064011 (2017)] to analyze the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasinormal modes of perturbed black holes may be affected by modifications to general relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyze odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

Phenomenological functions $\mathrm{\Sigma }$ and $\mu$, also known as $G_{\text{light}}/G$ and $G_{\text{matter}}/G$, are commonly used to parametrize modifications of the growth of large-scale structure in alternative theories of gravity. We study the values these functions can take in Horndeski theories, i.e., the class of scalar-tensor theories with second order equations of motion. We restrict our attention to models that are in broad agreement with tests of gravity and the observed cosmic expansion history. In particular, we require the speed of gravity to be equal to the speed of light today, as required by the recent detection of gravitational waves and electromagnetic emission from a binary neutron star merger. We examine the correlations between the values of $\mathrm{\Sigma }$ and $\mu$ analytically within the quasistatic approximation and numerically by sampling the space of allowed solutions. We confirm that the conjecture made in [L. Pogosian and A. Silvestri, Phys. Rev. D 94, 104014 (2016)], that $(\mathrm{\Sigma }-1)(\mu -1)\ge 0$ in viable Horndeski theories, holds very well. Along with that, we check the validity of the quasistatic approximation within different corners of Horndeski theory. Our results show that, even with the tight bound on the present-day speed of gravitational waves, there is room within Horndeski theories for nontrivial signatures of modified gravity at the level of linear perturbations.

It is well known that an extremely accurate parametrization of the growth function of matter density perturbations in $\mathrm{\Lambda }\mathrm{CDM}$ cosmology, with errors below 0.25%, is given by $f(a)={\mathrm{\Omega }}_m^{\gamma }(a)$ with $\gamma \simeq 0.55$. In this work, we show that a simple modification of this expression also provides a good description of growth in modified gravity theories. We consider the model-independent approach to modified gravity in terms of an effective Newton constant written as $\mu (a,k)=G_{\mathrm{eff}}/G$ and show that $f(a)=\beta (a){\mathrm{\Omega }}_m^{\gamma }(a)$ provides fits to the numerical solutions with similar accuracy to that of $\mathrm{\Lambda }\mathrm{CDM}$. In the time-independent case with $\mu =\mu (k)$, simple analytic expressions for $\beta (\mu )$ and $\gamma (\mu )$ are presented. In the time-dependent (but scale-independent) case $\mu =\mu (a)$, we show that $\beta (a)$ has the same time dependence as $\mu (a)$. As an example, explicit formulas are provided in the Dvali-Gabadadze-Porrati (DGP) model. In the general case, for theories with $\mu (a,k)$, we obtain a perturbative expansion for $\beta (\mu )$ around the general relativity case $\mu =1$ which, for $f(R)$ theories, reaches an accuracy below 1%. Finally, as an example we apply the obtained fitting functions in order to forecast the precision with which future galaxy surveys will be able to measure the $\mu$ parameter.

We consider an open universe created by bubble nucleation, and study possible effects of our “ancestor vacuum,” a de Sitter space in which bubble nucleation occurred, on the present universe. We compute vacuum expectation values of the energy-momentum tensor for a minimally coupled scalar field, carefully taking into account the effect of the ancestor vacuum by the Euclidean prescription. We pay particular attention to the so-called supercurvature mode, a non-normalizable mode on a spatial slice of the open universe, which has been known to exist for sufficiently light fields. This mode decays in time most slowly, and may leave residual effects of the ancestor vacuum, potentially observable in the present universe. We point out that the vacuum energy of the quantum field can be regarded as dark energy if mass of the field is of order the present Hubble parameter or smaller. We obtain preliminary results for the dark energy equation of state $w(z)$ as a function of the redshift.