The quantum Einstein gravity is treated by the functional renormalization group method using the Einstein-Hilbert action. The ultraviolet non-Gaussian fixed point is determined and its corresponding exponent of the correlation length is calculated for a wide range of regulators. It is shown that the exponent provides a minimal sensitivity to the parameters of the regulator which correspond to the Litim’s regulator.

The lowest dimensional gluon condensate $G_2$ is analyzed at finite temperature and chemical potential using a holographic model of QCD with conformal invariance broken by a background dilaton. Starting from the free energy of the model, the thermodynamical quantities needed to determine the $T$ and $\mu$ dependence of the gluon condensate are evaluated. At high temperature the gluon condensate is independent of chemical potential. Moreover, at $\mu =0$, the temporal and spatial Wilson loops at low temperature are computed; they are related to the (chromo)electric and magnetic components of $G_2$, respectively. The $T$ dependence of the two components is separately determined.

We study the full linear perturbations of a homogeneous and isotropic spacetime in the Eddington-inspired Born-Infeld gravity. The stabilities of the perturbations are analyzed in the Eddington regime. We find that, for positive $\kappa$, the scalar modes are stable in the infinite wavelength limit ($k=0$) but unstable for $k\ne 0$. The vector modes are stable and the tensor mode is unstable in the Eddington regime, independent of the wave vector $k$. However, these modes are unstable and hence cause the instabilities for negative $\kappa$.

In this paper, we study the cosmological viability conditions, the phase-space dynamics, and the cosmological evolution of $f(R)$ gravity. In contrast to most previous works in the literature, which analyzed the background dynamics of $f(R)$ gravity by means of a dynamical system, we proceed by focusing on the equivalent scalar field description of the theory, which we believe is a more intuitive way of treating the problem. In order to study how the physical solutions evolve in $f(R)$ cosmology, we explore the cosmological dynamics of a range of $f(R)$ models, including models that yield a large hierarchy of scales and are singularity free. We present generic features of the phase-space dynamics in $f(R)$ cosmology. We study the global structure of the phase space in $f(R)$ gravity by compactifying the infinite phase space into a finite space via the Poincaré transformation. On the expansion branch of the phase space, the constraint surface has a repeller and a de Sitter attractor, while on the contraction branch, the constraint surface has an attractor and a de Sitter repeller. Generally, the phase currents originate from the repeller and terminate at the corresponding attractor in each space. The trajectories between the repeller and the attractor in the presence of matter density are different from those in the vacuum case. The phase analysis techniques developed in this paper are very general, and can be applied to other similar dynamical systems.

We show that the Stephenson-Kilmister-Yang (SKY) equation combined with Camenzind’s matter current term naturally provides the cosmological constant and dark radiation as integration constants of the Stephenson-Kilmister-Yang-Camenzind (SKYC) field equation. To characterize the property of the dark radiation, we develop a method to separate it from the ordinary radiation. We find a special property of Camenzind’s matter current, namely that the solution space for radiation in fact belongs to that of the vacuum solution of the SKY equation. We also find that this matter current does not obey the conservation condition suggested by Kilmister. Finally, we discuss the possible role of dark radiation emergent from the SKYC theory in recent cosmic microwave background observations and its implications to the inflation scenario.

The well-studied radiative model of neutrino mass through $Z_2$ dark matter is shown to be naturally realizable in the context of $SU(6)$ grand unification. A recent new proposal based on $U(1{)}_D$ dark matter is similarly accommodated in $SU(7)$. Just as the proton is unstable at the scale of quark-lepton unification, dark matter is expected to be unstable at a similar scale.

In this article we propose an overview on the current theoretical and experimental limits on a Higgs singlet extension of the Standard Model (SM). We assume that the boson which has recently been observed by the LHC experiments is the lightest Higgs boson of such a model, while for the second Higgs boson we consider a mass range of $600\mathrm{GeV}\le m_H\le 1\mathrm{TeV}$, where our model directly corresponds to a benchmark scenario of the heavy Higgs working group. In this light, we study the impact of perturbative unitarity limits, renormalization group equations analysis, and experimental constraints (electroweak precision tests, measurements of the observed light Higgs coupling strength at the Large Hadron Collider). We show that, in the case of no additional hidden sector contributions, the largest constraints for higher Higgs masses stem from the assumption of perturbativity as well as vacuum stability for scales of the order of the SM metastability scale, and that the allowed mixing range is severely restricted. We discuss implications for current LHC searches in the singlet extension, especially the expected suppression factors for SM-like decays of the heavy Higgs. We present these results in terms of a global scaling factor $\kappa$ as well as the total width $\Gamma$ of the new scalar.

We compute the dimuon-excess invariant mass distribution at the $\rho$-meson peak in the context of relativistic heavy-ion collisions at Super Proton Synchrotron energies. The parameters describing the $\rho$ meson that depend on the temperature, $T$, and chemical potential, $\mu$—its width, mass and leptonic decay constant—are determined from finite-energy QCD sum rules. Results show that the $\rho$-meson width increases whereas its mass and leptonic decay constant decrease near the (chemical potential-dependent) critical temperature $T_c(\mu )$ for chiral symmetry restoration/quark-gluon deconfinement. As a consequence, starting from $T_c(\mu )$, for a short-lived cooling the main effect is a broadening of the dimuon distribution. However, when the evolution brings the system to a lower freeze-out temperature, with the $\rho$-meson parameters approaching their vacuum values, the dimuon distribution shows a broad peak centered at the vacuum $\rho$-meson mass. For even lower freeze-out temperatures the peak becomes less prominent since the thermal phase-space factor suppresses the distribution for larger values of the invariant dimuon mass, given that the average temperature is smaller. The dimuon distribution exhibits a nontrivial behavior with $\mu$. For small $\mu$ values the distribution broadens with increasing $\mu$ becoming a bit steeper at low invariant masses for larger values of $\mu$. Our results are in very good agreement with data from the NA60 Collaboration.

We evaluate both the Pomeron interactions and the inelastic Gribov corrections to the Glauber-Gribov formula, which is used to extract proton-proton cross sections from proton-air collisions at high energies. We demonstrate that these corrections are compatible with the errors for proton-air cross sections measured at ultrahigh energies in cosmic ray experiments. We present the results of a calculation of these cross sections based on our model for the soft interactions at high energies, which provides a good description of available accelerator data, including that for LHC energies.

We have searched for extremely high energy neutrinos using data taken with the IceCube detector between May 2010 and May 2012. Two neutrino-induced particle shower events with energies around 1 PeV were observed, as reported previously. In this work, we investigate whether these events could originate from cosmogenic neutrinos produced in the interactions of ultrahigh energy cosmic rays with ambient photons while propagating through intergalactic space. Exploiting IceCube’s large exposure for extremely high energy neutrinos and the lack of observed events above 100 PeV, we can rule out the corresponding models at more than 90% confidence level. The model-independent quasidifferential 90% C.L. upper limit, which amounts to $E^2{\varphi }_{{\nu }_e+{\nu }_{\mu }+{\nu }_{\tau }}=1.2\times {10}^{-7}\mathrm{GeV}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$ at 1 EeV, provides the most stringent constraint in the energy range from 10 PeV to 10 EeV. Our observation disfavors strong cosmological evolution of the highest energy cosmic-ray sources such as the Fanaroff-Riley type II class of radio galaxies.

We define an effective temperature and study its properties for a class of out-of-equilibrium steady states in a heat bath. Our analysis is based on the anti-de Sitter spacetime/conformal field theory (AdS/CFT) correspondence, and examples include systems driven by applied electric fields and branes dragged in plasmas. We found that the effective temperature can be lower than that of the heat bath and that the out-of-equilibrium noise can be smaller than that in equilibrium. We show that a generalization of the fluctuation-dissipation relation holds for the effective temperature. In particular, we generalize the Johnson-Nyquist relation for a large electric field.

We consider the consequences of having no prior knowledge of the true dark energy model for the interpretation of cosmological observations. The magnitude of redshift-space distortions and weak-lensing shear is determined by the metric on the geodesics of which galaxies and light propagate. We show that, given precise enough observations, we can use these data to completely reconstruct the metric on our past light cone and therefore to measure the scale and time dependence of the anisotropic stress and the evolution of the gravitational potentials in a model-independent manner. Since both dark matter and dark energy affect the visible sector only through the gravitational field they produce, they are inseparable without a model for dark energy: galaxy bias cannot be measured and therefore the distribution of dark matter determined; the peculiar velocity of dark matter can be identified with that of the galaxies only when the equivalence principle holds. Given these limitations, we show how one can nonetheless build tests for classes of dark energy models which depend on making measurements at multiple scales at a particular redshift. They are null tests on the model-independent observables, do not require modeling evolution in time, and do not require any parametrization of the free functions of these models—such as the sound speed. We show that one in principle could rule out or constrain the whole class of the most general scalar-tensor theories even without assuming the quasistatic limit.

We consider the effect of a logarithmic $f(R)$ theory, motivated by the form of the one-loop effective action arising from gluons in curved spacetime, on the structure of relativistic stars. In addition to analyzing the consistency constraints on the potential of the scalar degree of freedom, we discuss the possibility of observational features arising from a fifth force in the vicinity of the neutron star surface. We find that the model exhibits a chameleon effect that completely suppresses the effect of the modification on scales exceeding a few radii, but close to the surface of the neutron star, the deviation from general relativity can significantly affect the surface redshift that determines the shift in absorption (or emission) lines. We also use the method of perturbative constraints to solve the modified Tolman-Oppenheimer-Volkov equations for normal and self-bound neutron stars (quark stars).

We present compact $Q$-balls in an (anti–)de Sitter background in $D$ dimensions, obtained with a V-shaped potential of the scalar field. Beyond critical values of the cosmological constant ${\widehat{\Lambda }}_{\mathrm{cr}}(D)$ compact $Q$-shells arise. By including the gravitational backreaction, we obtain boson stars and boson shells with (anti–)de Sitter asymptotics. We analyze the physical properties of these solutions and determine their domain of existence. In four dimensions we address some astrophysical aspects.

We present a novel mechanism to generate the cosmic perturbation from evaporation of primordial black holes. A mass of a field is fluctuated if it is given by a vacuum expectation value of a light scalar field because of the quantum fluctuation during inflation. The fluctuated mass causes variations of the evaporation time of the primordial black holes. Therefore provided the primordial black holes dominate the Universe when they evaporate, primordial cosmic perturbations are generated. We find that the amplitude of the large scale curvature perturbation generated in this scenario can be consistent with the observed value. Interestingly, our mechanism works even if all fields that are responsible for inflation and the generation of the cosmic perturbation are decoupled from the visible sector except for the gravitational interaction. An implication to the running spectral index is also discussed.

Higgs $G$ inflation is a Higgs inflation model with a generalized Galileon term added to the standard model Higgs field, which realizes inflation compatible with observations. Recently, it was claimed that the generalized Galileon term induces instabilities during the oscillation phase and that the simplest Higgs $G$-inflation model inevitably suffers from this problem. In this paper, we extend the original Higgs $G$-inflation Lagrangian to a more general form, namely introducing a higher-order kinetic term and generalizing the form of the Galileon term, so that the Higgs field can oscillate after inflation without encountering instabilities. Moreover, it accommodates a large region of the $n_s\mathrm{\text{−}}r$ plane, most of which is consistent with current observations, leading us to expect the detection of B-mode polarization in the cosmic microwave background in the near future.

Long gamma-ray bursts (GRBs) have been linked to extreme core-collapse supernovae from massive stars. Gravitational waves (GW) offer a probe of the physics behind long GRBs. We investigate models of long-lived ($\sim 10–1000\mathrm{s}$) GW emission associated with the accretion disk of a collapsed star or with its protoneutron star remnant. Using data from LIGO’s fifth science run, and GRB triggers from the Swift experiment, we perform a search for unmodeled long-lived GW transients. Finding no evidence of GW emission, we place 90% confidence-level upper limits on the GW fluence at Earth from long GRBs for three waveforms inspired by a model of GWs from accretion disk instabilities. These limits range from $F<3.5\mathrm{ergs}{\mathrm{cm}}^{-2}$ to $F<1200\mathrm{ergs}{\mathrm{cm}}^{-2}$, depending on the GRB and on the model, allowing us to probe optimistic scenarios of GW production out to distances as far as $\approx 33\mathrm{Mpc}$. Advanced detectors are expected to achieve strain sensitivities $10\times$ better than initial LIGO, potentially allowing us to probe the engines of the nearest long GRBs.

Direct detection of gravitational radiation in the audio band is being pursued with a network of kilometer-scale interferometers (LIGO, Virgo, KAGRA). Several space missions (LISA, DECIGO, BBO) have been proposed to search for sub-hertz radiation from massive astrophysical sources. Here we examine the potential sensitivity of three ground-based detector concepts aimed at radiation in the 0.1–10 Hz band. We describe the plethora of potential astrophysical sources in this band and make estimates for their event rates and thereby, the sensitivity requirements for these detectors. The scientific payoff from measuring astrophysical gravitational waves in this frequency band is great. Although we find no fundamental limits to the detector sensitivity in this band, the remaining technical limits will be extremely challenging to overcome.

We study an improved method for detecting gravitational wave signals from perturbed black holes by Earth-based detectors in the search for intermediate-mass black holes. Such signals, called ringdowns, are damped sinusoids whose frequency and damping constant can be used to measure a black hole’s mass and spin. Utilizing the output from a matched-filter analysis pipeline, we present an improved statistic for the detection of a ringdown signal that is found to be coincident in multiple detectors. The statistic addresses the non-Gaussianity of the data without the use of an additional signal-based waveform consistency test. We also develop coherent network statistics to check for consistency of signal amplitudes and phases in the different detectors with their different orientations and signal arrival times. We find that the detection efficiency can be improved at least by a few tens of percent by applying these multidetector statistics primarily because of the ineffectiveness of single detector–based discriminators of nonstationary noise, such as the chi-square test, in the case of ringdown signals studied here.

Modifications of general relativity usually include extra dynamical degrees of freedom, which to date remain undetected. Here we explore the possibility of modifying Einstein’s theory by adding solely nondynamical fields. With the minimal requirement that the theory satisfies the weak equivalence principle and admits a covariant Lagrangian formulation, we show that the field equations generically have to include higher-order derivatives of the matter fields. This has profound consequences for the viability of these theories. We develop a parametrization based on a derivative expansion and show that—to next-to-leading order—all theories are described by just two parameters. Our approach can be used to put stringent, theory-independent constraints on such theories, as we demonstrate using the Newtonian limit as an example.