We address the infrared(IR) divergence problem during inflation that appears in the loop corrections to the primordial perturbations. In our previous paper, we claimed that, at least in single field models, the IR divergence is originating from the gauge artifact. Namely, diverging IR corrections should not appear in genuine gauge-invariant observables. We propose here one simple but explicit example of such gauge-invariant quantities. Then, we explicitly calculate such a quantity to find that the IR divergence is absent at the leading order in the slow-roll approximation for the usual scale invariant vacuum state. At the same time we notice that there is a subtle issue on the gauge-invariance in how to specify the initial vacuum state.
The impact of curvature divergences on physical observers in a black hole space-time which, nonetheless, is geodesically complete is investigated. This space-time is an exact solution of certain extensions of General Relativity coupled to Maxwell's electrodynamics and, roughly speaking, consists on two Reissner-Nordström (or Schwarzschild or Minkowski) geometries connected by a spherical wormhole near the center. We find that, despite the existence of infinite tidal forces, causal contact is never lost among the elements making up the observer. This suggests that curvature divergences may not …
We study the thermodynamics and thermodynamic geometry of a five-dimensional Reissner-Nordström-AdS black hole in the extended phase space by treating the cosmological constant as being related to the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. It is found that the contribution of the charge of the black hole to the chemical potential is always positive and the existence of charge make the chemical potential become positive more easily. We calculate the scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric …
The $P$-$V$ phase transition and critical behavior in the extended phase space of asymptotic Anti-de Sitter (AdS) black holes have been widely investigated, in which four critical exponents around critical point are found to be consistent with values in the mean field theory. Recently, another critical exponent $ν$ related to divergent correlation length at critical point is proposed by using thermodynamic curvature scalar $R_N$ in the charged AdS black hole. In this paper, we develop a method to investigate the divergent behavior of $R_N$ at critical point, and find that the divergent behavio…
In this paper, we report the results of constraining the dynamical dark energy with a divergence-free parameterization, $w(z) = w_{0} + w_{a}(\frac{\ln(2+z)}{1+z}-\ln2)$, in the presence of spatial curvature and massive neutrinos, with the 7-yr WMAP temperature and polarization data, the power spectrum of LRGs derived from SDSS DR7, the Type Ia supernova data from Union2 sample, and the new measurements of $H_0$ from HST, by using a MCMC global fit method. Our focus is on the determinations of the spatial curvature, $Ω_k$, and the total mass of neutrinos, $\sum m_ν$, in such a dynamical dark e…
In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature.ns of curvature divergences in the context of spac…
We study thermodynamics and thermodynamic geometry of a five-dimensional Schwarzschild AdS black hole in $AdS_5\times{S^5}$ spacetime by treating the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. It is found that the chemical potential is always negative in the stable branch of black hole thermodynamics and it has a chance to be positive, but appears in the unstable branch. We calculate scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric and Quevedo metric, respectively and we f…
We investigate static, spherically symmetric solutions in gravitational theories which have limited curvature invariants, aiming to remove the singularity in the Schwarzschild space-time. We find that if we only limit the Gauss-Bonnet term and the Ricci scalar, then the singularity at the origin persists. Moreover we find that the event horizon can develop a curvature singularity. We also investigate a new class of theories in which all components of the Riemann tensor are bounded. We find that the divergence of the quadratic curvature invariants at the event horizon is avoidable in this theor…
The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of General Relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.
Inflationary correlation functions are potentially affected by infrared divergences. For example, the two-point correlator of curvature perturbation at momentum k receives corrections ~ln(kL), where L is the size of the region in which the measurement is performed. We define infrared-safe correlation functions which have no sensitivity to the size L of the box used for the observation. The conventional correlators with their familiar log-enhanced corrections (both from scalar and tensor long-wavelength modes) are easily recovered from our IR-safe correlation functions. Among other examples, we…
We study the divergences of Wilson loops for a contour with a cusp of zero opening angle, combined with a nonzero discontinuity of its curvature. The analysis is performed in lowest order, both for weak and strong coupling. Such a spike contributes a leading divergent term proportional to the inverse of the square root of the cutoff times the jump of the curvature. As nextleading term appears a logarithmic one in the supersymmetric case, but it is absent in QCD. The strong coupling result, obtained from minimal surfaces in AdS via holography, can be used also for applications to entanglement e…
It is widely known that the primordial curvature perturbation $ζ$ has several universal properties in the infrared (IR) such as the soft theorem, which is also known as the consistency relation, and the conservation in time. They are valid in rather general single clock models of inflation. It has been argued that these universal properties are deeply related to the large gauge transformations in inflationary spacetime. However, the invariance under the large gauge transformations is not sufficient to show these IR properties. In this paper, we show that the locality condition is crucial to sh…
We describe a simple way of incorporating fluctuations of the Hubble scale during the horizon exit of scalar perturbations into the delta N formalism. The dominant effect comes from the dependence of the Hubble scale on low-frequency modes of the inflaton. This modifies the coefficient of the log-enhanced term appearing in the curvature spectrum at second order in field fluctuations. With this modification, the relevant coefficient turns out to be proportional to the second derivative of the tree-level spectrum with respect to the inflaton phi at horizon exit. A logarithm with precisely the sa…
We study leading order perturbative corrections to the two point correlation function of the scalar field describing the curvature perturbation in a slow-roll inflationary background, paying particular attention to the contribution of entropy mode loops. We find that the infrared divergences are worse than in pure de Sitter space: they are power law rather than logarithmic. The validity of perturbation theory and thus of the effective field theory of cosmological perturbations leads to stringent constraints on the coupling constants describing the interactions, in our model the quartic self-in…
We examine the NS-NS corrections to the type II supergravity given by Gross and Sloan, under the linear T-duality transformations. We show that the gravity and the B-field couplings are invariant under off-shell T-duality, whereas the dilaton couplings are invariant under on-shell T-duality. Requiring the compatibility of the dilaton couplings with off-shell T-duality as a guiding principle, we extend them to include the appropriate Ricci curvature and the divergence of the B-field strength.
We study the higher-derivative equations for gauge potentials of arbitrary mixed-symmetry type obtained by setting to zero the divergences of the corresponding curvature tensors. We show that they propagate the same reducible multiplets as the Maxwell-like second-order equations for gauge fields subject to constrained gauge transformations. As an additional output of our analysis, we provide a streamlined presentation of the Ricci-like case, where the traces of the same curvature tensors are set to zero, and we present a simple algebraic evaluation of the particle content associated with the L…
Three dimensional abelian gauge theories classically in a Coulomb phase are affected by IR divergences even when the matter fields are all massive. Using generalizations of Ward-Takahashi identities, we show that correlation functions of gauge-invariant operators are IR finite to all orders in perturbation theory. Gauge invariance is sufficient but not necessary for IR finiteness. In particular we show that specific gauge-variant correlators, including the two-point function of matter fields, are also IR finite to all orders in perturbation theory. Possible applications of these results are br…
The Higgs effective potential in the Standard Model (SM), calculated perturbatively, generically suffers from infrared (IR) divergences when the (field-dependent) tree-level mass of the Goldstone bosons goes to zero. Such divergences can affect both the potential and its first derivative and become worse with increasing loop order. In this paper we show that these IR divergences are spurious, we perform a simple resummation of all IR-problematic terms known (up to three loops) and explain how to extend the resummation to cure all such divergences to any order. The method is of general applicab…
We study the effects of including higher-curvature corrections to the Einstein gravity bulk action on the holographic entanglement entropy (HEE) expression for geometries with hyperscaling violation (hvLf). For $θ< 0$ we show that one single new divergence arises for general curvature-squared gravities, which allows us to conjecture the general expression of HEE for any higher-order gravity action. For $0<θ<d$, we assume the hvLf geometry to arise above some intermediate scale $r_F$, becoming AdS in the UV and perform a similar analysis for $R^n$ gravities. For negative values of $θ$ we find t…
Computing renormalized curvature integrals on Poincaré-Einstein manifolds
Penn State University（宾夕法尼亚州立大学）；Rutgers University（罗格斯大学）；Wichita State University（威奇托州立大学）；University of Notre Dame（圣母大学）；Sun Yat-sen University（中山大学）
