Higher Curvature Terms Research Articles

Cosmology of linear Higgs-sigma models with conformal invariance

We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the R2 term and the tracker solution for dark energy at late times can be realized for the Rp+1 term with −1 < p < 0. We also discuss the implications of Higgs-sigma interactions for the inflation and the vacuum stability in the Standard Model.

CMB from a Gauss-Bonnet-induced de Sitter fixed point

In the gravitational effective theories including higher curvature terms, cosmological solutions can have nontrivial de Sitter fixed points. We study phenomenological implications of such points, focusing on a theory in which a massive scalar field is nonminimally coupled to the Euler density. We first analyze the phase portrait of the dynamical system and show that the fixed point can be a sink or a saddle, depending on the strength of the coupling. Then, we compute the perturbation spectra generated in the vicinity of the fixed point in order to investigate whether the fixed point may be considered as cosmic inflation. We find parameter regions that are consistent with the cosmological data, given that the anisotropies in the cosmic microwave background are seeded by the fluctuations generated near the fixed point. Future observation may be used to further constrain the coupling function of this model. We also comment briefly on the swampland conjecture.

Effects of short-distance modifications to general relativity in spinning binary systems

We investigate the possibility of testing short distance modifications to General Relativity via higher curvature terms in the fundamental gravity Lagrangian by analysing their impact on observations of spinning astronomical binary systems. By using effective field theory methods applied to the 2-body problem, generic lower bounds on the short-distance scale accompanying high curvature terms can be set. In particular we extend known results by deriving spin-dependent effects in binding energy, radiation emission process, and spin precession equations in binary systems, which are the fundamental ingredients to observe spin-dependent effects in gravitational wave detections from compact binary coalescences and spin precession in double binary pulsars.

Proper time to the black hole singularity from thermal one-point functions

We argue that the proper time from the event horizon to the black hole singularity can be extracted from the thermal expectation values of certain operators outside the horizon. This works for fields which couple to higher-curvature terms, so that they can decay into two gravitons. To extract this proper time, it is necessary to vary the mass of the field.

Nonlinearly ghost-free higher curvature gravity

We find unitary and local theories of higher curvature gravity in the vielbein formalism, known as Poincar\'e gauge theory, by utilizing the equivalence to ghost-free massive bigravity. We especially focus on three and four dimensions, but extensions into a higher-dimensional spacetime are straightforward. In three dimensions, quadratic gravity $\mathcal{L}=R+{T}^{2}+{R}^{2}$, where $R$ is the curvature and $T$ is the torsion with indices omitted, is shown to be equivalent to zwei-dreibein gravity and free from the ghost at fully nonlinear orders. In a special limit, new massive gravity is recovered. When the model is applied to the $\mathrm{AdS}/\mathrm{CFT}$ correspondence, unitarity both in the bulk theory and in the boundary theory implies that the torsion must not vanish. On the other hand, in four dimensions, the absence of a ghost at nonlinear order requires an infinite number of higher curvature terms, and these terms can be given by a schematic form $R(1+R/\ensuremath{\alpha}{m}^{2}{)}^{\ensuremath{-}1}R$, where $m$ is the mass of the massive spin-2 mode originating from the higher curvature terms and $\ensuremath{\alpha}$ is an additional parameter that determines the amplitude of the torsion. We also provide another four-dimensional ghost-free higher curvature theory that contains a massive spin-0 mode as well as a massive spin-2 mode.

Higher derivative scalar-tensor monomials and their classification

We make a full classification of scalar monomials built of the Riemann curvature tensor up to the quadratic order and of the covariant derivatives of the scalar field up to the third order. From the point of view of the effective field theory, the third or even higher order covariant derivatives of the scalar field are of the same importance as the higher curvature terms, and thus should be taken into account. Moreover, the higher curvature terms and the higher order derivatives of the scalar field are complementary to each other, of which novel ghostfree combinations may exist. We make a systematic classification of all the possible monomials, according to the numbers of the Riemann tensor and the higher derivatives of the scalar field in each monomial. A complete basis of monomials at each order is derived, of which the linear combinations may yield novel ghostfree Lagrangians. We also develop diagrammatic representations for the monomials, which may help to simplify the analysis.

Black hole zeroth law in higher curvature gravity

The zeroth law of black hole mechanics is an assertion of constancy of the surface gravity on a stationary Killing horizon. The Hawking temperature of the black hole horizon is proportional to the surface gravity. Therefore, the constancy of the surface gravity is reminiscent of the zeroth law of ordinary thermodynamics. In this work, we provide a proof of the zeroth law in Lanczos-Lovelock theories of gravity, where the Einstein Hilbert action is supplemented by higher curvature terms.

Scalaron tunneling and the fate of antisymmetric tensor fields in F(R) gravity

The work provides a possible explanation of a well motivated question—why the present Universe is practically free from any noticeable footmarks of higher rank antisymmetric tensor fields, despite having the signatures of scalar, vector, fermion as well as symmetric rank 2 tensor field in the form of gravity? The explanation proposed here originates from the higher curvature degrees of freedom present in a F(R) gravity model. In such a model, we show that the scalar degree of freedom (also known as scalaron) associated with the higher curvature term may undergo a quantum tunneling which in turn suppresses the couplings of antisymmetric massless tensor fields with various standard model fields.

General parametrization of higher-dimensional black holes and its application to Einstein-Lovelock theory

Here we have developed the general parametrization for spherically symmetric and asymptotically flat black-hole spacetimes in an arbitrary metric theory of gravity. The parametrization is similar in spirit to the parametrized post-Newtonian (PPN) approximation, but valid in the whole space outside the event horizon, including the near horizon region. This generalizes the continued-fraction expansion method in terms of a compact radial coordinate suggested by Rezzolla and Zhidenko [Phys.Rev.D 90 8, 084009 (2014)] for the four-dimensional case. As the first application of our higher-dimensional parametrization we have approximated black-hole solutions of the Einstein-Lovelock theory in various dimensions. This allows one to write down the black-hole solution which depends on many parameters (coupling constants in front of higher curvature terms) in a very compact analytic form, which depends only upon a few parameters of the parametrization. The approximate metric deviates from the exact (but extremely cumbersome) expressions by fractions of one percent even at the first order of the continued-fraction expansion, which is confirmed here by computation of observable quantities, such as quasinormal modes of the black hole.

Antisymmetric Tensor Fields in Modified Gravity: A Summary

We provide various aspects of second rank antisymmetric Kalb–Ramond (KR) field in modified theories of gravity. The KR field energy density is found to decrease with the expansion of our universe at a faster rate in comparison to radiation and matter components. Thus as the universe evolves and cools down, the contribution of the KR field on the evolutionary process reduces significantly, and at present it almost does not affect the universe evolution. However the KR field has a significant contribution during early universe; in particular, it affects the beginning of inflation as well as increases the amount of primordial gravitational radiation and hence enlarges the value of tensor-to-scalar ratio in respect to the case when the KR field is absent. In regard to the KR field couplings, it turns out that in four dimensional higher curvature inflationary model the couplings of the KR field to other matter fields is given by 1/MPl (where MPl is known as the “reduced Planck mass” defined by MPl=18πG with G is the “Newton’s constant”) i.e., same as the usual gravity–matter coupling; however in the context of higher dimensional higher curvature model the KR couplings get an additional suppression over 1/MPl. Thus in comparison to the four dimensional model, the higher curvature braneworld scenario gives a better explanation of why the present universe carries practically no footprint of the Kalb–Ramond field. The higher curvature term in the higher dimensional gravitational action acts as a suitable stabilizing agent in the dynamical stabilization mechanism of the extra dimensional modulus field from the perspective of effective on-brane theory. Based on the evolution of KR field, one intriguing question can be—“sitting in present day universe, how do we confirm the existence of the Kalb–Ramond field which has considerably low energy density (with respect to the other components) in our present universe but has a significant impact during early universe?” We try to answer this question by the phenomena “cosmological quantum entanglement” which indeed carries the information of early universe. Finally, we briefly discuss some future perspectives of Kalb–Ramond cosmology at the end of the paper.

Softly broken conformal symmetry with higher curvature terms

In a scalar-coupled-gravity model, the quadratically divergent counter term appearing in the mass renormalization of the scalar fields must inherit corrections arising out of gravitational interactions. In this work we have explicitly demonstrated that there are no such corrections of gravitational origin to the quadratic divergences in the mass counter terms. This statement holds true irrespective of the nature of the gravitational interaction, i.e., whether gravity is described by general relativity or f(R) theory. Interestingly, it also turns out that the one loop effective action of scalar-coupled-gravity system will be well-behaved \emph{if and only if} the $f(R)$ theory is free from ghosts. In particular, the results derived in the context of f(R) theory are shown to be in exact agreement with the corresponding results derived from the equivalent scalar-tensor representation. Our analysis suggests the tantalizing possibility that the masses of the scalar fields can be consistently kept smaller than some Ultra Violet (UV) cutoff scale and is independent of the nature of the gravity theory, which may involve higher curvature corrections. All these will be true provided the matter fields and the gravity theory can be embedded consistently into a UV complete theory at the Planck scale.

Parametrized test of parity-violating gravity using GWTC-1 events

Abstract Parity-violating (PV) gravity has recently attracted interest in several aspects. One of them is the axion–graviton coupling to test the axion–dark matter model. Moreover, by extending Chern–Simons (CS) gravity to include derivatives of a scalar field up to the second order, a more general class of PV gravity theory, which we call the CNCL model, has been proposed [M. Crisostomi et al., Phys. Rev. D, 97, 044034 (2018)]. The model can be further extended by including even higher derivatives of the scalar field and/or higher curvature terms. In this paper, we discuss the effect of parity violation in the gravitational sector on the propagation of gravitational waves from binary coalescence by introducing a model-independent parametrization of modification. Our parametrization includes the CNCL model as well as CS gravity. The effect of parity violation on the gravitational waveform is maximum when the source binary orientation to our line of sight is edge-on, while the modified waveform reduces to the parity-symmetric one when the source is face-on. We perform a search for the signature of such modification by using the LIGO/Virgo O1/O2 catalog. We find that the catalog data is consistent with general relativity and obtain constraints on parity violation in gravity for various post-Newtonian order modifications for the first time. The obtained constraint on CS gravity is consistent with the results in previous works. On the other hand, the constraint on the CNCL model that we obtain is tighter than the previous results by roughly 7 orders of magnitude.

Corrections to de Sitter entropy through holography

The holographic entanglement entropy is computed for an entangling surface that coincides with the horizon of a boundary de Sitter metric. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. The entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

Entropy increases at linear order in scalar-hairy Lovelock gravity

In this paper, we investigate the second law of the black holes in Lovelock gravity sourced by a conformally coupled scalar field under the first-order approximation when the perturbation matter fields satisfy the null energy condition. First of all, we show that the Wald entropy of this theory does not obey the linearized second law for the scalar-hairy Lovelock gravity which contains the higher curvature terms even if we replace the gravitational part of Wald entropy with Jacobson-Myers (JM) entropy. This implies that we cannot naively add the scalar field term of the Wald entropy to the JM entropy of the purely Lovelock gravity to get a valid linearized second law. By rescaling the metric, the action of the scalar field can be written as a purely Lovelock action with another metric. Using this property, by analogy with the JM entropy of the purely Lovelock gravity, we introduce a new formula of the entropy in the scalar-hairy Lovelock gravity. Then, we show that this new JM entropy increases along the event horizon for Vaidya-like black hole solutions and therefore it obeys a linearized second law. Moreover, we show that different from the entropy in F (Riemann) gravity, the difference between the JM entropy and Wald entropy also contains some additional corrections from the scalar field.

Strong cosmic censorship conjecture in higher curvature gravity

Deterministic nature of general relativity is ensured by the strong cosmic censorship conjecture, which asserts that spacetime cannot be extended beyond Cauchy horizon with square integrable connection. Although this conjecture holds true for asymptotically flat black hole spacetimes in general relativity, a potential violation of this conjecture occurs in charged asymptotically de Sitter spacetimes. Since it is expected that Einstein-Hilbert action will involve higher curvature corrections, in this article we have studied whether one can restore faith in the strong cosmic censorship when higher curvature corrections to general relativity are considered. Contrary to our expectations, we have explicitly demonstrated that not only a violation to the conjecture occurs near extremality, but the violation appears to become stronger as the strength of the higher curvature term increases.

Higher-curvature corrections to holographic mutual information

In this paper, we study some non-local measurements of quantum correlations in extended gravities with higher-order curvature terms, including conformal gravity. Precisely, we consider higher-curvature correction on holographic mutual information in conformal gravity. There is in fact one deformation in the states because of the higher-curvature corrections. Here by making use of the holographic methods, we study the deformation in the holographic mutual information due to the higher-curvature terms. We also address the change in the quantum phase transition due to these deformations.

On the extremality bound of stringy black holes

A mild version of the weak gravity conjecture (WGC) states that extremal black holes have charge-to-mass ratio larger or equal than one when higher-curvature interactions are taken into account. Since these corrections become more relevant in the low-mass regime, this would allow the decay of extremal black holes in terms of energy and charge conservation. Evidence in this direction has been mainly given in the context of corrections to Einstein-Maxwell theory. Here we compute corrections to the charge-to-mass ratio of some dyonic extremal black holes explicitly embedded in the heterotic string effective theory. We find that modifications of the extremality bound depend on the solution considered, with the charge-to-mass ratio remaining unchanged or deviating positively from one. Additionally, we observe that the introduction of the higher-curvature terms increases the Wald entropy in all cases considered, whose variation does not seem to be correlated with the charge-to-mass ratio, contrary to the situation in Einstein-Maxwell theory.

Does black hole continuum spectrum signal f(R) gravity in higher dimensions?

Extra dimensions, which led to the foundation and inception of string theory, provide an elegant approach to force-unification. With bulk curvature as high as the Planck scale, higher curvature terms, namely f(R) gravity seems to be a natural addendum in the bulk action. These can not only pass the classic tests of general relativity but also serve as potential alternatives to dark matter and dark energy. With interesting implications in inflationary cosmology, gravitational waves and particle phenomenology it is worth exploring the impact of extra dimensions and f(R) gravity in black hole accretion. Various classes of black hole solutions have been derived which bear non-trivial imprints of these ultraviolet corrections to general relativity. This in turn gets engraved in the continuum spectrum emitted by the accretion disk around black holes. Since the near horizon regime of supermassive black holes manifest maximum curvature effects, we compare the theoretical estimates of disk luminosity with quasar optical data to discern the effect of the modified background on the spectrum. In particular, we explore a certain class of black hole solution bearing a striking resemblance with the well-known Reissner Nordstrom de Sitter/anti-de Sitter/flat spacetime which unlike general relativity can also accommodate a negative charge parameter. By computing error estimators like chi-square, Nash-Sutcliffe efficiency, index of agreement, etc. we infer that optical observations of quasars favor a negative charge parameter which can be a possible indicator of extra dimensions. The analysis also supports an asymptotically de Sitter spacetime with an estimate of the magnitude of the cosmological constant whose origin is solely attributed to f(R) gravity in higher dimensions.

Constant potentials in 6D Einstein-Gauss-Bonnet theory

The qualitative physical behavior of six-dimensional perfect fluid spheres is studied in the context of Einstein-Gauss-Bonnet (EGB) gravity theory, and a contrast is drawn with the associated Einstein model. At first we seek an analogue of the defective Einstein universe by setting the temporal potential to be constant. The equation of state $\ensuremath{\rho}+\frac{5}{3}p=$ a constant multiple of the Gauss-Bonnet coupling $\ensuremath{\alpha}$ is obtained, and in the case of vanishing $\ensuremath{\alpha}$ the six-dimensional Einstein universe is recovered. More significantly the case of a constant spatial potential generated an exact solution in terms of hypergeometric functions. No solution in terms of elementary functions was located; however it was still possible to construct a compact star with finite radius for a specific choice of potential and suitable parameter values obtained by fine-tuning. It emerged that the EGB model was singularity free and displayed a number of pleasing physical features which were extrapolated from the usual restrictions placed on Einstein spheres. It was found that the EGB higher curvature terms allowed for the existence of stellar radius some 20 times larger than its Einstein counterpart. Moreover, the Einstein model suffered the permanent defect of a central singularity. In many respects the Gauss-Bonnet offered corrections to the corresponding Einstein model.

Review of inflationary cosmology via quantum corrections in M-theory

In this paper, we review inflationary cosmology in M-theory with quantum corrections. In old days the inflation was proposed as a resolution to the cosmological problems, and nowadays models of the inflation are severely restricted by the observations. Among them, the predictions of the Starobinsky model, which contains scalar curvature squared term, is consistent with the observations. The higher curvature terms will come from quantum effect of the gravity, and it is natural to ask its origin in superstring theory or M-theory. We investigate inflationary solution in the M-theory with higher curvature terms. We show that higher curvature terms induce an exponentially expanding solution in the early universe, and the inflation naturally ends when the corrections are suppressed. We also discuss that the ambiguity of the higher curvature terms do not affect the inflationary scenario in the M-theory.