Quantum Gravitational Corrections Research Articles

A high quality composite axion

The strong CP problem is a compelling motivation for physics beyond the Standard Model. The most popular solutions invoke a global U(1)PQ symmetry, but are challenged by quantum gravitational corrections which are thought to be incompatible with global symmetries, arguing that realistic theories contain additional structure. We explore a construction in which the U(1)PQ symmetry is protected to arbitrary order by virtue of a supersymmetric, confining SU(N)L × SU(N) × SU(N)R × U(1)X product gauge group, achieving left|overline{uptheta}right| < 10−11 for an SU(5) model with fa ≲ 3 × 1011 GeV. This construction leads to low energy predictions such as a U(1)X gauge symmetry, and for X = B − L engineers a naturally mathcal{O} (TeV) value for the μ parameter of the MSSM.

Vanishing of quantum gravitational corrections to vacuum solutions of general relativity at second order in curvature

In this note we prove that quantum gravitational corrections to vacuum solutions of Einstein's equations vanish at second order in curvature.

Gravitational radiation in quantum gravity

The effective field theory of quantum gravity generically predicts non-locality to be present in the effective action, which results from the low-energy propagation of gravitons and massless matter. Working to second order in gravitational curvature, we reconsider the effects of quantum gravity on the gravitational radiation emitted from a binary system. In particular, we calculate for the first time the leading order quantum gravitational correction to the classical quadrupole radiation formula which appears at second order in Newton’s constant.

Generalized uncertainty principle, black holes, and white dwarfs: a tale of two infinities

It is often argued that quantum gravitational correction to the Heisenberg's uncertainty principle leads to, among other things, a black hole remnant with finite temperature. However, such a generalized uncertainty principle also seemingly removes the Chandrasekhar limit, i.e., it permits white dwarfs to be arbitrarily large, which is at odds with astrophysical observations. We show that this problem can be resolved if the parameter in the generalized uncertainty principle is negative. We also discuss the Planck scale physics of such a model.

Quantum gravitational corrections from the Wheeler–DeWitt equation for scalar–tensor theories

We perform the canonical quantization of a general scalar–tensor theory and derive the first quantum gravitational corrections following from a semiclassical expansion of the Wheeler–DeWitt equation. The non-minimal coupling of the scalar field to gravity induces a derivative coupling between the scalar field and the gravitational degrees of freedom, which prevents a direct application of the expansion scheme. We address this technical difficulty by transforming the theory from the Jordan frame to the Einstein frame. We find that a large non-minimal coupling can have strong effects on the quantum gravitational correction terms. We briefly discuss these effects in the context of the specific model of Higgs inflation.

Bouncing and emergent cosmologies from Arnowitt–Deser–Misner RG flows

Asymptotically safe gravity provides a framework for the description of gravity from the trans-Planckian regime to cosmological scales. According to this scenario, the cosmological constant and Newton’s coupling are functions of the energy scale whose evolution is dictated by the renormalization group (RG) equations. The formulation of the RG equations on foliated spacetimes, based on the Arnowitt–Deser–Misner (ADM) formalism, furnishes a natural way to construct the RG energy scale from the spectrum of the Laplacian operator on the spatial slices. Combining this idea with an RG improvement procedure, in this work we study quantum gravitational corrections to the Einstein–Hilbert action on Friedmann–Lemaître–Robertson–Walker backgrounds. The resulting quantum-corrected Friedmann equations can give rise to both bouncing cosmologies and emergent Universe solutions. Our bouncing models do not require the presence of exotic matter and emergent Universe solutions can be constructed for any allowed topology of the spatial slices.

Gauge-invariant quantum gravitational corrections to correlation functions

A recent proposal for gauge-invariant observables in inflation (Brunetti et al 2016 J. High Energy Phys. JHEP08(2016)032) is examined. We give a generalisation of their construction to general background spacetimes. In flat space, we calculate one-loop graviton corrections to a scalar two-point function in a general gauge for the graviton. We explicitely show how the gauge-dependent terms cancel between the usual self-energy contributions and the additional corrections inherent in these observables. The one-loop corrections have the expected functional form, contrary to another recently studied proposal for gauge-invariant observables (Fröb 2018 Class. Quantum Grav. 35 035005) where this is not the case. Furthermore, we determine the one-loop graviton corrections to the four-point coupling of the gauge-invariant scalar field, and the corresponding running of the coupling constant induced by graviton loops. Interestingly, the β function is negative for all values of the non-minimal coupling of the scalar field to curvature.

One-loop quantum gravitational corrections to the scalar two-point function at fixed geodesic distance

We study a proposal for gauge-invariant correlation functions in perturbative quantum gravity, which are obtained by fixing the geodesic distance between points in the fluctuating geometry. These correlation functions are non-local and strongly divergent, and we show how to renormalise them by performing a ‘wave function renormalisation’ of the geodesic embedding coordinates. The result is finite and gauge-independent, but displays unusual features such as double logarithms at one-loop order.

Deducing cosmological observables from the S matrix

We study one loop quantum gravitational corrections to the long range force induced by the exchange of a massless scalar between two massive scalars. The various diagrams contributing to the flat space S-matrix are evaluated in a general covariant gauge and we show that dependence on the gauge parameters cancels at a point considerably {\it before} forming the full S-matrix, which is unobservable in cosmology. It is possible to interpret our computation as a solution to the effective field equations --- which could be done even in cosmology --- but taking account of quantum gravitational corrections from the source and from the observer.

Planck-Scale Corrections to the Cardy–Verlinde Formula in SAdS Black Hole

Possible corrections to the thermodynamic quantities of a 4D Schwarzschild–anti–de Sitter (SAdS) black hole are investigated by considering the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) separately. The quantum gravitational corrections to the Hawking temperature, energy and entropy of the black hole are calculated based on both the GUP and the MDR analysis. The explicit form of the corrections is worked out up to the sixth power of the Planck length. The quantum-corrected thermodynamic quantities due to GUP and MDR are used separately to obtain the quantum-gravitational corrections to the Cardy–Verlinde (C–V) formula. It is found that the C–V formula receives some new corrections in either of approaches. Through comparison of the corrections obtained from GUP and MDR approaches, it is shown that the results of these two alternative approaches should be identical if one uses the suitable expansion coefficients. Finally, the renormalized form of the C–V formula is introduced by redefining the Virasoro operator and the central charge within both the GUP and the MDR.

Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The slow-roll approximation

We continue our study on corrections from canonical quantum gravity to the power spectra of gauge-invariant inflationary scalar and tensor perturbations. A direct canonical quantization of a perturbed inflationary universe model is implemented, which leads to a Wheeler-DeWitt equation. For this equation, a semiclassical approximation is applied in order to obtain a Schroedinger equation with quantum-gravitational correction terms, from which we calculate the corrections to the power spectra. We go beyond the de Sitter case discussed earlier and analyze our model in the first slow-roll approximation, considering terms linear in the slow-roll parameters. We find that the dominant correction term from the de Sitter case, which leads to an enhancement of power on the largest scales, gets modified by terms proportional to the slow-roll parameters. A correction to the tensor-to-scalar ratio is also found at second order in the slow-roll parameters. Making use of the available experimental data, the magnitude of these quantum-gravitational corrections is estimated. Finally, the effects for the temperature anisotropies in the cosmic microwave background are qualitatively obtained.

Quantum cosmology and the evolution of inflationary spectra

We illustrate how it is possible to calculate the quantum gravitational effects on the spectra of primordial scalar/tensor perturbations starting from the canonical, Wheeler-De Witt, approach to quantum cosmology. The composite matter-gravity system is analysed through a Born-Oppenheimer approach in which gravitation is associated with the heavy degrees of freedom and matter (here represented by a scalar field) with the light ones. Once the independent degrees of freedom are identified the system is canonically quantised. The differential equation governing the dynamics of the primordial spectra with its quantum-gravitational corrections is then obtained and is applied to diverse inflationary evolutions. Finally, the analytical results are compared to observations through a Monte Carlo Markov Chain technique and an estimate of the free parameters of our approach is finally presented and the results obtained are compared with previous ones.

Erratum to: Quantum gravitational corrections for spinning particles

Erratum to: Quantum gravitational corrections for spinning particles

Corrections to the Cardy-Verlinde formula at the Planck scale

The possible corrections to the thermodynamic quantities of higher dimensional Schwa-rzschild black hole have been investigated by considering the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) separately. The quantum gravitational corrections to the Hawking temperature, energy and entropy of the black hole have been calculated based on both the GUP and the MDR analysis. The explicit form of the corrections are worked out up to the sixth power of the Planck length. The impacts of GUP and MDR have been used separately to obtain the quantum gravitational corrections to the Cardy-Verlinde (C-V) formula. It has been shown that the usual C-V entropy formula receives some new corrections. Also the renormalized form of the C-V formula has been introduced by redefining Virasoro operator and central charge within both the GUP and the MDR. Through comparison of the corrections obtained from GUP and MDR approaches it has been found that the results of these two alternative approaches should be identical if one uses the suitable expansion coefficients.

Gravitational Waves in Effective Quantum Gravity

In this short paper we investigate quantum gravitational effects on Einstein's equations using effective field theory techniques. We consider the leading order quantum gravitational correction to the wave equation. Besides the usual massless mode, we find a pair of modes with complex masses. These massive particles have a width and could thus lead to a damping of gravitational waves if excited in violent astrophysical processes producing gravitational waves such as e.g. black hole mergers. We discuss the consequences for gravitational wave events such as GW 150914 recently observed by the Advanced LIGO collaboration.

High-order primordial perturbations with quantum gravitational effects

In this paper, we provide a systematic investigation of high-order primordial perturbations with nonlinear dispersion relations due to quantum gravitational effects in the framework of {\em uniform asymptotic approximations}. Because of these effects, the equation of motion of the mode function in general has multiple-turning points. After obtaining analytically approximated solutions to any order in different regions, associated with different types of turning points, we match them to the third one. To this order the errors are less than $0.15\%$. General expressions of the power spectra of the primordial tensor and scalar perturbations are derived explicitly. We also investigate effects of back-reactions of the quantum gravitational corrections, and make sure that inflation lasts long enough in order to solve the underlying problems, such as flatness, horizon and monopole. Then, we study various features of the spectra that are observationally relevant. In particular, under a moderate assumption about the energy scale of the underlying theory of quantum gravity, we have shown that the quantum gravitational effects may alter significantly the ratio between the tensor and scalar power spectra, thereby providing a natural mechanism to alleviate the tension between observations and certain inflationary models, including the one with a quadratic potential.

Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The de Sitter case

We present detailed calculations for quantum-gravitational corrections to the power spectra of gauge-invariant scalar and tensor perturbations during inflation. This is done by performing a semiclassical Born-Oppenheimer type of approximation to the Wheeler-DeWitt equation, from which we obtain a Schroedinger equation with quantum-gravitational correction terms. As a first step, we perform our calculation for a de Sitter universe and find that the correction terms lead to an enhancement of power on the largest scales.

Inflation with the Starobinsky potential in loop quantum cosmology

A self-consistent pre-inflationary extension of the inflationary scenario with the Starobinsky potential, favored by Planck data, is studied using techniques from loop quantum cosmology (LQC). The results are compared with the quadratic potential previously studied. Planck scale completion of the inflationary paradigm and observable signatures of LQC are found to be robust under the change of the inflaton potential. The entire evolution, from the quantum bounce all the way to the end of inflation, is compatible with observations. Occurrence of desired slow-roll phase is almost inevitable and natural initial conditions exist for both the background and perturbations for which the resulting power spectrum agrees with recent observations. There exist initial data for which the quantum gravitational corrections to the power spectrum are potentially observable.

Inflationary spectra with inverse-volume corrections in loop quantum cosmology and their observational constraints from Planck 2015 data

We first derive the primordial power spectra, spectral indices and runnings of both scalar and tensor perturbations of a flat inflationary universe to the second-order approximations of the slow-roll parameters, in the framework of loop quantum cosmology with the inverse-volume quantum corrections. This represents an extension of our previous work in which the parameter σ was assumed to be an integer, where σ characterizes the quantum corrections and in general can take any of values from the range σ ∊ (0, 6]. Restricting to the first-order approximations of the slow-roll parameters, we find corrections to the results obtained previously in the literature, and point out the causes for such errors. To our best knowledge, these represent the most accurate calculations of scalar and tensor perturbations given so far in the literature. Then, fitting the perturbations to the recently released data by Planck (2015), we obtain the most severe constraints for various values of σ. Using these constraints as our referring point, we discuss whether these quantum gravitational corrections can lead to measurable signatures in the future cosmological observations. We show that, depending on the value of σ, the scale-dependent contributions to the relativistic inflationary spectra due to the inverse-volume corrections could be well within the range of the detectability of the forthcoming generations of experiments, such as the Stage IV experiments.

Higgs inflation and quantum gravity: an exact renormalisation group approach

We use the Wilsonian functional Renormalisation Group (RG) to study quantum corrections for the Higgs inflationary action including the effect of gravitons, and analyse the leading-order quantum gravitational corrections to the Higgs' quartic coupling, as well as its non-minimal coupling to gravity and Newton's constant, at the inflationary regime and beyond. We explain how within this framework the effect of Higgs and graviton loops can be sufficiently suppressed during inflation, and we also place a bound on the corresponding value of the infrared RG cut-off scale during inflation. Finally, we briefly discuss the potential embedding of the model within the scenario of Asymptotic Safety, while all main equations are explicitly presented.