The Gao-Wald theorem says that the Penrose diagram of de Sitter spacetime reacts to a positive energy perturbation by getting “taller”. How does this change in the presence of timelike boundaries? We study this question in two-dimensional de Sitter JT gravity coupled to conformal matter. The effect of the boundaries has its roots in quantum corrections to the vacuum energy of the CFT due to Casimir-like effects. We consider two different kinds of timelike boundaries, and for each kind we compute the vacuum expectation value of the matter CFT stress tensor. The stress tensor violates the null energy condition in the first case and saturates it in the second case, with each case exhibiting a negative energy density in the vacuum state. We then compute the semiclassical backreaction of this energy density and show how it can make the spacetime “fatter” or “taller” or a combination of both, depending on the regime. The spacetime getting fatter corresponds to an increase in the value of the dilaton at the horizon and hence also in the static patch horizon area in the higher-dimensional solution. We comment on the implications of our results for the quantum theories living on the timelike boundaries.

United States

Gauri Batra

Timelike boundaries in de Sitter JT gravity and the Gao-Wald theorem

We investigate the parity-violating scalar-tensor theory and pay special attention to terms that are free of the Ostrogradsky ghost in the unitary gauge, i.e., when the scalar field possesses a timelike gradient. We exhaustively identify the generally covariant scalar-tensor theory (GST) monomials with parity violation up to <math><mi>d</mi><mo>=</mo><mn>4</mn></math>, where <math><mi>d</mi></math> is the total number of derivatives in the unitary gauge. According to the correspondence between GST terms and the spatially covariant gravity (SCG) terms in the unitary gauge, we also exhaustively identify the SCG monomials with parity violation up to <math><mi>d</mi><mo>=</mo><mn>4</mn></math>, where the Lie derivatives of the extrinsic curvature and the lapse function are necessarily introduced. We find a total of nine independent parity-violating SCG monomials, of which seven contain no higher-order Lie derivatives and are thus automatically free of ghosts, while two involve Lie derivatives of the extrinsic curvature and the lapse function and are thus potentially dangerous. By explicitly deriving their generally covariant correspondence, we obtain seven independent scalar-tensor terms dubbed the “Qi-Xiu” Lagrangians, which are the most general parity-violating scalar-tensor theories that are ghost-free in the unitary gauge up to <math><mi>d</mi><mo>=</mo><mn>4</mn></math>. Our results include the existing theories in the literature, such as the Chern-Simons term and the chiral scalar-tensor theories, as special cases.

China

Yu-Min Hu

Xian Gao

Parity-violating scalar-tensor theory

We study the scalar induced gravitational waves (SIGWs) from a chiral scalar–tensor theory of gravity. The parity-violating (PV) Lagrangian contains the Chern–Simons (CS) term and PV scalar–tensor terms, which are built of the quadratic Riemann tensor term and first-order derivatives of a scalar field. We consider SIGWs in two cases, in which the semi-analytic expression to calculate SIGWs can be obtained. Then, we calculate the fractional energy density of SIGWs with a monochromatic power spectrum for the curvature perturbation. We find that the SIGWs in chiral scalar–tensor gravity behave differently from those in GR before and after the peak frequency, which results in a large degree of circular polarization.

Jia-Xi Feng

Fengge Zhang

Scalar induced gravitational waves in chiral scalar–tensor theory of gravity

Scalar fields play an important role in constructing modified gravity theories. In the case of a single scalar field with timelike gradient, the corresponding Lagrangian in the unitary gauge takes the form of spatially covariant gravity (SCG), which is proved useful in analyzing and extending the generally covariant theories. In this work, we apply the SCG method to the scalar-nonmetricity theory, of which the Lagrangian is built of the nonmetricity tensor and a scalar field. We derive the 3+1 decomposition of the geometric quantities and especially covariant derivatives of the scalar field up to the third order in the presence of a nonvanishing nonmetricity tensor. By fixing the unitary gauge, the resulting Lagrangian takes the form of a SCG with nonmetricity, in which all the ingredients are spatial tensors. We then exhaust the scalar monomials of SCG with nonmetricity up to  $$d=3$$  <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>3</mn> </mrow> </math>   with d the total number of derivatives. Since the disformation tensor plays as an auxiliary variable, we take the Lagrangian with  $$d=2$$  <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>2</mn> </mrow> </math>   as an example to show that after solving the disformation tensor, we can get an effective SCG theory for the metric variables but with modified coefficients. Our results provides a novel approach to extending the scalar-nonmetricity theory.

Yang Yu

Zheng Chen

Spatially covariant gravity with nonmetricity

We investigate the scalar perturbations in a class of spatially covariant gravity theory with a dynamical lapse function. Generally, there are two scalar degrees of freedom due to the presence of the velocity of the lapse function. We treat the scalar perturbations as analogues of those in a two-field inflationary mode, in which one is light mode and the other is the heavy mode. This is justified by the fact that the scalar mode due to the dynamical lapse function becomes infinitely heavy in the limit when the lapse function reduces to be an auxiliary variable. The standard approaches of multiple filed perturbations can be applied to deal with our model. By integrating out the heavy mode and derive the effective theory for the single light field, we find the solution to the single mode in the form of plane waves. Then we calculate the corrections to the power spectrum of the light mode from the heavy mode, by making use of the standard perturbative method of field theory. At last, when the two fields are not weakly coupled, we find a power law mode for the coupled system in large scales.

Xue-Zheng Zhu

Cosmological perturbations in the spatially covariant gravity with a dynamical lapse function

We investigate primordial perturbations and non-gaussianities in the Hořava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Hořava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are " slow-roll suppressed” in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral-type non-gaussianity is of the order of unity, while the local-type non-gaussianity remains small, as in the usual single-field slow-roll inflation model in general relativity. Our result is a new constraint on Hořava-Lifshitz gravity.

Primordial perturbations and non-gaussianities in Hořava-Lifshitz gravity Partly supported by the Chinese National Youth Thou-sand Talents Program (71000-41180003)

In the context of massive (bi-)gravity, non-minimal matter couplings have been proposed. These couplings are special in the sense that they are free of the Boulware-Deser ghost below the strong coupling scale and can be used consistently as an effective field theory. Furthermore, they enrich the phenomenology of massive gravity. We consider these couplings in the framework of bimetric gravity and study the cosmological implications for background and linear tensor, vector, and scalar Previous works have investigated special branches of solutions. Here we perform a complete perturbation analysis for the general background equations of motion, completing previous analyses.

Japan

Switzerland

Lavinia Heisenberg

Doubly coupled matter fields in massive bigravitySupported by the Chinese National Youth Thousand Talents Program (71000-41180003), JSPS Grant-in-Aid for Scientific Research (15H02082, 25287054, 26610062), L. H. Acknowledges Financial Support from Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation

In this work we study the cosmological perturbations in massive bigravity in the presence of non-minimal derivative couplings. For this purpose we consider a specific subclass of Horndeski scalar-tensor interactions that live on the unique composite effective metric. For the viability of the model both metrics have to be dynamical. Nevertheless, the number of allowed kinetic terms is crucial. We adapt to the restriction of having one single kinetic term. After deriving the full set of equations of motion for flat Friedmann-Lemaitre-Robertson-Walker background, we study linear perturbations on top of it. We show explicitly that only four tensor, two vector and two scalar degrees of freedom propagate, one of which being the Horndeski scalar, while the Boulware-Deser ghost can be integrated out.

Derivative couplings in massive bigravity

We investigate the consequences of general curved trajectories in multi-field inflation. After setting up a completely general formalism using the mass basis, which naturally accommodates the notion of light and heavy modes, we study in detail the simple case of two successive turns in two-field system. We find the power spectrum of the curvature perturbation receives corrections that exhibit oscillatory features sinusoidal in the logarithm of the comoving wavenumber without slow-roll suppression. We show that this is because of the resonance of the heavy modes inside and outside the mass horizon.

South Korea

Jinn-Ouk Gong

Towards general patterns of features in multi-field inflation

None Supervisory Editors of Nuclear Physics B

Editorial note on “Lepton-flavor violation and (g−2)μ in the μν SSM” by Hai-Bin Zhang, Tai-Fu Feng, Shu-Min Zhao and Tie-Jun Gao [Nucl. Phys. B 873 (2) (2013) 300–324]