Constraints on Hořava–Lifshitz gravity from GRB 170817A

Abstract

In this work we focus on a toy model: ($$3+1$$ 3 + 1 )-dimensional Hořava–Lifshitz gravity coupling with an anisotropic electromagnetic (EM) field which is generated through a Kaluza-Klein reduction of a ($$4+1$$ 4 + 1 )-dimensional Hořava–Lifshitz gravity. This model exhibits a remarkable feature that it has the same velocity for both gravitational and electromagnetic waves. This feature makes it possible to restrict the parameters of the theory from GRB 170817A. In this work we use this feature to discuss possible constraints on the parameter $$\beta $$ β in the theory, by analyzing the possible Lorentz invariance violation effect of the GRB 170817A. This is achieved by analyzing potential time delay of gamma-ray photons in this event. It turns out that it places a stringent constraint on this parameter. In the most ideal case, it gives $$|1-\sqrt{\beta }|<(10^{-19}-10^{-18})$$ | 1 - β | < ( 10 - 19 - 10 - 18 ) .

Extended Hořava Gravity with Physical Ground-State Wavefunction

“…This is because our model recovers the IR action of the BPS model at low energy, as shown in the action (9). The IR behavior of the BPS model is compatible with many current observations, such as binary pulsar [11], gravitational waves [2,13], and binary black hole [15] . However, if λ does not flow to 1 in the IR, General Relativity is not recovered at low energies, and the theory reduces to a LIV gravitational theory, which could be incompatible with current experiments [67].…”

“…It is assumed that the theory will flow to z = 1 in the infrared (IR) region. The Lorentz invariance is violated as z > 1 but it assumes that there is a foliated diffeomorphism invariance with respect to the spatial sector (although the Lorentz invariance has been verified experimentally at sufficiently large scales, it is possible to have a Lorentz invariance violation at high energies (Please see [2] for details). This possibility also has been partially confirmed in some recent experiments, see [3,4] for examples.).…”

Wave zone of the Hořava--Lifshitz gravity coupled to a gauge vector

“…These requirements are necessary, since we expect that the pure anisotropic gravity-gauge vector wave zone exits. Then, both the gravitational TT-modes and the T-modes associated with the gauge sector behave as (53) on a gravitational background like (54). Therefore, from the above statements one directly obtains the following estimates on the gravitational and gauge sectors…”

“…Concerning the experimental challenges, recent detection of gravitational waves [4,5] restricts the coupling parameter α and β (both appearing in the potential in the low energy regime z = 1). Using the data of the GW170817 they find {β ∼ 1, α ∼ 0} [51][52][53], what is more using the data of GRB170817A in a FLRW background in [54] the authors determined that |1 − √ β| < 10 −19 − 10 −18 , thus β ∼ 1. In this regard, the generation of gravitational waves in the Hořava-Lifshitz theory and its properties were analyzed in [55].…”

Quantum aspects of the gravitational-gauge vector coupling in the Hořava-Lifshitz theory at the kinetic conformal point

“…In [9,36,37] they determined restrictions on the low energy coupling constants of the theory, they must be {β ∼ 1, α ∼ 0}, in requirement to the relativistic observational constraints at low energies. Following the theoretical studies developed in [38,39] where it was proved that in the limit at low energies the gravitational and electromagnetic waves propagate at the same speed √ β, in [40] by using the GRB170817A data within a cosmological FLRW background and placing the theory at the KC point the authors showed that in the most ideal case |1 − √ β| < (10 −19 − 10 −18 ), thus β ∼ 1.…”