Thick braneworld model in nonmetricity formulation of general relativity and its stability

Abstract

In this paper, we study the thick brane system in the so-called f(Q) gravity, where the gravitational interaction was encoded by the nonmetricity Q like scalar curvature R in general relativity. With a special choice of $$f(Q)=Q-b Q^n$$ f ( Q ) = Q - b Q n , we find that the thick brane system can be solved analytically with the first-order formalism, where the complicated second-order differential equation is transformed to several first-order differential equations. Moreover, the stability of the thick brane system under tensor perturbation is also investigated. It is shown that the tachyonic states are absent and the graviton zero mode can be localized on the brane. Thus, the four-dimensional Newtonian potential can be recovered at low energy. Besides, the corrections of the massive graviton Kaluza–Klein modes to the Newtonian potential are also analyzed briefly.

Braneworlds in $f(Q)$ gravity

“…It is worth noting that in the particular case in which we recover GR, when c 1 = −c 3 = −1/4, c 2 = −c 5 = 1/2, c 4 = 0, the above equations coincide with those obtained in 1 Ref. [48]. Moreover, it is easy to see that there are only two free effective parameters in those equations, namely σ 0 = c 5 + 2c 3 and σ 1 ≡ c 1 + 4c 3 , whose values in the STEGR case are just σ GR 0 = 0 and σ GR 1 = 3/4.…”

“…Note that the modified gravitational dynamics also influences the scalar field profile and the potential properties. Similar BPS equations were found in teleparallel f (T ) [43][44][45], f (T, B) [46] and f (Q) [48].…”

“…We also mention that our analysis here departs from that of Ref [48]. regarding scalar fields in that we also consider effects due to a generalized superpotential(7).…”

“…Recently, an STEGR f (Q) braneworld has been proposed in Ref. [48], studying thick brane solutions and the propagation of gravitons in the extra dimension.…”

Late-time cosmology with phantom dark-energy in $f(Q)$ gravity

“…This recent class of modification of f (Q) gravity, has attracted a lot of interest in the literature. From its application to cosmology and astrophysics [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], to interesting cosmological phenomenology at the background level [39,44,48,50,[53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. Additionally, it can fit observations in a very satisfactory way, through its confrontation with various background and perturbation observational data [36,42,45,49,[73]…”