Holographic complexity growth in an FLRW universe

Abstract

In this paper, taking the large R limit and using the complexity-volume duality, we investigate the holographic complexity growth rate of a field state defined on the universe located at an asymptotical AdS boundary in Gauss-Bonnet gravity and massive gravity, respectively. For the Gauss-Bonnet gravity case, its growth behavior of the state mainly presents three kinds of contributions: one, as a finite term viewed as an interaction term, comes from a conserved charge, the second one is from the spatial volume of the universe and the third one relates the curvature of the horizon in the AdS Gauss-Bonnet black hole, where the Gauss-Bonnet effect plays a vital role on such growth rate. For massive gravity case, except the first divergent term still obeying the growth rate of the spatial volume of the Universe, its results reveal the more interesting novel phenomenons: beside the conserved charge E, the graviton mass term also provides its effect to the finite term ; and the third divergent term is determined by the spatial curvature of its horizon k and graviton mass effect; furthermore, the graviton mass effect can be completely responsible for the second divergent term as a new additional term saturating an area law. * Electronic address: wjpan˙zhgkxy@163.com

Quantum extremal islands made easy. Part III. Complexity on the brane

“…where G N is the Newton's constant of bulk gravity theory and is some undetermined length scale. Various aspects of the CV proposal have been studied on the gravitational side of the duality, e.g., see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. The above conjecture assumes that the state in question is a pure state defined on a global time slice, i.e., the time slice S spans the entire asymptotic boundary.…”

“…Both the holographic CV proposal (1.1) and our proposed generalization (1.6) involve an undetermined length scale . In most previous studies, e.g., [9][10][11][12][13][14][15][16][17][18][19][20][21][22], 19 this length scale is simply chosen to be the AdS curvature scale. However, our analysis was simplified by leaving undetermined, and in particular, we found a simple relation (2.31) between the scales associated with the holographic complexity in the bulk and on the brane.…”

Revisit on holographic complexity in two-dimensional gravity

“…Although there have been extensive studies on CV and CA conjectures from the bulk side (see, e.g. charged black holes [16,17], UV divergences [18][19][20][21], subregion complexity [20,22,23], time-evolution [24,25], higher derivative gravities [16,26,27], Einstein-Maxwell-dilaton gravities [17,[28][29][30], Vaidya spacetimes [31,32], switchback effect and quenches [33,34], and dS/FLRW boundaries [35,36]), the difficulty to establish a convincing holographic complexity lies in the lack of unique and well-defined notion for the complexity in the field theory from the boundary side . Note that the Lloyd bound [65] on complexity growth rate was initially founded in quantum mechanical system, it makes the two-dimensional (2D) gravity [66][67][68] be a special case to understand holographic complexity since the boundary theory could be a (super)conformal quantum mechanics (CQM) [69].…”

Brane universe and holography in the spacetime of a charged AdS dilaton black hole

“…note that the extra minus sign in (32) and (34) are originated from the derivative of implicit functions Q(b, r + ) = Q 0 , S(b, r + ) = S 0 . After some tedious but straightforward caculations, it's easy to check that…”

“…Besides, [31] constructs a holographic reheating model by considering the movement of a probe brane in AdS-Vaidya spacetime, and the formation process of AdS black hole dual to the thermalization process of brane universe. Recently, through constructing a model of moving brane in AdS-Schwarzchild black hole, the holographic complexity growth in a FLRW universe is considered by [32].…”