The nature of singularity in multidimensional anisotropic Gauss–Bonnet cosmology with a perfect fluid

Abstract

We investigate dynamics of (4 + 1) and (5 + 1) dimensional flat anisotropic Universe filled with a perfect fluid in the Gauss-Bonnet gravity. An analytical solutions valid for particular values of the equation of state parameter w = 1/3 have been found. For other values of w structure of cosmological singularity have been studied numerically. We found that for w > 1/3 the singularity is isotropic. Several important differences between (4 + 1) and (5 + 1) dimensional cases are discussed.

Exact exponential solutions in Einstein–Gauss–Bonnet flat anisotropic cosmology

“…Mainly because of this, since 1980s the studies of the modified multidimensional cosmology were quite intense (see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). …”

Cosmological dynamics of spatially flat Einstein–Gauss–Bonnet models in various dimensions: high-dimensional $$\Lambda $$ Λ -term case

“…This kind of singularity is "weak" by Tipler's classification [69], and "type II" in the classification by Kitaura and Wheeler [70,71]. Recent studies of the singularities of this kind in the cosmological context in Lovelock and Einstein-Gauss-Bonnet gravity demonstrate [27,49,50,52,54] that their presence is not suppressed and they are abundant for a wide range of initial conditions and parameters and sometimes [50] they are the only option for future behavior.…”

“…Exact solutions with exponents for both the (3+1)-and extra-dimensional scale factors were studied for the first time in [47], where an exponentially increasing (3+1)-dimensional scale factor and an exponentially shrinking extra-dimensional scale factor were described. Power-law solutions have been analyzed in [18,48] and more recently in [20,[49][50][51][52], so that by now there is an almost complete description of the solutions of this kind (see also [53] for comments regarding physical branches of the power-law solutions). Solutions with exponential scale factors [54] have also been studied in detail, namely, the models with both variable [55] and constant [56] volume; the general scheme for constructing solutions in EGB was developed and generalized for general Lovelock gravity of any order and in any dimensions [57].…”

On stability of exponential cosmological solutions with non-static volume factor in the Einstein–Gauss–Bonnet model

“…The appearance of the Gauss-Bonnet term was motivated by string theory [1][2][3]. At present, the so-called Einstein-Gauss-Bonnet (EGB) gravitational model which is governed by the action (1.1) a e-mail: ivashchuk@mail.ru and its modifications are intensively used in cosmology; see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and references therein, e.g. for explanation of accelerating expansion of the Universe following from supernovae (type Ia) observational data [24][25][26].…”