Quintessential perturbations during scaling regime

Abstract

The scalar field with an exponential potential allows a scaling solution where the the density of the field follows the density of the dominating fluid. Such a scaling regime is often used as an important ingredient in many models of quintessence. We analyse evolution of perturbations while the background follows the scaling. As the results, the perturbed scalar field also scales with the perturbed fluid, and the perturbations accompany the adiabatic as well as the isocurvature mode between the fluid and the field.PACS numbers: 98.80. Hw, Recent observational advances in high redshift supernovae, and the small angular-scale CMBR temperature anisotropy had spurred renewed interest in the possible acceleration of the present day universe. The cosmological constant would be the first available and historically well studied explanation for such an unexpected state of the present universe. In order to make the universe to start accelerating only in the latest moment in logarithmic time interval we need high level of fine tuning of the amount of the cosmological constant. In a way to avoid such a fine tuning a new paradigm of simulating the late acceleration based on a minimally coupled scalar field has been proposed, with such a field termed a quintessence. Although the prime motivation of reducing the fine tuning problem has not been quite successful, we notice a variety of roles the field with different potential could achieve diverse evolutions of the world model [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].It has been known that an exponential potential supports a scaling attractor regime where the density of the field follows the density of the dominating fluid in the background [1][2][3][4]. Although the scaling by itself cannot explain the acceleration in the present epoch, since the scaling works as an attractor we find many implementation of quintessence idea having such an attractor in the early evolution stage. The evolution of perturbation during the scaling regime as well as the following quintessential development has been actively studied in recent literature [3,5,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].In this paper we study the evolution of perturbations in a fluid-field system with an exponential field potential. We will show that the conventional growing and decaying solutions of the fluid without the field remain valid with two additional decaying solutions due to the coupling, eqs. (7,13,16). The perturbed scalar field also scales the perturbed density field of the fluid, eqs. (8,14,17). As a result we show that while the background evolution follows the scaling solution the perturbations accompany both the adiabatic and the isocurvature modes, eqs. (9,15,18). In order to make the paper self contained, and for future convenient usage, the notations and basic set of equations are summarized in the Appendix. Perturbed equations:The pressureless matter (c) or the radiation (r) dominated eras in three component system (r, c and a scalar field φ) can be hand...

Cosmological perturbations with multiple fluids and fields

“…Assuming the gauge degrees of freedom are properly fixed, for the n component medium with fluids or fields in Einstein gravity we anticipate a set of n coupled second-order differential equations for the scalar-type perturbation, a set of n (in general) coupled first-order differential equations for the vector-type perturbation, and one second-order differential equation for the tensor-type perturbation. The situations of the vector-and tensor-type perturbations are rather trivial to handle, and, in fact, the situation is similar even in some classes of generalized versions of gravity theories [1,2]. However, the scalar-type perturbation in such a multi-component system is naturally more complicated, and often requires numerical methods.…”

“…The rotational perturbation of the individual fluid is described by the angular-momentum conservation where the vector-type anisotropic stress and the mutual interaction terms among fluids can work as the source or sink of the rotation of individual component. The most general situations of vector-and tensor-type perturbations are presented in [1,2]. In the following we will consider the scalar-type perturbation only.…”

“…We present a complete set of equations describing the scalar-type perturbation without fixing the temporal gauge condition, i.e., in a gauge-ready form [8,1,2]:…”

“…Although, we intentionally have kept the presentation formal, many new results are presented together with the known ones; see §6 for a summary. Previous studies of perturbations in the multi-component fluid system in a similar spirit can be found in [4,5,6,7,1,2]. We start by introducing our notations, fundamental equations, and strategy in §2.…”

Unified dark fluid with constant adiabatic sound speed: Including entropic perturbations

“…For the gauge ready formalism about the perturbation theory, please see [20]. For a pure barotropic fluid, it has an imaginary adiabatic sound speed which causes instability of the perturbations when its EoS is negative, for example the w = constant quintessence dark energy model.…”