skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Anisotropic k-essence cosmologies

Abstract

We investigate a Bianchi type-I cosmology with k-essence and find the set of models which dissipate the initial anisotropy. There are cosmological models with extended tachyon fields and k-essence having a constant barotropic index. We obtain the conditions leading to a regular bounce of the average geometry and the residual anisotropy on the bounce. For constant potential, we develop purely kinetic k-essence models which are dust dominated in their early stages, dissipate the initial anisotropy, and end in a stable de Sitter accelerated expansion scenario. We show that linear k-field and polynomial kinetic function models evolve asymptotically to Friedmann-Robertson-Walker cosmologies. The linear case is compatible with an asymptotic potential interpolating between V{sub l}{proportional_to}{phi}{sup -{gamma}{sub l}}, in the shear dominated regime, and V{sub l}{proportional_to}{phi}{sup -2} at late time. In the polynomial case, the general solution contains cosmological models with an oscillatory average geometry. For linear k-essence, we find the general solution in the Bianchi type-I cosmology when the k field is driven by an inverse square potential. This model shares the same geometry as a quintessence field driven by an exponential potential.

Authors:
;  [1]
  1. Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)
Publication Date:
OSTI Identifier:
20782606
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.063502; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; COSMOLOGICAL MODELS; COSMOLOGY; DE SITTER GROUP; DUSTS; GEOMETRY; MATHEMATICAL SOLUTIONS; NONLUMINOUS MATTER; POLYNOMIALS; POTENTIALS; SHEAR

Citation Formats

Chimento, Luis P., and Forte, Monica. Anisotropic k-essence cosmologies. United States: N. p., 2006. Web. doi:10.1103/PHYSREVD.73.063502.
Chimento, Luis P., & Forte, Monica. Anisotropic k-essence cosmologies. United States. doi:10.1103/PHYSREVD.73.063502.
Chimento, Luis P., and Forte, Monica. Wed . "Anisotropic k-essence cosmologies". United States. doi:10.1103/PHYSREVD.73.063502.
@article{osti_20782606,
title = {Anisotropic k-essence cosmologies},
author = {Chimento, Luis P. and Forte, Monica},
abstractNote = {We investigate a Bianchi type-I cosmology with k-essence and find the set of models which dissipate the initial anisotropy. There are cosmological models with extended tachyon fields and k-essence having a constant barotropic index. We obtain the conditions leading to a regular bounce of the average geometry and the residual anisotropy on the bounce. For constant potential, we develop purely kinetic k-essence models which are dust dominated in their early stages, dissipate the initial anisotropy, and end in a stable de Sitter accelerated expansion scenario. We show that linear k-field and polynomial kinetic function models evolve asymptotically to Friedmann-Robertson-Walker cosmologies. The linear case is compatible with an asymptotic potential interpolating between V{sub l}{proportional_to}{phi}{sup -{gamma}{sub l}}, in the shear dominated regime, and V{sub l}{proportional_to}{phi}{sup -2} at late time. In the polynomial case, the general solution contains cosmological models with an oscillatory average geometry. For linear k-essence, we find the general solution in the Bianchi type-I cosmology when the k field is driven by an inverse square potential. This model shares the same geometry as a quintessence field driven by an exponential potential.},
doi = {10.1103/PHYSREVD.73.063502},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}
  • We analyze the implications of having a divergent speed of sound in k-essence cosmological models. We first study a known theory of that kind, for which the Lagrangian density depends linearly on the time derivative of the k-field. We show that when k-essence is the only source consistency requires that the potential of the k-field be of the inverse square form. Then, we review the known result that the corresponding power-law solutions can be mapped to power-law solutions of theories with no divergence in the speed of sound. After that, we argue that the requirement of a divergent sound speedmore » at some point fixes uniquely the form of the Lagrangian to be exactly the one considered earlier and prove the asymptotic stability of the most interesting solutions belonging to the divergent theory. Then, we discuss the implications of having not just k-essence but also matter. This is interesting because introducing another component breaks the rigidity of the theory, and the form of the potential ceases to be unique as happened in the pure k-essence case. Finally, we show the finiteness of the effective sound speed under an appropiate definition.« less
  • We show that phantom dark energy, if it is described by a k-essence theory, has three fundamental problems: first, its Hamiltonian is unbounded from below. Second, classical stability precludes the equation of state from crossing the 'Lambda-barrier', w{sub {lambda}}=-1. Finally, both the equation of state and the sound speed are unbounded - the first, from below, the second, from above - if the kinetic term is not bounded by dynamics.
  • We demonstrate that if k-essence can solve the coincidence problem and play the role of dark energy in the Universe, the fluctuations of the field have to propagate superluminally at some stage. We argue that this implies that successful k-essence models violate causality. It is not possible to define a time ordered succession of events in a Lorentz invariant way. Therefore, k-essence cannot arise as a low energy effective field theory of a causal, consistent high energy theory.
  • We derive conditions for stable tracker solutions for both quintessence and k-essence in a general cosmological background, H{sup 2}{proportional_to}f({rho}). We find that tracker solutions are possible only when {eta}{identical_to}dlnf/dln{rho}{approx_equal}constant, aside from a few special cases, which are enumerated. Expressions for the quintessence or k-essence equation of state are derived as a function of {eta} and the equation of state of the dominant background component.
  • The dilaton-gravity sector of the two-measures field theory (TMT) is explored in detail in the context of spatially flat Friedman-Robertson-Walker (FRW) cosmology. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. The dilaton {phi} dependence of the effective Lagrangian appears only as a result of the spontaneous breakdown of the scale invariance. If no fine-tuning is made, the effective {phi}-Lagrangian p({phi},X) depends quadratically upon the kinetic term X. Hence TMT represents an explicit example of the effective k-essence resulting from first principles without any exotic term in the underlying action intendedmore » for obtaining this result. Depending of the choice of regions in the parameter space (but without fine-tuning), TMT exhibits different possible outputs for cosmological dynamics: (a) Absence of initial singularity of the curvature while its time derivative is singular. This is a sort of sudden singularities studied by Barrow on purely kinematic grounds. (b) Power law inflation in the subsequent stage of evolution. Depending on the region in the parameter space the inflation ends with a graceful exit either into the state with zero cosmological constant (CC) or into the state driven by both a small CC and the field {phi} with a quintessencelike potential. (c) Possibility of resolution of the old CC problem. From the point of view of TMT, it becomes clear why the old CC problem cannot be solved (without fine-tuning) in conventional field theories. (d) TMT enables two ways for achieving small CC without fine-tuning of dimensionful parameters: either by a seesaw type mechanism or due to a correspondence principle between TMT and conventional field theories (i.e. theories with only the measure of integration {radical}(-g) in the action). (e) There is a wide range of the parameters such that in the late time universe: the equation of state w=p/{rho}<-1; w asymptotically (as t{yields}{infinity}) approaches -1 from below; {rho} approaches a constant, the smallness of which does not require fine-tuning of dimensionful parameters.« less