摘要
Firstly, we explore the cosmological evolutions in four viable f(R) gravity models: Exponential, Hu-Sawicki, Starobinsky and Tsujikawa models. We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized in these viable models. We also study equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur and the future crossings of the phantom divide line wDE = −1 are the generic feature. The curvature singularities in viable f(R) gravity models are examined when the background density is dense. These singularities could be eliminated by adding the R2 term in the Lagrangian. Some of cosmological consequences, in particular the sources for the scalar mode of gravitational waves, are discussed. To illustrate the cosmological constraints on f(R), we concentrate on the exponential gravity model. We use the observational data including Supernova Cosmology Project (SCP) Union2 compilation, Two-Degree Field Galaxy Redshift Survey (2dFGRS), Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP7) in our analysis. Secondly, using the “teleparallel” equivalent of General Relativity as the gravitational sector, which is based on torsion instead of curvature, we add a canonical scalar field, allowing for a nonminimal coupling with gravity. Although the minimal case is completely equivalent to standard quintessence, the nonminimal scenario has a richer structure, exhibiting quintessence-like or phantom-like behavior, or experiencing the phantom-divide crossing. The richer structure is manifested in the absence of a conformal transformation to an equivalent minimally-coupled model. Moreover, we propose the simplest model of teleparallel dark energy with purely a non-minimal coupling to gravity but no self-potential, leading to a single model possessing various interesting features: simplicity, self-potential-free, the guaranteed late-time cosmic acceleration driven by the non-minimal coupling to gravity, tracker behavior of the dark energy equation of state at earlier times, a crossing of the phantom divide at a late time, and the existence of a finite-time future singularity. We find the analytic solutions of the dark-energy scalar field respectively in the radiation, matter, and dark energy dominated eras, thereby revealing the above features. We further illustrate possible cosmic evolution patterns and present the observational constraint of this model obtained by numerical analysis and data fitting. Thirdly, we examine the cosmological evolutions of the equation of state for dark energy wDE in the exponential and logarithmic as well as their combination f(T) theories. We show that the crossing of the phantom divide line of wDE = −1 can be realized in the combined f(T) theory even though it cannot be in the exponential or logarithmic f(T) theory. In particular, the crossing is from wDE > −1 to wDE < −1, in the opposite manner from f(R) gravity models. We also demonstrate that this feature is favored by the recent observational data.
並列摘要
Firstly, we explore the cosmological evolutions in four viable f(R) gravity models: Exponential, Hu-Sawicki, Starobinsky and Tsujikawa models. We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized in these viable models. We also study equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur and the future crossings of the phantom divide line wDE = −1 are the generic feature. The curvature singularities in viable f(R) gravity models are examined when the background density is dense. These singularities could be eliminated by adding the R2 term in the Lagrangian. Some of cosmological consequences, in particular the sources for the scalar mode of gravitational waves, are discussed. To illustrate the cosmological constraints on f(R), we concentrate on the exponential gravity model. We use the observational data including Supernova Cosmology Project (SCP) Union2 compilation, Two-Degree Field Galaxy Redshift Survey (2dFGRS), Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP7) in our analysis. Secondly, using the “teleparallel” equivalent of General Relativity as the gravitational sector, which is based on torsion instead of curvature, we add a canonical scalar field, allowing for a nonminimal coupling with gravity. Although the minimal case is completely equivalent to standard quintessence, the nonminimal scenario has a richer structure, exhibiting quintessence-like or phantom-like behavior, or experiencing the phantom-divide crossing. The richer structure is manifested in the absence of a conformal transformation to an equivalent minimally-coupled model. Moreover, we propose the simplest model of teleparallel dark energy with purely a non-minimal coupling to gravity but no self-potential, leading to a single model possessing various interesting features: simplicity, self-potential-free, the guaranteed late-time cosmic acceleration driven by the non-minimal coupling to gravity, tracker behavior of the dark energy equation of state at earlier times, a crossing of the phantom divide at a late time, and the existence of a finite-time future singularity. We find the analytic solutions of the dark-energy scalar field respectively in the radiation, matter, and dark energy dominated eras, thereby revealing the above features. We further illustrate possible cosmic evolution patterns and present the observational constraint of this model obtained by numerical analysis and data fitting. Thirdly, we examine the cosmological evolutions of the equation of state for dark energy wDE in the exponential and logarithmic as well as their combination f(T) theories. We show that the crossing of the phantom divide line of wDE = −1 can be realized in the combined f(T) theory even though it cannot be in the exponential or logarithmic f(T) theory. In particular, the crossing is from wDE > −1 to wDE < −1, in the opposite manner from f(R) gravity models. We also demonstrate that this feature is favored by the recent observational data.
參考文獻
延伸閱讀
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