185 research outputs found

### The general property of dynamical quintessence field

We discuss the general dynamical behaviors of quintessence field, in
particular, the general conditions for tracking and thawing solutions are
discussed. We explain what the tracking solutions mean and in what sense the
results depend on the initial conditions. Based on the definition of tracking
solution, we give a simple explanation on the existence of a general relation
between $w_\phi$ and $\Omega_\phi$ which is independent of the initial
conditions for the tracking solution. A more general tracker theorem which
requires large initial values of the roll parameter is then proposed. To get
thawing solutions, the initial value of the roll parameter needs to be small.
The power-law and pseudo-Nambu Goldstone boson potentials are used to discuss
the tracking and thawing solutions. A more general $w_\phi-\Omega_\phi$
relation is derived for the thawing solutions. Based on the asymptotical
behavior of the $w_\phi-\Omega_\phi$ relation, the flow parameter is used to
give an upper limit on $w_\phi'$ for the thawing solutions. If we use the
observational constraint $w_{\phi 0}<-0.8$ and $0.2<\Omega_{m0}<0.4$, then we
require $n\lesssim 1$ for the inverse power-law potential
$V(\phi)=V_0(\phi/m_{pl})^{-n}$ with tracking solutions and the initial value
of the roll parameter $|\lambda_i|<1.3$ for the potentials with the thawing
solutions.Comment: 11 figures, corrected some typos and presentation improved, PLB in
pres

### Friedmann Equations and Thermodynamics of Apparent Horizons

With the help of a masslike function which has dimension of energy and equals
to the Misner-Sharp mass at the apparent horizon, we show that the first law of
thermodynamics of the apparent horizon $dE=T_AdS_A$ can be derived from the
Friedmann equation in various theories of gravity, including the Einstein,
Lovelock, nonlinear, and scalar-tensor theories. This result strongly suggests
that the relationship between the first law of thermodynamics of the apparent
horizon and the Friedmann equation is not just a simple coincidence, but rather
a more profound physical connection.Comment: no figures, V2: re-organized and re-writtend, main results and
conclusion unchanged, Phys. Rev. Lett. in pres

### The challenge for single field inflation with BICEP2 result

The detection of B-mode power spectrum by the BICEP2 collaboration constrains
the tensor-to-scalar ratio $r=0.20^{+0.07}_{-0.05}$ for the lensed-$\Lambda$CDM
model. The consistency of this big value with the {\em Planck} results requires
a large running of the spectral index. The large values of the tensor-to-scalar
ratio and the running of the spectral index put a challenge to single field
inflation. For the chaotic inflation, the larger the value of the
tensor-to-scalar ratio is, the smaller the value of the running of the spectral
index is. For the natural inflation, the absolute value of the running of the
spectral index has an upper limit.Comment: 4 figures, 3 pages, some references added, PLB in pres

- β¦