Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPower-law inflation with a nonminimally coupled scalar field
232
0
0.0
(
0
)
Authors
S. Tsujikawa
Ask ChatGPT about the research
No Arabic abstract
We consider the dynamics of power-law inflation with a nonminimally coupled scalar field $phi$. It is well known that multiple scalar fields with exponential potentials $V(phi)=V_0 {rm exp}(-sqrt{16pi/p m_{rm pl}^2} phi)$ lead to an inflationary solution even if the each scalar field is not capable to sustain inflation. In this paper, we show that inflation can be assisted even in the one-field case by the effect of nonminimal coupling. When $xi$ is positive, since an effective potential which arises by a conformal transformation becomes flatter compared with the case of $xi=0$ for $phi>0$, we have an inflationary solution even when the universe evolves as non-inflationary in the minimally coupled case. For the negative $xi$, the assisted inflation can take place when $phi$ evolves in the region of $phi<0$ .
rate research
Read More
It is known that power-law k-inflation can be realized for the Lagrangian $P=Xg(Y)$, where $X=-(partial phi)^2/2$ is the kinetic energy of a scalar field $phi$ and $g$ is an arbitrary function in terms of $Y=Xe^{lambda phi/M_{pl}}$ ($lambda$ is a constant and $M_{pl}$ is the reduced Planck mass). In the presence of a vector field coupled to the inflaton with an exponential coupling $f(phi) propto e^{mu phi/M_{pl}}$, we show that the models with the Lagrangian $P=Xg(Y)$ generally give rise to anisotropic inflationary solutions with $Sigma/H=constant$, where $Sigma$ is an anisotropic shear and $H$ is an isotropic expansion rate. Provided these anisotropic solutions exist in the regime where the ratio $Sigma/H$ is much smaller than 1, they are stable attractors irrespective of the forms of $g(Y)$. We apply our results to concrete models of k-inflation such as the generalized dilatonic ghost condensate/the DBI model and we numerically show that the solutions with different initial conditions converge to the anisotropic power-law inflationary attractors. Even in the de Sitter limit ($lambda to 0$) such solutions can exist, but in this case the null energy condition is generally violated. The latter property is consistent with the Walds cosmic conjecture stating that the anisotropic hair does not survive on the de Sitter background in the presence of matter respecting the dominant/strong energy conditions.
We perform adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation with varying speed of sound. The subtraction is performed within the framework of earlier study by Urakawa and Starobinsky dealing with the canonical inflation. Inspired by Fakir and Unruhs model on nonminimally coupled chaotic inflation, we find upon imposing near scale-invariant condition, that the subtraction term exponentially decays with the number of $ e $-folds. As in the result for the canonical inflation, the regularized power spectrum tends to the bare power spectrum as the Universe expands during (and even after) inflation. This work justifies the use of the bare power spectrum in standard calculation in the most general context of slow-roll single-field inflation involving non-minimal coupling and varying speed of sound.
We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demonstrate the physical equivalence between the Jordan and Einstein frames at the level of quadratic perturbations. We show how to generalize the formalism to the case of a more complicated scalar sector with an internal symmetry, such as Higgs inflation. This work represents a first step in developing gauge invariant perturbation theory for nonminimally coupled inflationary models.
In higher-curvature inflation models ($R+alpha_n R^n$), we study a parametric preheating of a scalar field $chi$ coupled non-minimally to a spacetime curvature $R$ ($xi R chi^2$). In the case of $R^2$-inflation model, efficient preheating becomes possible for rather small values of $xi$, i.e. $|xi|< several. Although the maximal fluctuation $sqrt{< chi^2 >}_{max} approx 2 times10^{17}$ GeV for $xi approx -4$ is almost the same as the chaotic inflation model with a non-minimally coupled $chi$ field, the growth rate of the fluctuation becomes much larger and efficient preheating is realized. We also investigate preheating for $R^4$ model and find that the maximal fluctuation is $sqrt{< chi^2 >}_{max} approx 8 times 10^{16}$ GeV for $xi approx -35$.
We consider the non-Gaussianity of the nonlinear density perturbations in a single-field inflationary model when a scalar field couples nonminimally with gravity. Gravity theories with a nonminimal coupling can be transformed into the Einstein gravity with canonical kinetic terms by using a suitable conformal transformation. We find that a nonlinear generalization of the gauge invariant quantity $zeta_i$ is invariant under the conformal transformation. With the help of this conformal invariant property, we calculate the non-Gaussianity, which is characterized by a nonlinear parameter $f_{NL}$, in nonminimal coupled scalar field theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
