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We study constant-roll inflation in the presence of a gauge field coupled to an inflaton. By imposing the constant anisotropy condition, we find new exact anisotropic constant-roll inflationary solutions which include anisotropic power-law inflation as a special case. We also numerically show that the new anisotropic solutions are attractors in the phase space.
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Loop corrections to observables in slow-roll inflation are found to diverge no worse than powers of the log of the scale factor, extending Weinbergs theorem to quasi-single field inflation models. Demanding perturbation theory be valid during primordial inflation leads to constraints on the effective lagrangian. This leads to some interesting constraints and coincidences on the landscape of inflationary vacua.
In this paper, we study a non-canonical extension of a supergravity-motivated model acting as a vivid counterexample to the cosmic no-hair conjecture due to its unusual coupling between scalar and electromagnetic fields. In particular, a canonical scalar field is replaced by the string-inspired Dirac-Born-Infeld one in this extension. As a result, exact anisotropic inflationary solutions for this Dirac-Born-Infeld model are figured out under a constant-roll condition. Furthermore, numerical calculations are performed to verify that these anisotropic constant-roll solutions are indeed attractive during their inflationary phase.
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.
The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation. For constant-roll or ultra slow-roll inflation, the method of Bessel function approximation may be invalid. We compare the numerical results with the analytical results derived from the Bessel function approximation, and we find that they differ significantly on super-horizon scales if the constant slow-roll parameter $eta_H$ is not small. More accurate method is needed for calculating the primordial power spectrum for constant-roll inflation.
We study inflation with anisotropic hair induced by form fields. In four dimensions, the relevant form fields are gauge (one-form) fields and two-form fields. Assuming the exponential form of potential and gauge kinetic functions, we find new exact power-law solutions endowed with anisotropic hair. We also explore the phase space of anisotropic inflation and find fixed points corresponding to the exact power-law solutions. Moreover, we perform the stability analysis around the fixed points to reveal the structure of the phase space. It turns out that one of the fixed points becomes an attractor and others (if any) are saddle points. In particular, the one corresponding to anisotropic inflation becomes an attractor when it exists. We also argue that various anisotropic inflation models can be designed by choosing coupling constants.
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