We investigate the scalar and tensor spectral indices of the quadratic inflation model in Eddington-inspired Born-Infeld (EiBI) gravity. We find that the EiBI corrections to the spectral indices are of second and first order in the slow-roll approxim
ation for the scalar and tensor perturbations respectively. This is very promising since the quadratic inflation model in general relativity provides a very nice fit for the spectral indices. Together with the suppression of the tensor-to-scalar ratio EiBI inflation agrees well with the observational data.
We investigate the scalar and the tensor perturbations of the $varphi^2$ inflation model in the strong-gravity limit of Eddington-inspired Born-Infeld (EiBI) theory. In order to consider the strong EiBI-gravity effect, we take the value of $kappa$ la
rge, where $kappa$ is the EiBI theory parameter. The energy density of the Universe at the early stage is very high, and the Universe is in a strong-gravity regime. Therefore, the perturbation feature is not altered from what was investigated earlier. At the attractor inflationary stage, however, the feature is changed in the strong EiBI-gravity limit. The correction to the scalar perturbation in this limit comes mainly via the background matter field, while that to the tensor perturbation comes directly from the gravity ($kappa$) effect. The change in the value of the scalar spectrum is little compared with that in the weak EiBI-gravity limit, or in GR. The form of the tensor spectrum is the same with that in the weak limit, but the value of the spectrum can be suppressed down to zero in the strong limit. Therefore, the resulting tensor-to-scalar ratio can also be suppressed in the same way, which makes $varphi^2$ model in EiBI theory viable.
We investigate the scalar perturbation produced at the pre-inflationary stage driven by a massive scalar field in Eddington-inspired Born-Infeld gravity. The scalar power spectrum exhibits a peculiar rise for low $k$-modes. The tensor-to-scalar ratio
can be significantly lowered compared with that in the standard chaotic inflation model in general relativity. This result is very affirmative considering the recent dispute on the detection of the gravitational wave radiation between PLANCK and BICEP2.
We investigate inflation and its scalar perturbation driven by a massive scalar field in the unimodular theory of gravity. We introduce a parameter $xi$ with which the theory is invariant under general unimodular coordinate transformations. When the
unimodular parameter is $xi=6$, the classical picture of inflation is reproduced in the unimodular theory because it recovers the background equations of the standard theory of general relativity. We show that for $xi=6$, the theory is equivalent to the standard theory of general relativity at the perturbation level. Unimodular gravity constrains the gauge degree of freedom in the scalar perturbation, but the perturbation equations are similar to those in general relativity. For $xi eq 6$, we derive the power spectrum and the spectral index, and obtain the unimodular correction to the tensor-to-scalar ratio. Depending on the value of $xi$, the correction can either raise or lower the value of the tensor-to-scalar ratio.
We investigate the scalar perturbation of the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. We focus on the perturbation at the attractor stage in which the first and the second slow-roll conditions are s
atisfied. The scalar perturbation exhibits the corrections to the chaotic inflation model in general relativity. We find that the tensor-to-scalar ratio becomes smaller than that of the usual chaotic inflation.
We investigate the tensor perturbation in the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. For short wave-length modes, the perturbation feature is very similar to that of the usual chaotic inflation. Fo
r long wave-length modes, the perturbation exhibits a peculiar rise in the power spectrum which may leave a signature in the cosmic microwave background radiation.
We investigate the tensor and the scalar perturbations in the symmetric bouncing universe driven by one ordinary field and its Lee-Wick partner field which is a ghost. We obtain the even- and the odd-mode functions of the tensor perturbation in the m
atter-dominated regime. The tensor perturbation grows in time during the contracting phase of the Universe, and decays during the expanding phase. The power spectrum for the tensor perturbation is evaluated and the spectral index is given by $n_{rm T} =6$. We add the analysis on the scalar perturbation by inspecting the even- and the odd-mode functions in the matter-dominated regime, which was studied numerically in our previous work. We conclude that the comoving curvature by the scalar perturbation is constant in the super-horizon scale and starts to decay in the far sub-horizon scale while the Universe expands.
We investigate string-like solutions in four dimensions based on Hov{r}ava-Lifshitz gravity. For a restricted class of solutions where the Cotton tensor vanishes, we find that the string-like solutions in Einstein gravity including the BTZ black stri
ngs are solutions in Hov{r}ava-Lifshitz gravity as well. The geometry is warped in the same way as in Einstein gravity, but the conformal lapse function is not constrained in Hov{r}ava-Lifshitz gravity. It turns out that if $lambda e 1$, there exist no other solutions. For the value of model parameter with which Einstein gravity recovers in IR limit (i.e., $lambda=1$), there exists an additional solution of which the conformal lapse function is determined. Interestingly, this solution admits a uniform BTZ black string along the string direction, which is distinguished from the warped BTZ black string in Einstein gravity. Therefore, it is a good candidate for the test of the theory.
We investigate vortex configurations with the vulcanization term inspired by the renormalization of $phi_star^4$ theory in the canonical $theta$-deformed noncommutativity. We focus on the classical limit of the theory described by a single parameter
which is the ratio of the vulcanization and the noncommutativity parameters. We perform numerical calculations and find that nontopological vortex solutions exist as well as Q-ball type solutions, but topological vortex solutions are not admitted.
We investigate geometrical properties of 5D cylindrical vacuum solutions with a transverse spherical symmetry. The metric is uniform along the fifth direction and characterized by tension and mass densities. The solutions are classified by the tensio
n-to-mass ratio. One particular example is the well-known Schwarzschild black string which has a curvature singularity enclosed by a horizon. We focus mainly on geometry of other solutions which possess a naked singularity. The light signal emitted by an object approaching the singularity reaches a distant observer with finite time, but is infinitely red-shifted.
