Inflation with a class of concave inflaton potentials in Randall–Sundrum model

Abstract

We investigate inflation with a class of concave inflaton potentials of the form $$\sim \phi ^n$$∼ϕn$$(0<n<1)$$(0<n<1) in the Randall–Sundrum model with an infinite extra spatial dimension. We show that this class of models is much more in good agreement with observations compared to the standard inflation. We also find the range of the five-dimensional Planck scale ($$M_5$$M5) and show that large tensor-to-scalar ratios do not eliminate small-field inflation in braneworld cosmology.

Shaft inflation in Randall-Sundrum model

“…From the more important observational perspective, the predictions of shaft inflation in RSII model are in excellent agreement with observation, though the case n = 2 is ruled out when taking into account the BICEP/Keck result. The fundamental five-dimensional Planck scale was found to be M 5 10 16 GeV, which is consistent with the previously found lower bound of this parameter M 5 10 9 GeV obtained from Newtonian gravitational bound [15]. The value of M 5 that we found is close to the GUT scale and the energy scale of inflation which is of order 10 15 GeV.…”

“…(3.23) match the observed value A Planck s ∼ 2.0989 × 10 −9 [2]. It is found that M 5 is typically of order M 5 ∼ 10 16 GeV (it depends only weakly on n and N ); this is consistent with a previously found lower bound of M 5 of order 10 9 GeV [15]. 4 So, we find the results in table 2.…”

“…This is more or less an expected feature of inflation in RSII model (for example, in ref. [15] it was found that the tensor-to-scalar ratio in RSII model is larger than that in 4D spacetime for the concave inflaton potential of the form V ∝ φ n with 0 < n < 1).…”

“…A familiar argument for why these extra dimensions have not yet popped out in experiments is that they are tiny compact dimensions (such as RSI and ADD models), which means that we need a very high-energy scale and a very delicate instrument to detect, for example, a quick energy non-conservation process. An even more ambitious idea is that the extra dimensions are not small at all (such as RSII and DGP models), but still they do not cause any significant effects that can be easily detectable in a lab; for example, the RSII model predicts a modification to the Newton's gravitational law at small distance but there is a parameter space of the model that is still allowed within the experimental bound [15]. In this paper, we shall work on the Randall-Sundrum type II model (RSII) [9] as it is more…”