Reheating constraints on modified single-field natural inflation models

Abstract

In this paper, we discuss three modified single-field natural inflation models in detail, including Special generalized natural inflation model (SNI), extended natural inflation model (ENI) and natural inflation inspired model (NII). We derive the analytical expression of the tensor-to-scalar ratio r and the spectral index $$n_s$$ n s for those models. Then the reheating temperature $$T_{re}$$ T re and reheating duration $$N_{re}$$ N re are analytically derived. Moreover, considering the CMB constraints, the feasible space of the SNI model in $$(n_s, r)$$ ( n s , r ) plane is almost covered by that of the NII, which means the NII is more general than the SNI. In addition, there is no overlapping space between the ENI and the other two models in $$(n_s, r)$$ ( n s , r ) plane, which indicates that the ENI and the other two models exclude each other, and more accurate experiments can verify them. Furthermore, the reheating brings tighter constraints to the inflation models, but they still work for a different reheating universe. Considering the constraints of $$n_s$$ n s , r, $$N_k$$ N k and choosing $$T_{re}$$ T re near the electroweak energy scale, one can find that the decay constants of the three models have no overlapping area and the effective equations of state $$\omega _{re}$$ ω re should be within $$\frac{1}{4}\lesssim \omega _{re} \lesssim \frac{4}{5}$$ 1 4 ≲ ω re ≲ 4 5 for the three models.

Non-minimally coupled Natural Inflation: Palatini and Metric formalism with the recent BICEP/Keck

“…where f is the symmetry-breaking scale. In literature, many studies have examined the Natural Inflation potential for minimal (ξ = 0) and non-minimal couplings (ξ ̸ = 0), such as [26,[107][108][109][110][111][112]. In this work, we investigate the non-minimally coupled Natural inflation potential by using a non-minimal coupling function, which is in the form…”

Non-minimal coupling inflation and dark matter under the ℤ3 symmetry

“…Palatini formalism is more concerned by cosmologists, such as studies in refs. [29][30][31][32][33][34][35][36], however, the non-minimum coupling correction in the Palatini form has less joint study with DM.…”

Spatially flat universes with isotropic tidal forces

“…The universe would commence a strong isotropization process, with Σ decreasing twice as fast as its expansion rate (b ≈ 2). At the end of this era, when w ∼ −1/3 [27], the (pre)reheating epoch would have begun, with −1/3 ≤ w ≤ 1. As we put the e-fold duration of inflation and reheating as N inf and N rh , with w = −1 and w = 1, respectively, we would have a estimate for the net decrease of the anisotropy as e −N , where N ∼ 2N inf − N rh , according to our analysis following the formula (23).…”

“…As we put the e-fold duration of inflation and reheating as N inf and N rh , with w = −1 and w = 1, respectively, we would have a estimate for the net decrease of the anisotropy as e −N , where N ∼ 2N inf − N rh , according to our analysis following the formula (23). Recent estimates point to N inf ∼ N rh ∼ 60 [21,27]. This would led the anisotropy still insignificant to be detected in the latetime sky, for the periods coming afterwards which are dominated by radiation (anisotropization with b ≈ 0), dust (anisotropization with b ≈ 1/2) and dark energy (isotropization with b ≈ 2), would not last long enough to significantly change this tiny scale.…”