In this paper we will analyze generic predictions of an inflection-point model of inflation with Hubble-induced corrections and study them in light of the Planck data. Typically inflection-point models of inflation can be embedded within Minimal Supersymmetric Standard Model (MSSM) where inflation can occur below the Planck scale. The flexibility of the potential allows us to match the observed amplitude of the TT-power spectrum of the cosmic microwave background radiation with low and high multipoles, spectral tilt, and virtually mild running of the spectral tilt, which can put a bound on an upper limit on the tensor-to-scalar ratio, r ≤ 0.12. Since the inflaton within MSSM carries the Standard Model charges, therefore it is the minimal model of inflation beyond the Standard Model which can reheat the universe with the right thermal degrees of freedom without any dark-radiation.

We have studied primordial non-Gaussian features of a model of potential-driven single field DBI Galileon inflation. We have computed the bispectrum from the three-point correlation function considering all possible cross correlations between the scalar and tensor modes of the proposed setup. Further, we have computed the trispectrum from a four-point correlation function considering the contribution from contact interaction, and scalar and graviton exchange diagrams in the in–in picture. Finally we have obtained the non-Gaussian consistency conditions from the four-point correlator, which results in partial violation of the Suyama–Yamaguchi four-point consistency relation. This further leads to the conclusion that sufficient primordial non-Gaussianities can be obtained from DBI Galileon inflation.

We propose a model of inflation with a suitable potential for a single scalar field which falls in the wide class of hilltop inflation. We derive the analytical expressions for most of the physical quantities related to inflation and show that all of them represent the true behavior as required from a model of inflation. We further subject the results to observational verification by formulating the theory of perturbations based on our model followed by an estimation for the values of those observable parameters. Our model is found to be in excellent agreement with observational data. Thus, the features related to the model leads us to infer that this type of hilltop inflation may be a natural choice for explaining the early universe.

Possible interaction between dark energy and dark matter has previously shown promise in alleviating the clustering tension, without exacerbating the Hubble tension, when Baryon Acoustic Oscillations (BAO) data from the Sloan Digital Sky Survey (SDSS) DR16 is combined with Cosmic Microwave Background (CMB) and Type-Ia Supernovae (SNIa) data sets. With the recent Dark Energy Spectroscopic Instrument (DESI) BAO DR2, there is now a compelling need to re-evaluate this scenario. We combine DESI DR2 with Planck 2018 and Pantheon + SNIa data sets to constrain interacting dark matter dark energy models, accounting for interaction effects in both the background and perturbation sectors. Our results exhibit similar trends to those observed with SDSS, albeit with improved precision, reinforcing the consistency between the two BAO data sets. In addition to offering a resolution to the $S_8$ tension, in the phantom-limit, the dark energy equation of state exhibits an early-phantom behaviour, aligning with DESI DR2 findings, before transitioning to $w\sim -1$ at lower redshifts, regardless of the DE parametrization. However, the statistical significance of excluding $w=-1$ is reduced compared to their non-interacting counterparts.

We constrain plausible dark energy models using the recently published cosmic microwave background (CMB) temperature anisotropy data from Planck together with WMAP9 low-$\ell$ polarization data and the data from low redshift surveys. To circumvent the limitations of any particular equation of state toward describing all existing dark energy models, we work with three different equations of state covering a wider class of dark energy models and hence provide more robust and generic constraints on the dark energy behavior. We show that a possible tension exists between constraints from CMB and non-CMB observations when one allows for both phantom and nonphantom behavior for the dark energy. Further, we reconstruct the equation of state of dark energy as a function of redshift using the combined CMB and non-CMB data and show that cosmological constant behavior is disallowed at the 68.3% confidence level. A fully nonphantom history is also disallowed at the 68.3% confidence level, and a considerable fine-tuning is also needed to keep it inside the 95.5% confidence limit. This result might motivate one to construct phantom models for dark energy, which may be achievable in the presence of higher derivative operators as in string theory. However, for a theoretical model that allows only nonphantom behavior, both CMB and non-CMB data sets agree on the dark energy constraint with the mean equation of state being very close to the cosmological constant.